diff options
Diffstat (limited to 'libgo/go/crypto/elliptic')
33 files changed, 13291 insertions, 4148 deletions
diff --git a/libgo/go/crypto/elliptic/elliptic.go b/libgo/go/crypto/elliptic/elliptic.go index f072960..d06a284 100644 --- a/libgo/go/crypto/elliptic/elliptic.go +++ b/libgo/go/crypto/elliptic/elliptic.go @@ -21,9 +21,12 @@ import ( // A Curve represents a short-form Weierstrass curve with a=-3. // -// Note that the point at infinity (0, 0) is not considered on the curve, and -// although it can be returned by Add, Double, ScalarMult, or ScalarBaseMult, it -// can't be marshaled or unmarshaled, and IsOnCurve will return false for it. +// The output of Add, Double, and ScalarMult when the input is not a point on +// the curve is undefined. +// +// Note that the conventional point at infinity (0, 0) is not considered on the +// curve, although it can be returned by Add, Double, ScalarMult, or +// ScalarBaseMult (but not Unmarshal or UnmarshalCompressed). type Curve interface { // Params returns the parameters for the curve. Params() *CurveParams @@ -82,7 +85,7 @@ func (curve *CurveParams) polynomial(x *big.Int) *big.Int { func (curve *CurveParams) IsOnCurve(x, y *big.Int) bool { // If there is a dedicated constant-time implementation for this curve operation, // use that instead of the generic one. - if specific, ok := matchesSpecificCurve(curve, p224, p521); ok { + if specific, ok := matchesSpecificCurve(curve, p224, p384, p521); ok { return specific.IsOnCurve(x, y) } @@ -125,7 +128,7 @@ func (curve *CurveParams) affineFromJacobian(x, y, z *big.Int) (xOut, yOut *big. func (curve *CurveParams) Add(x1, y1, x2, y2 *big.Int) (*big.Int, *big.Int) { // If there is a dedicated constant-time implementation for this curve operation, // use that instead of the generic one. - if specific, ok := matchesSpecificCurve(curve, p224, p521); ok { + if specific, ok := matchesSpecificCurve(curve, p224, p384, p521); ok { return specific.Add(x1, y1, x2, y2) } @@ -215,7 +218,7 @@ func (curve *CurveParams) addJacobian(x1, y1, z1, x2, y2, z2 *big.Int) (*big.Int func (curve *CurveParams) Double(x1, y1 *big.Int) (*big.Int, *big.Int) { // If there is a dedicated constant-time implementation for this curve operation, // use that instead of the generic one. - if specific, ok := matchesSpecificCurve(curve, p224, p521); ok { + if specific, ok := matchesSpecificCurve(curve, p224, p384, p521); ok { return specific.Double(x1, y1) } @@ -287,7 +290,7 @@ func (curve *CurveParams) doubleJacobian(x, y, z *big.Int) (*big.Int, *big.Int, func (curve *CurveParams) ScalarMult(Bx, By *big.Int, k []byte) (*big.Int, *big.Int) { // If there is a dedicated constant-time implementation for this curve operation, // use that instead of the generic one. - if specific, ok := matchesSpecificCurve(curve, p224, p256, p521); ok { + if specific, ok := matchesSpecificCurve(curve, p224, p256, p384, p521); ok { return specific.ScalarMult(Bx, By, k) } @@ -310,7 +313,7 @@ func (curve *CurveParams) ScalarMult(Bx, By *big.Int, k []byte) (*big.Int, *big. func (curve *CurveParams) ScalarBaseMult(k []byte) (*big.Int, *big.Int) { // If there is a dedicated constant-time implementation for this curve operation, // use that instead of the generic one. - if specific, ok := matchesSpecificCurve(curve, p224, p256, p521); ok { + if specific, ok := matchesSpecificCurve(curve, p224, p256, p384, p521); ok { return specific.ScalarBaseMult(k) } @@ -428,7 +431,6 @@ func UnmarshalCompressed(curve Curve, data []byte) (x, y *big.Int) { } var initonce sync.Once -var p384 *CurveParams func initAll() { initP224() @@ -437,15 +439,16 @@ func initAll() { initP521() } -func initP384() { - // See FIPS 186-3, section D.2.4 - p384 = &CurveParams{Name: "P-384"} - p384.P, _ = new(big.Int).SetString("39402006196394479212279040100143613805079739270465446667948293404245721771496870329047266088258938001861606973112319", 10) - p384.N, _ = new(big.Int).SetString("39402006196394479212279040100143613805079739270465446667946905279627659399113263569398956308152294913554433653942643", 10) - p384.B, _ = new(big.Int).SetString("b3312fa7e23ee7e4988e056be3f82d19181d9c6efe8141120314088f5013875ac656398d8a2ed19d2a85c8edd3ec2aef", 16) - p384.Gx, _ = new(big.Int).SetString("aa87ca22be8b05378eb1c71ef320ad746e1d3b628ba79b9859f741e082542a385502f25dbf55296c3a545e3872760ab7", 16) - p384.Gy, _ = new(big.Int).SetString("3617de4a96262c6f5d9e98bf9292dc29f8f41dbd289a147ce9da3113b5f0b8c00a60b1ce1d7e819d7a431d7c90ea0e5f", 16) - p384.BitSize = 384 +// P224 returns a Curve which implements NIST P-224 (FIPS 186-3, section D.2.2), +// also known as secp224r1. The CurveParams.Name of this Curve is "P-224". +// +// Multiple invocations of this function will return the same value, so it can +// be used for equality checks and switch statements. +// +// The cryptographic operations are implemented using constant-time algorithms. +func P224() Curve { + initonce.Do(initAll) + return p224 } // P256 returns a Curve which implements NIST P-256 (FIPS 186-3, section D.2.3), @@ -467,7 +470,7 @@ func P256() Curve { // Multiple invocations of this function will return the same value, so it can // be used for equality checks and switch statements. // -// The cryptographic operations do not use constant-time algorithms. +// The cryptographic operations are implemented using constant-time algorithms. func P384() Curve { initonce.Do(initAll) return p384 diff --git a/libgo/go/crypto/elliptic/elliptic_test.go b/libgo/go/crypto/elliptic/elliptic_test.go index 183861a..f5b36f7 100644 --- a/libgo/go/crypto/elliptic/elliptic_test.go +++ b/libgo/go/crypto/elliptic/elliptic_test.go @@ -14,9 +14,8 @@ import ( // genericParamsForCurve returns the dereferenced CurveParams for // the specified curve. This is used to avoid the logic for -// upgrading a curve to it's specific implementation, forcing -// usage of the generic implementation. This is only relevant -// for the P224, P256, and P521 curves. +// upgrading a curve to its specific implementation, forcing +// usage of the generic implementation. func genericParamsForCurve(c Curve) *CurveParams { d := *(c.Params()) return &d @@ -109,6 +108,15 @@ func testInfinity(t *testing.T, curve Curve) { if curve.IsOnCurve(x, y) { t.Errorf("IsOnCurve(∞) == true") } + + if xx, yy := Unmarshal(curve, Marshal(curve, x, y)); xx != nil || yy != nil { + t.Errorf("Unmarshal(Marshal(∞)) did not return an error") + } + // We don't test UnmarshalCompressed(MarshalCompressed(∞)) because there are + // two valid points with x = 0. + if xx, yy := Unmarshal(curve, []byte{0x00}); xx != nil || yy != nil { + t.Errorf("Unmarshal(∞) did not return an error") + } } func TestMarshal(t *testing.T) { @@ -232,6 +240,16 @@ func testMarshalCompressed(t *testing.T, curve Curve, x, y *big.Int, want []byte } } +func TestLargeIsOnCurve(t *testing.T) { + testAllCurves(t, func(t *testing.T, curve Curve) { + large := big.NewInt(1) + large.Lsh(large, 1000) + if curve.IsOnCurve(large, large) { + t.Errorf("(2^1000, 2^1000) is reported on the curve") + } + }) +} + func benchmarkAllCurves(t *testing.B, f func(*testing.B, Curve)) { tests := []struct { name string @@ -274,3 +292,29 @@ func BenchmarkScalarMult(b *testing.B) { } }) } + +func BenchmarkMarshalUnmarshal(b *testing.B) { + benchmarkAllCurves(b, func(b *testing.B, curve Curve) { + _, x, y, _ := GenerateKey(curve, rand.Reader) + b.Run("Uncompressed", func(b *testing.B) { + b.ReportAllocs() + for i := 0; i < b.N; i++ { + buf := Marshal(curve, x, y) + xx, yy := Unmarshal(curve, buf) + if xx.Cmp(x) != 0 || yy.Cmp(y) != 0 { + b.Error("Unmarshal output different from Marshal input") + } + } + }) + b.Run("Compressed", func(b *testing.B) { + b.ReportAllocs() + for i := 0; i < b.N; i++ { + buf := Marshal(curve, x, y) + xx, yy := Unmarshal(curve, buf) + if xx.Cmp(x) != 0 || yy.Cmp(y) != 0 { + b.Error("Unmarshal output different from Marshal input") + } + } + }) + }) +} diff --git a/libgo/go/crypto/elliptic/export_generate.go b/libgo/go/crypto/elliptic/export_generate.go new file mode 100644 index 0000000..f15b302 --- /dev/null +++ b/libgo/go/crypto/elliptic/export_generate.go @@ -0,0 +1,16 @@ +// Copyright 2021 The Go Authors. All rights reserved. +// Use of this source code is governed by a BSD-style +// license that can be found in the LICENSE file. + +//go:build tablegen + +package elliptic + +// This block exports p256-related internals for the p256 table generator in internal/gen. +var ( + P256PointDoubleAsm = p256PointDoubleAsm + P256PointAddAsm = p256PointAddAsm + P256Inverse = p256Inverse + P256Sqr = p256Sqr + P256Mul = p256Mul +) diff --git a/libgo/go/crypto/elliptic/fuzz_test.go b/libgo/go/crypto/elliptic/fuzz_test.go index 8ff3bf3..2b5ddae 100644 --- a/libgo/go/crypto/elliptic/fuzz_test.go +++ b/libgo/go/crypto/elliptic/fuzz_test.go @@ -3,7 +3,6 @@ // license that can be found in the LICENSE file. //go:build amd64 || arm64 || ppc64le -// +build amd64 arm64 ppc64le package elliptic diff --git a/libgo/go/crypto/elliptic/gen_p256_table.go b/libgo/go/crypto/elliptic/gen_p256_table.go new file mode 100644 index 0000000..367bd4b --- /dev/null +++ b/libgo/go/crypto/elliptic/gen_p256_table.go @@ -0,0 +1,110 @@ +// Copyright 2021 The Go Authors. All rights reserved. +// Use of this source code is governed by a BSD-style +// license that can be found in the LICENSE file. + +//go:build ignore + +package main + +import ( + "bytes" + "crypto/elliptic" + "encoding/binary" + "fmt" + "go/format" + "log" + "os" +) + +func main() { + buf := new(bytes.Buffer) + fmt.Fprint(buf, ` +// Copyright 2021 The Go Authors. All rights reserved. +// Use of this source code is governed by a BSD-style +// license that can be found in the LICENSE file. + +// Generated by gen_p256_table.go. DO NOT EDIT. + +//go:build amd64 || arm64 + +package elliptic + +`[1:]) + + // Generate precomputed p256 tables. + var pre [43][32 * 8]uint64 + basePoint := []uint64{ + 0x79e730d418a9143c, 0x75ba95fc5fedb601, 0x79fb732b77622510, 0x18905f76a53755c6, + 0xddf25357ce95560a, 0x8b4ab8e4ba19e45c, 0xd2e88688dd21f325, 0x8571ff1825885d85, + 0x0000000000000001, 0xffffffff00000000, 0xffffffffffffffff, 0x00000000fffffffe, + } + t1 := make([]uint64, 12) + t2 := make([]uint64, 12) + copy(t2, basePoint) + zInv := make([]uint64, 4) + zInvSq := make([]uint64, 4) + for j := 0; j < 32; j++ { + copy(t1, t2) + for i := 0; i < 43; i++ { + // The window size is 6 so we need to double 6 times. + if i != 0 { + for k := 0; k < 6; k++ { + elliptic.P256PointDoubleAsm(t1, t1) + } + } + // Convert the point to affine form. (Its values are + // still in Montgomery form however.) + elliptic.P256Inverse(zInv, t1[8:12]) + elliptic.P256Sqr(zInvSq, zInv, 1) + elliptic.P256Mul(zInv, zInv, zInvSq) + elliptic.P256Mul(t1[:4], t1[:4], zInvSq) + elliptic.P256Mul(t1[4:8], t1[4:8], zInv) + copy(t1[8:12], basePoint[8:12]) + // Update the table entry + copy(pre[i][j*8:], t1[:8]) + } + if j == 0 { + elliptic.P256PointDoubleAsm(t2, basePoint) + } else { + elliptic.P256PointAddAsm(t2, t2, basePoint) + } + } + + fmt.Fprint(buf, "const p256Precomputed = \"\" +\n\n") + + // Dump the precomputed tables, flattened, little-endian. + // These tables are used directly by assembly on little-endian platforms. + // Putting the data in a const string lets it be stored readonly. + for i := range &pre { + for j, v := range &pre[i] { + fmt.Fprintf(buf, "\"") + var u8 [8]byte + binary.LittleEndian.PutUint64(u8[:], v) + for _, b := range &u8 { + fmt.Fprintf(buf, "\\x%02x", b) + } + fmt.Fprintf(buf, "\"") + if i < len(pre)-1 || j < len(pre[i])-1 { + fmt.Fprint(buf, "+") + } + if j%8 == 7 { + fmt.Fprint(buf, "\n") + } + } + fmt.Fprint(buf, "\n") + } + + src := buf.Bytes() + fmtsrc, fmterr := format.Source(src) + // If formatting failed, keep the original source for debugging. + if fmterr == nil { + src = fmtsrc + } + err := os.WriteFile("p256_asm_table.go", src, 0644) + if err != nil { + log.Fatal(err) + } + if fmterr != nil { + log.Fatal(fmterr) + } +} diff --git a/libgo/go/crypto/elliptic/internal/fiat/fiat_test.go b/libgo/go/crypto/elliptic/internal/fiat/fiat_test.go new file mode 100644 index 0000000..9ecd863 --- /dev/null +++ b/libgo/go/crypto/elliptic/internal/fiat/fiat_test.go @@ -0,0 +1,64 @@ +// Copyright 2021 The Go Authors. All rights reserved. +// Use of this source code is governed by a BSD-style +// license that can be found in the LICENSE file. + +package fiat_test + +import ( + "crypto/elliptic/internal/fiat" + "testing" +) + +func BenchmarkMul(b *testing.B) { + b.Run("P224", func(b *testing.B) { + v := new(fiat.P224Element).One() + b.ReportAllocs() + b.ResetTimer() + for i := 0; i < b.N; i++ { + v.Mul(v, v) + } + }) + b.Run("P384", func(b *testing.B) { + v := new(fiat.P384Element).One() + b.ReportAllocs() + b.ResetTimer() + for i := 0; i < b.N; i++ { + v.Mul(v, v) + } + }) + b.Run("P521", func(b *testing.B) { + v := new(fiat.P521Element).One() + b.ReportAllocs() + b.ResetTimer() + for i := 0; i < b.N; i++ { + v.Mul(v, v) + } + }) +} + +func BenchmarkSquare(b *testing.B) { + b.Run("P224", func(b *testing.B) { + v := new(fiat.P224Element).One() + b.ReportAllocs() + b.ResetTimer() + for i := 0; i < b.N; i++ { + v.Square(v) + } + }) + b.Run("P384", func(b *testing.B) { + v := new(fiat.P384Element).One() + b.ReportAllocs() + b.ResetTimer() + for i := 0; i < b.N; i++ { + v.Square(v) + } + }) + b.Run("P521", func(b *testing.B) { + v := new(fiat.P521Element).One() + b.ReportAllocs() + b.ResetTimer() + for i := 0; i < b.N; i++ { + v.Square(v) + } + }) +} diff --git a/libgo/go/crypto/elliptic/internal/fiat/generate.go b/libgo/go/crypto/elliptic/internal/fiat/generate.go new file mode 100644 index 0000000..fd8509d --- /dev/null +++ b/libgo/go/crypto/elliptic/internal/fiat/generate.go @@ -0,0 +1,330 @@ +// Copyright 2021 The Go Authors. All rights reserved. +// Use of this source code is governed by a BSD-style +// license that can be found in the LICENSE file. + +//go:build ignore + +package main + +import ( + "bytes" + "go/format" + "io" + "log" + "os" + "os/exec" + "text/template" +) + +var curves = []struct { + Element string + Prime string + Prefix string + FiatType string + BytesLen int +}{ + { + Element: "P224Element", + Prime: "2^224 - 2^96 + 1", + Prefix: "p224", + FiatType: "[4]uint64", + BytesLen: 28, + }, + // The 32-bit pure Go P-256 in crypto/elliptic is still faster than the + // autogenerated code here, regrettably. + // { + // Element: "P256Element", + // Prime: "2^256 - 2^224 + 2^192 + 2^96 - 1", + // Prefix: "p256", + // FiatType: "[4]uint64", + // BytesLen: 32, + // }, + { + Element: "P384Element", + Prime: "2^384 - 2^128 - 2^96 + 2^32 - 1", + Prefix: "p384", + FiatType: "[6]uint64", + BytesLen: 48, + }, + // Note that unsaturated_solinas would be about 2x faster than + // word_by_word_montgomery for P-521, but this curve is used rarely enough + // that it's not worth carrying unsaturated_solinas support for it. + { + Element: "P521Element", + Prime: "2^521 - 1", + Prefix: "p521", + FiatType: "[9]uint64", + BytesLen: 66, + }, +} + +func main() { + t := template.Must(template.New("montgomery").Parse(tmplWrapper)) + + tmplAddchainFile, err := os.CreateTemp("", "addchain-template") + if err != nil { + log.Fatal(err) + } + defer os.Remove(tmplAddchainFile.Name()) + if _, err := io.WriteString(tmplAddchainFile, tmplAddchain); err != nil { + log.Fatal(err) + } + if err := tmplAddchainFile.Close(); err != nil { + log.Fatal(err) + } + + for _, c := range curves { + log.Printf("Generating %s.go...", c.Prefix) + f, err := os.Create(c.Prefix + ".go") + if err != nil { + log.Fatal(err) + } + if err := t.Execute(f, c); err != nil { + log.Fatal(err) + } + if err := f.Close(); err != nil { + log.Fatal(err) + } + + log.Printf("Generating %s_fiat64.go...", c.Prefix) + cmd := exec.Command("docker", "run", "--rm", "--entrypoint", "word_by_word_montgomery", + "fiat-crypto:v0.0.9", "--lang", "Go", "--no-wide-int", "--cmovznz-by-mul", + "--relax-primitive-carry-to-bitwidth", "32,64", "--internal-static", + "--public-function-case", "camelCase", "--public-type-case", "camelCase", + "--private-function-case", "camelCase", "--private-type-case", "camelCase", + "--doc-text-before-function-name", "", "--doc-newline-before-package-declaration", + "--doc-prepend-header", "Code generated by Fiat Cryptography. DO NOT EDIT.", + "--package-name", "fiat", "--no-prefix-fiat", c.Prefix, "64", c.Prime, + "mul", "square", "add", "sub", "one", "from_montgomery", "to_montgomery", + "selectznz", "to_bytes", "from_bytes") + cmd.Stderr = os.Stderr + out, err := cmd.Output() + if err != nil { + log.Fatal(err) + } + out, err = format.Source(out) + if err != nil { + log.Fatal(err) + } + if err := os.WriteFile(c.Prefix+"_fiat64.go", out, 0644); err != nil { + log.Fatal(err) + } + + log.Printf("Generating %s_invert.go...", c.Prefix) + f, err = os.CreateTemp("", "addchain-"+c.Prefix) + if err != nil { + log.Fatal(err) + } + defer os.Remove(f.Name()) + cmd = exec.Command("addchain", "search", c.Prime+" - 2") + cmd.Stderr = os.Stderr + cmd.Stdout = f + if err := cmd.Run(); err != nil { + log.Fatal(err) + } + if err := f.Close(); err != nil { + log.Fatal(err) + } + cmd = exec.Command("addchain", "gen", "-tmpl", tmplAddchainFile.Name(), f.Name()) + cmd.Stderr = os.Stderr + out, err = cmd.Output() + if err != nil { + log.Fatal(err) + } + out = bytes.Replace(out, []byte("Element"), []byte(c.Element), -1) + out, err = format.Source(out) + if err != nil { + log.Fatal(err) + } + if err := os.WriteFile(c.Prefix+"_invert.go", out, 0644); err != nil { + log.Fatal(err) + } + } +} + +const tmplWrapper = `// Copyright 2021 The Go Authors. All rights reserved. +// Use of this source code is governed by a BSD-style +// license that can be found in the LICENSE file. + +// Code generated by generate.go. DO NOT EDIT. + +package fiat + +import ( + "crypto/subtle" + "errors" +) + +// {{ .Element }} is an integer modulo {{ .Prime }}. +// +// The zero value is a valid zero element. +type {{ .Element }} struct { + // Values are represented internally always in the Montgomery domain, and + // converted in Bytes and SetBytes. + x {{ .Prefix }}MontgomeryDomainFieldElement +} + +const {{ .Prefix }}ElementLen = {{ .BytesLen }} + +type {{ .Prefix }}UntypedFieldElement = {{ .FiatType }} + +// One sets e = 1, and returns e. +func (e *{{ .Element }}) One() *{{ .Element }} { + {{ .Prefix }}SetOne(&e.x) + return e +} + +// Equal returns 1 if e == t, and zero otherwise. +func (e *{{ .Element }}) Equal(t *{{ .Element }}) int { + eBytes := e.Bytes() + tBytes := t.Bytes() + return subtle.ConstantTimeCompare(eBytes, tBytes) +} + +var {{ .Prefix }}ZeroEncoding = new({{ .Element }}).Bytes() + +// IsZero returns 1 if e == 0, and zero otherwise. +func (e *{{ .Element }}) IsZero() int { + eBytes := e.Bytes() + return subtle.ConstantTimeCompare(eBytes, {{ .Prefix }}ZeroEncoding) +} + +// Set sets e = t, and returns e. +func (e *{{ .Element }}) Set(t *{{ .Element }}) *{{ .Element }} { + e.x = t.x + return e +} + +// Bytes returns the {{ .BytesLen }}-byte big-endian encoding of e. +func (e *{{ .Element }}) Bytes() []byte { + // This function is outlined to make the allocations inline in the caller + // rather than happen on the heap. + var out [{{ .Prefix }}ElementLen]byte + return e.bytes(&out) +} + +func (e *{{ .Element }}) bytes(out *[{{ .Prefix }}ElementLen]byte) []byte { + var tmp {{ .Prefix }}NonMontgomeryDomainFieldElement + {{ .Prefix }}FromMontgomery(&tmp, &e.x) + {{ .Prefix }}ToBytes(out, (*{{ .Prefix }}UntypedFieldElement)(&tmp)) + {{ .Prefix }}InvertEndianness(out[:]) + return out[:] +} + +// {{ .Prefix }}MinusOneEncoding is the encoding of -1 mod p, so p - 1, the +// highest canonical encoding. It is used by SetBytes to check for non-canonical +// encodings such as p + k, 2p + k, etc. +var {{ .Prefix }}MinusOneEncoding = new({{ .Element }}).Sub( + new({{ .Element }}), new({{ .Element }}).One()).Bytes() + +// SetBytes sets e = v, where v is a big-endian {{ .BytesLen }}-byte encoding, and returns e. +// If v is not {{ .BytesLen }} bytes or it encodes a value higher than {{ .Prime }}, +// SetBytes returns nil and an error, and e is unchanged. +func (e *{{ .Element }}) SetBytes(v []byte) (*{{ .Element }}, error) { + if len(v) != {{ .Prefix }}ElementLen { + return nil, errors.New("invalid {{ .Element }} encoding") + } + for i := range v { + if v[i] < {{ .Prefix }}MinusOneEncoding[i] { + break + } + if v[i] > {{ .Prefix }}MinusOneEncoding[i] { + return nil, errors.New("invalid {{ .Element }} encoding") + } + } + var in [{{ .Prefix }}ElementLen]byte + copy(in[:], v) + {{ .Prefix }}InvertEndianness(in[:]) + var tmp {{ .Prefix }}NonMontgomeryDomainFieldElement + {{ .Prefix }}FromBytes((*{{ .Prefix }}UntypedFieldElement)(&tmp), &in) + {{ .Prefix }}ToMontgomery(&e.x, &tmp) + return e, nil +} + +// Add sets e = t1 + t2, and returns e. +func (e *{{ .Element }}) Add(t1, t2 *{{ .Element }}) *{{ .Element }} { + {{ .Prefix }}Add(&e.x, &t1.x, &t2.x) + return e +} + +// Sub sets e = t1 - t2, and returns e. +func (e *{{ .Element }}) Sub(t1, t2 *{{ .Element }}) *{{ .Element }} { + {{ .Prefix }}Sub(&e.x, &t1.x, &t2.x) + return e +} + +// Mul sets e = t1 * t2, and returns e. +func (e *{{ .Element }}) Mul(t1, t2 *{{ .Element }}) *{{ .Element }} { + {{ .Prefix }}Mul(&e.x, &t1.x, &t2.x) + return e +} + +// Square sets e = t * t, and returns e. +func (e *{{ .Element }}) Square(t *{{ .Element }}) *{{ .Element }} { + {{ .Prefix }}Square(&e.x, &t.x) + return e +} + +// Select sets v to a if cond == 1, and to b if cond == 0. +func (v *{{ .Element }}) Select(a, b *{{ .Element }}, cond int) *{{ .Element }} { + {{ .Prefix }}Selectznz((*{{ .Prefix }}UntypedFieldElement)(&v.x), {{ .Prefix }}Uint1(cond), + (*{{ .Prefix }}UntypedFieldElement)(&b.x), (*{{ .Prefix }}UntypedFieldElement)(&a.x)) + return v +} + +func {{ .Prefix }}InvertEndianness(v []byte) { + for i := 0; i < len(v)/2; i++ { + v[i], v[len(v)-1-i] = v[len(v)-1-i], v[i] + } +} +` + +const tmplAddchain = `// Copyright 2021 The Go Authors. All rights reserved. +// Use of this source code is governed by a BSD-style +// license that can be found in the LICENSE file. + +// Code generated by {{ .Meta.Name }}. DO NOT EDIT. + +package fiat + +// Invert sets e = 1/x, and returns e. +// +// If x == 0, Invert returns e = 0. +func (e *Element) Invert(x *Element) *Element { + // Inversion is implemented as exponentiation with exponent p − 2. + // The sequence of {{ .Ops.Adds }} multiplications and {{ .Ops.Doubles }} squarings is derived from the + // following addition chain generated with {{ .Meta.Module }} {{ .Meta.ReleaseTag }}. + // + {{- range lines (format .Script) }} + // {{ . }} + {{- end }} + // + + var z = new(Element).Set(e) + {{- range .Program.Temporaries }} + var {{ . }} = new(Element) + {{- end }} + {{ range $i := .Program.Instructions -}} + {{- with add $i.Op }} + {{ $i.Output }}.Mul({{ .X }}, {{ .Y }}) + {{- end -}} + + {{- with double $i.Op }} + {{ $i.Output }}.Square({{ .X }}) + {{- end -}} + + {{- with shift $i.Op -}} + {{- $first := 0 -}} + {{- if ne $i.Output.Identifier .X.Identifier }} + {{ $i.Output }}.Square({{ .X }}) + {{- $first = 1 -}} + {{- end }} + for s := {{ $first }}; s < {{ .S }}; s++ { + {{ $i.Output }}.Square({{ $i.Output }}) + } + {{- end -}} + {{- end }} + + return e.Set(z) +} +` diff --git a/libgo/go/crypto/elliptic/internal/fiat/p224.go b/libgo/go/crypto/elliptic/internal/fiat/p224.go new file mode 100644 index 0000000..4dddeb0 --- /dev/null +++ b/libgo/go/crypto/elliptic/internal/fiat/p224.go @@ -0,0 +1,135 @@ +// Copyright 2021 The Go Authors. All rights reserved. +// Use of this source code is governed by a BSD-style +// license that can be found in the LICENSE file. + +// Code generated by generate.go. DO NOT EDIT. + +package fiat + +import ( + "crypto/subtle" + "errors" +) + +// P224Element is an integer modulo 2^224 - 2^96 + 1. +// +// The zero value is a valid zero element. +type P224Element struct { + // Values are represented internally always in the Montgomery domain, and + // converted in Bytes and SetBytes. + x p224MontgomeryDomainFieldElement +} + +const p224ElementLen = 28 + +type p224UntypedFieldElement = [4]uint64 + +// One sets e = 1, and returns e. +func (e *P224Element) One() *P224Element { + p224SetOne(&e.x) + return e +} + +// Equal returns 1 if e == t, and zero otherwise. +func (e *P224Element) Equal(t *P224Element) int { + eBytes := e.Bytes() + tBytes := t.Bytes() + return subtle.ConstantTimeCompare(eBytes, tBytes) +} + +var p224ZeroEncoding = new(P224Element).Bytes() + +// IsZero returns 1 if e == 0, and zero otherwise. +func (e *P224Element) IsZero() int { + eBytes := e.Bytes() + return subtle.ConstantTimeCompare(eBytes, p224ZeroEncoding) +} + +// Set sets e = t, and returns e. +func (e *P224Element) Set(t *P224Element) *P224Element { + e.x = t.x + return e +} + +// Bytes returns the 28-byte big-endian encoding of e. +func (e *P224Element) Bytes() []byte { + // This function is outlined to make the allocations inline in the caller + // rather than happen on the heap. + var out [p224ElementLen]byte + return e.bytes(&out) +} + +func (e *P224Element) bytes(out *[p224ElementLen]byte) []byte { + var tmp p224NonMontgomeryDomainFieldElement + p224FromMontgomery(&tmp, &e.x) + p224ToBytes(out, (*p224UntypedFieldElement)(&tmp)) + p224InvertEndianness(out[:]) + return out[:] +} + +// p224MinusOneEncoding is the encoding of -1 mod p, so p - 1, the +// highest canonical encoding. It is used by SetBytes to check for non-canonical +// encodings such as p + k, 2p + k, etc. +var p224MinusOneEncoding = new(P224Element).Sub( + new(P224Element), new(P224Element).One()).Bytes() + +// SetBytes sets e = v, where v is a big-endian 28-byte encoding, and returns e. +// If v is not 28 bytes or it encodes a value higher than 2^224 - 2^96 + 1, +// SetBytes returns nil and an error, and e is unchanged. +func (e *P224Element) SetBytes(v []byte) (*P224Element, error) { + if len(v) != p224ElementLen { + return nil, errors.New("invalid P224Element encoding") + } + for i := range v { + if v[i] < p224MinusOneEncoding[i] { + break + } + if v[i] > p224MinusOneEncoding[i] { + return nil, errors.New("invalid P224Element encoding") + } + } + var in [p224ElementLen]byte + copy(in[:], v) + p224InvertEndianness(in[:]) + var tmp p224NonMontgomeryDomainFieldElement + p224FromBytes((*p224UntypedFieldElement)(&tmp), &in) + p224ToMontgomery(&e.x, &tmp) + return e, nil +} + +// Add sets e = t1 + t2, and returns e. +func (e *P224Element) Add(t1, t2 *P224Element) *P224Element { + p224Add(&e.x, &t1.x, &t2.x) + return e +} + +// Sub sets e = t1 - t2, and returns e. +func (e *P224Element) Sub(t1, t2 *P224Element) *P224Element { + p224Sub(&e.x, &t1.x, &t2.x) + return e +} + +// Mul sets e = t1 * t2, and returns e. +func (e *P224Element) Mul(t1, t2 *P224Element) *P224Element { + p224Mul(&e.x, &t1.x, &t2.x) + return e +} + +// Square sets e = t * t, and returns e. +func (e *P224Element) Square(t *P224Element) *P224Element { + p224Square(&e.x, &t.x) + return e +} + +// Select sets v to a if cond == 1, and to b if cond == 0. +func (v *P224Element) Select(a, b *P224Element, cond int) *P224Element { + p224Selectznz((*p224UntypedFieldElement)(&v.x), p224Uint1(cond), + (*p224UntypedFieldElement)(&b.x), (*p224UntypedFieldElement)(&a.x)) + return v +} + +func p224InvertEndianness(v []byte) { + for i := 0; i < len(v)/2; i++ { + v[i], v[len(v)-1-i] = v[len(v)-1-i], v[i] + } +} diff --git a/libgo/go/crypto/elliptic/internal/fiat/p224_fiat64.go b/libgo/go/crypto/elliptic/internal/fiat/p224_fiat64.go new file mode 100644 index 0000000..4ece3e9 --- /dev/null +++ b/libgo/go/crypto/elliptic/internal/fiat/p224_fiat64.go @@ -0,0 +1,1429 @@ +// Code generated by Fiat Cryptography. DO NOT EDIT. +// +// Autogenerated: word_by_word_montgomery --lang Go --no-wide-int --cmovznz-by-mul --relax-primitive-carry-to-bitwidth 32,64 --internal-static --public-function-case camelCase --public-type-case camelCase --private-function-case camelCase --private-type-case camelCase --doc-text-before-function-name '' --doc-newline-before-package-declaration --doc-prepend-header 'Code generated by Fiat Cryptography. DO NOT EDIT.' --package-name fiat --no-prefix-fiat p224 64 '2^224 - 2^96 + 1' mul square add sub one from_montgomery to_montgomery selectznz to_bytes from_bytes +// +// curve description: p224 +// +// machine_wordsize = 64 (from "64") +// +// requested operations: mul, square, add, sub, one, from_montgomery, to_montgomery, selectznz, to_bytes, from_bytes +// +// m = 0xffffffffffffffffffffffffffffffff000000000000000000000001 (from "2^224 - 2^96 + 1") +// +// +// +// NOTE: In addition to the bounds specified above each function, all +// +// functions synthesized for this Montgomery arithmetic require the +// +// input to be strictly less than the prime modulus (m), and also +// +// require the input to be in the unique saturated representation. +// +// All functions also ensure that these two properties are true of +// +// return values. +// +// +// +// Computed values: +// +// eval z = z[0] + (z[1] << 64) + (z[2] << 128) + (z[3] << 192) +// +// bytes_eval z = z[0] + (z[1] << 8) + (z[2] << 16) + (z[3] << 24) + (z[4] << 32) + (z[5] << 40) + (z[6] << 48) + (z[7] << 56) + (z[8] << 64) + (z[9] << 72) + (z[10] << 80) + (z[11] << 88) + (z[12] << 96) + (z[13] << 104) + (z[14] << 112) + (z[15] << 120) + (z[16] << 128) + (z[17] << 136) + (z[18] << 144) + (z[19] << 152) + (z[20] << 160) + (z[21] << 168) + (z[22] << 176) + (z[23] << 184) + (z[24] << 192) + (z[25] << 200) + (z[26] << 208) + (z[27] << 216) +// +// twos_complement_eval z = let x1 := z[0] + (z[1] << 64) + (z[2] << 128) + (z[3] << 192) in +// +// if x1 & (2^256-1) < 2^255 then x1 & (2^256-1) else (x1 & (2^256-1)) - 2^256 + +package fiat + +import "math/bits" + +type p224Uint1 uint64 // We use uint64 instead of a more narrow type for performance reasons; see https://github.com/mit-plv/fiat-crypto/pull/1006#issuecomment-892625927 +type p224Int1 int64 // We use uint64 instead of a more narrow type for performance reasons; see https://github.com/mit-plv/fiat-crypto/pull/1006#issuecomment-892625927 + +// The type p224MontgomeryDomainFieldElement is a field element in the Montgomery domain. +// +// Bounds: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]] +type p224MontgomeryDomainFieldElement [4]uint64 + +// The type p224NonMontgomeryDomainFieldElement is a field element NOT in the Montgomery domain. +// +// Bounds: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]] +type p224NonMontgomeryDomainFieldElement [4]uint64 + +// p224CmovznzU64 is a single-word conditional move. +// +// Postconditions: +// out1 = (if arg1 = 0 then arg2 else arg3) +// +// Input Bounds: +// arg1: [0x0 ~> 0x1] +// arg2: [0x0 ~> 0xffffffffffffffff] +// arg3: [0x0 ~> 0xffffffffffffffff] +// Output Bounds: +// out1: [0x0 ~> 0xffffffffffffffff] +func p224CmovznzU64(out1 *uint64, arg1 p224Uint1, arg2 uint64, arg3 uint64) { + x1 := (uint64(arg1) * 0xffffffffffffffff) + x2 := ((x1 & arg3) | ((^x1) & arg2)) + *out1 = x2 +} + +// p224Mul multiplies two field elements in the Montgomery domain. +// +// Preconditions: +// 0 ≤ eval arg1 < m +// 0 ≤ eval arg2 < m +// Postconditions: +// eval (from_montgomery out1) mod m = (eval (from_montgomery arg1) * eval (from_montgomery arg2)) mod m +// 0 ≤ eval out1 < m +// +func p224Mul(out1 *p224MontgomeryDomainFieldElement, arg1 *p224MontgomeryDomainFieldElement, arg2 *p224MontgomeryDomainFieldElement) { + x1 := arg1[1] + x2 := arg1[2] + x3 := arg1[3] + x4 := arg1[0] + var x5 uint64 + var x6 uint64 + x6, x5 = bits.Mul64(x4, arg2[3]) + var x7 uint64 + var x8 uint64 + x8, x7 = bits.Mul64(x4, arg2[2]) + var x9 uint64 + var x10 uint64 + x10, x9 = bits.Mul64(x4, arg2[1]) + var x11 uint64 + var x12 uint64 + x12, x11 = bits.Mul64(x4, arg2[0]) + var x13 uint64 + var x14 uint64 + x13, x14 = bits.Add64(x12, x9, uint64(0x0)) + var x15 uint64 + var x16 uint64 + x15, x16 = bits.Add64(x10, x7, uint64(p224Uint1(x14))) + var x17 uint64 + var x18 uint64 + x17, x18 = bits.Add64(x8, x5, uint64(p224Uint1(x16))) + x19 := (uint64(p224Uint1(x18)) + x6) + var x20 uint64 + _, x20 = bits.Mul64(x11, 0xffffffffffffffff) + var x22 uint64 + var x23 uint64 + x23, x22 = bits.Mul64(x20, 0xffffffff) + var x24 uint64 + var x25 uint64 + x25, x24 = bits.Mul64(x20, 0xffffffffffffffff) + var x26 uint64 + var x27 uint64 + x27, x26 = bits.Mul64(x20, 0xffffffff00000000) + var x28 uint64 + var x29 uint64 + x28, x29 = bits.Add64(x27, x24, uint64(0x0)) + var x30 uint64 + var x31 uint64 + x30, x31 = bits.Add64(x25, x22, uint64(p224Uint1(x29))) + x32 := (uint64(p224Uint1(x31)) + x23) + var x34 uint64 + _, x34 = bits.Add64(x11, x20, uint64(0x0)) + var x35 uint64 + var x36 uint64 + x35, x36 = bits.Add64(x13, x26, uint64(p224Uint1(x34))) + var x37 uint64 + var x38 uint64 + x37, x38 = bits.Add64(x15, x28, uint64(p224Uint1(x36))) + var x39 uint64 + var x40 uint64 + x39, x40 = bits.Add64(x17, x30, uint64(p224Uint1(x38))) + var x41 uint64 + var x42 uint64 + x41, x42 = bits.Add64(x19, x32, uint64(p224Uint1(x40))) + var x43 uint64 + var x44 uint64 + x44, x43 = bits.Mul64(x1, arg2[3]) + var x45 uint64 + var x46 uint64 + x46, x45 = bits.Mul64(x1, arg2[2]) + var x47 uint64 + var x48 uint64 + x48, x47 = bits.Mul64(x1, arg2[1]) + var x49 uint64 + var x50 uint64 + x50, x49 = bits.Mul64(x1, arg2[0]) + var x51 uint64 + var x52 uint64 + x51, x52 = bits.Add64(x50, x47, uint64(0x0)) + var x53 uint64 + var x54 uint64 + x53, x54 = bits.Add64(x48, x45, uint64(p224Uint1(x52))) + var x55 uint64 + var x56 uint64 + x55, x56 = bits.Add64(x46, x43, uint64(p224Uint1(x54))) + x57 := (uint64(p224Uint1(x56)) + x44) + var x58 uint64 + var x59 uint64 + x58, x59 = bits.Add64(x35, x49, uint64(0x0)) + var x60 uint64 + var x61 uint64 + x60, x61 = bits.Add64(x37, x51, uint64(p224Uint1(x59))) + var x62 uint64 + var x63 uint64 + x62, x63 = bits.Add64(x39, x53, uint64(p224Uint1(x61))) + var x64 uint64 + var x65 uint64 + x64, x65 = bits.Add64(x41, x55, uint64(p224Uint1(x63))) + var x66 uint64 + var x67 uint64 + x66, x67 = bits.Add64(uint64(p224Uint1(x42)), x57, uint64(p224Uint1(x65))) + var x68 uint64 + _, x68 = bits.Mul64(x58, 0xffffffffffffffff) + var x70 uint64 + var x71 uint64 + x71, x70 = bits.Mul64(x68, 0xffffffff) + var x72 uint64 + var x73 uint64 + x73, x72 = bits.Mul64(x68, 0xffffffffffffffff) + var x74 uint64 + var x75 uint64 + x75, x74 = bits.Mul64(x68, 0xffffffff00000000) + var x76 uint64 + var x77 uint64 + x76, x77 = bits.Add64(x75, x72, uint64(0x0)) + var x78 uint64 + var x79 uint64 + x78, x79 = bits.Add64(x73, x70, uint64(p224Uint1(x77))) + x80 := (uint64(p224Uint1(x79)) + x71) + var x82 uint64 + _, x82 = bits.Add64(x58, x68, uint64(0x0)) + var x83 uint64 + var x84 uint64 + x83, x84 = bits.Add64(x60, x74, uint64(p224Uint1(x82))) + var x85 uint64 + var x86 uint64 + x85, x86 = bits.Add64(x62, x76, uint64(p224Uint1(x84))) + var x87 uint64 + var x88 uint64 + x87, x88 = bits.Add64(x64, x78, uint64(p224Uint1(x86))) + var x89 uint64 + var x90 uint64 + x89, x90 = bits.Add64(x66, x80, uint64(p224Uint1(x88))) + x91 := (uint64(p224Uint1(x90)) + uint64(p224Uint1(x67))) + var x92 uint64 + var x93 uint64 + x93, x92 = bits.Mul64(x2, arg2[3]) + var x94 uint64 + var x95 uint64 + x95, x94 = bits.Mul64(x2, arg2[2]) + var x96 uint64 + var x97 uint64 + x97, x96 = bits.Mul64(x2, arg2[1]) + var x98 uint64 + var x99 uint64 + x99, x98 = bits.Mul64(x2, arg2[0]) + var x100 uint64 + var x101 uint64 + x100, x101 = bits.Add64(x99, x96, uint64(0x0)) + var x102 uint64 + var x103 uint64 + x102, x103 = bits.Add64(x97, x94, uint64(p224Uint1(x101))) + var x104 uint64 + var x105 uint64 + x104, x105 = bits.Add64(x95, x92, uint64(p224Uint1(x103))) + x106 := (uint64(p224Uint1(x105)) + x93) + var x107 uint64 + var x108 uint64 + x107, x108 = bits.Add64(x83, x98, uint64(0x0)) + var x109 uint64 + var x110 uint64 + x109, x110 = bits.Add64(x85, x100, uint64(p224Uint1(x108))) + var x111 uint64 + var x112 uint64 + x111, x112 = bits.Add64(x87, x102, uint64(p224Uint1(x110))) + var x113 uint64 + var x114 uint64 + x113, x114 = bits.Add64(x89, x104, uint64(p224Uint1(x112))) + var x115 uint64 + var x116 uint64 + x115, x116 = bits.Add64(x91, x106, uint64(p224Uint1(x114))) + var x117 uint64 + _, x117 = bits.Mul64(x107, 0xffffffffffffffff) + var x119 uint64 + var x120 uint64 + x120, x119 = bits.Mul64(x117, 0xffffffff) + var x121 uint64 + var x122 uint64 + x122, x121 = bits.Mul64(x117, 0xffffffffffffffff) + var x123 uint64 + var x124 uint64 + x124, x123 = bits.Mul64(x117, 0xffffffff00000000) + var x125 uint64 + var x126 uint64 + x125, x126 = bits.Add64(x124, x121, uint64(0x0)) + var x127 uint64 + var x128 uint64 + x127, x128 = bits.Add64(x122, x119, uint64(p224Uint1(x126))) + x129 := (uint64(p224Uint1(x128)) + x120) + var x131 uint64 + _, x131 = bits.Add64(x107, x117, uint64(0x0)) + var x132 uint64 + var x133 uint64 + x132, x133 = bits.Add64(x109, x123, uint64(p224Uint1(x131))) + var x134 uint64 + var x135 uint64 + x134, x135 = bits.Add64(x111, x125, uint64(p224Uint1(x133))) + var x136 uint64 + var x137 uint64 + x136, x137 = bits.Add64(x113, x127, uint64(p224Uint1(x135))) + var x138 uint64 + var x139 uint64 + x138, x139 = bits.Add64(x115, x129, uint64(p224Uint1(x137))) + x140 := (uint64(p224Uint1(x139)) + uint64(p224Uint1(x116))) + var x141 uint64 + var x142 uint64 + x142, x141 = bits.Mul64(x3, arg2[3]) + var x143 uint64 + var x144 uint64 + x144, x143 = bits.Mul64(x3, arg2[2]) + var x145 uint64 + var x146 uint64 + x146, x145 = bits.Mul64(x3, arg2[1]) + var x147 uint64 + var x148 uint64 + x148, x147 = bits.Mul64(x3, arg2[0]) + var x149 uint64 + var x150 uint64 + x149, x150 = bits.Add64(x148, x145, uint64(0x0)) + var x151 uint64 + var x152 uint64 + x151, x152 = bits.Add64(x146, x143, uint64(p224Uint1(x150))) + var x153 uint64 + var x154 uint64 + x153, x154 = bits.Add64(x144, x141, uint64(p224Uint1(x152))) + x155 := (uint64(p224Uint1(x154)) + x142) + var x156 uint64 + var x157 uint64 + x156, x157 = bits.Add64(x132, x147, uint64(0x0)) + var x158 uint64 + var x159 uint64 + x158, x159 = bits.Add64(x134, x149, uint64(p224Uint1(x157))) + var x160 uint64 + var x161 uint64 + x160, x161 = bits.Add64(x136, x151, uint64(p224Uint1(x159))) + var x162 uint64 + var x163 uint64 + x162, x163 = bits.Add64(x138, x153, uint64(p224Uint1(x161))) + var x164 uint64 + var x165 uint64 + x164, x165 = bits.Add64(x140, x155, uint64(p224Uint1(x163))) + var x166 uint64 + _, x166 = bits.Mul64(x156, 0xffffffffffffffff) + var x168 uint64 + var x169 uint64 + x169, x168 = bits.Mul64(x166, 0xffffffff) + var x170 uint64 + var x171 uint64 + x171, x170 = bits.Mul64(x166, 0xffffffffffffffff) + var x172 uint64 + var x173 uint64 + x173, x172 = bits.Mul64(x166, 0xffffffff00000000) + var x174 uint64 + var x175 uint64 + x174, x175 = bits.Add64(x173, x170, uint64(0x0)) + var x176 uint64 + var x177 uint64 + x176, x177 = bits.Add64(x171, x168, uint64(p224Uint1(x175))) + x178 := (uint64(p224Uint1(x177)) + x169) + var x180 uint64 + _, x180 = bits.Add64(x156, x166, uint64(0x0)) + var x181 uint64 + var x182 uint64 + x181, x182 = bits.Add64(x158, x172, uint64(p224Uint1(x180))) + var x183 uint64 + var x184 uint64 + x183, x184 = bits.Add64(x160, x174, uint64(p224Uint1(x182))) + var x185 uint64 + var x186 uint64 + x185, x186 = bits.Add64(x162, x176, uint64(p224Uint1(x184))) + var x187 uint64 + var x188 uint64 + x187, x188 = bits.Add64(x164, x178, uint64(p224Uint1(x186))) + x189 := (uint64(p224Uint1(x188)) + uint64(p224Uint1(x165))) + var x190 uint64 + var x191 uint64 + x190, x191 = bits.Sub64(x181, uint64(0x1), uint64(0x0)) + var x192 uint64 + var x193 uint64 + x192, x193 = bits.Sub64(x183, 0xffffffff00000000, uint64(p224Uint1(x191))) + var x194 uint64 + var x195 uint64 + x194, x195 = bits.Sub64(x185, 0xffffffffffffffff, uint64(p224Uint1(x193))) + var x196 uint64 + var x197 uint64 + x196, x197 = bits.Sub64(x187, 0xffffffff, uint64(p224Uint1(x195))) + var x199 uint64 + _, x199 = bits.Sub64(x189, uint64(0x0), uint64(p224Uint1(x197))) + var x200 uint64 + p224CmovznzU64(&x200, p224Uint1(x199), x190, x181) + var x201 uint64 + p224CmovznzU64(&x201, p224Uint1(x199), x192, x183) + var x202 uint64 + p224CmovznzU64(&x202, p224Uint1(x199), x194, x185) + var x203 uint64 + p224CmovznzU64(&x203, p224Uint1(x199), x196, x187) + out1[0] = x200 + out1[1] = x201 + out1[2] = x202 + out1[3] = x203 +} + +// p224Square squares a field element in the Montgomery domain. +// +// Preconditions: +// 0 ≤ eval arg1 < m +// Postconditions: +// eval (from_montgomery out1) mod m = (eval (from_montgomery arg1) * eval (from_montgomery arg1)) mod m +// 0 ≤ eval out1 < m +// +func p224Square(out1 *p224MontgomeryDomainFieldElement, arg1 *p224MontgomeryDomainFieldElement) { + x1 := arg1[1] + x2 := arg1[2] + x3 := arg1[3] + x4 := arg1[0] + var x5 uint64 + var x6 uint64 + x6, x5 = bits.Mul64(x4, arg1[3]) + var x7 uint64 + var x8 uint64 + x8, x7 = bits.Mul64(x4, arg1[2]) + var x9 uint64 + var x10 uint64 + x10, x9 = bits.Mul64(x4, arg1[1]) + var x11 uint64 + var x12 uint64 + x12, x11 = bits.Mul64(x4, arg1[0]) + var x13 uint64 + var x14 uint64 + x13, x14 = bits.Add64(x12, x9, uint64(0x0)) + var x15 uint64 + var x16 uint64 + x15, x16 = bits.Add64(x10, x7, uint64(p224Uint1(x14))) + var x17 uint64 + var x18 uint64 + x17, x18 = bits.Add64(x8, x5, uint64(p224Uint1(x16))) + x19 := (uint64(p224Uint1(x18)) + x6) + var x20 uint64 + _, x20 = bits.Mul64(x11, 0xffffffffffffffff) + var x22 uint64 + var x23 uint64 + x23, x22 = bits.Mul64(x20, 0xffffffff) + var x24 uint64 + var x25 uint64 + x25, x24 = bits.Mul64(x20, 0xffffffffffffffff) + var x26 uint64 + var x27 uint64 + x27, x26 = bits.Mul64(x20, 0xffffffff00000000) + var x28 uint64 + var x29 uint64 + x28, x29 = bits.Add64(x27, x24, uint64(0x0)) + var x30 uint64 + var x31 uint64 + x30, x31 = bits.Add64(x25, x22, uint64(p224Uint1(x29))) + x32 := (uint64(p224Uint1(x31)) + x23) + var x34 uint64 + _, x34 = bits.Add64(x11, x20, uint64(0x0)) + var x35 uint64 + var x36 uint64 + x35, x36 = bits.Add64(x13, x26, uint64(p224Uint1(x34))) + var x37 uint64 + var x38 uint64 + x37, x38 = bits.Add64(x15, x28, uint64(p224Uint1(x36))) + var x39 uint64 + var x40 uint64 + x39, x40 = bits.Add64(x17, x30, uint64(p224Uint1(x38))) + var x41 uint64 + var x42 uint64 + x41, x42 = bits.Add64(x19, x32, uint64(p224Uint1(x40))) + var x43 uint64 + var x44 uint64 + x44, x43 = bits.Mul64(x1, arg1[3]) + var x45 uint64 + var x46 uint64 + x46, x45 = bits.Mul64(x1, arg1[2]) + var x47 uint64 + var x48 uint64 + x48, x47 = bits.Mul64(x1, arg1[1]) + var x49 uint64 + var x50 uint64 + x50, x49 = bits.Mul64(x1, arg1[0]) + var x51 uint64 + var x52 uint64 + x51, x52 = bits.Add64(x50, x47, uint64(0x0)) + var x53 uint64 + var x54 uint64 + x53, x54 = bits.Add64(x48, x45, uint64(p224Uint1(x52))) + var x55 uint64 + var x56 uint64 + x55, x56 = bits.Add64(x46, x43, uint64(p224Uint1(x54))) + x57 := (uint64(p224Uint1(x56)) + x44) + var x58 uint64 + var x59 uint64 + x58, x59 = bits.Add64(x35, x49, uint64(0x0)) + var x60 uint64 + var x61 uint64 + x60, x61 = bits.Add64(x37, x51, uint64(p224Uint1(x59))) + var x62 uint64 + var x63 uint64 + x62, x63 = bits.Add64(x39, x53, uint64(p224Uint1(x61))) + var x64 uint64 + var x65 uint64 + x64, x65 = bits.Add64(x41, x55, uint64(p224Uint1(x63))) + var x66 uint64 + var x67 uint64 + x66, x67 = bits.Add64(uint64(p224Uint1(x42)), x57, uint64(p224Uint1(x65))) + var x68 uint64 + _, x68 = bits.Mul64(x58, 0xffffffffffffffff) + var x70 uint64 + var x71 uint64 + x71, x70 = bits.Mul64(x68, 0xffffffff) + var x72 uint64 + var x73 uint64 + x73, x72 = bits.Mul64(x68, 0xffffffffffffffff) + var x74 uint64 + var x75 uint64 + x75, x74 = bits.Mul64(x68, 0xffffffff00000000) + var x76 uint64 + var x77 uint64 + x76, x77 = bits.Add64(x75, x72, uint64(0x0)) + var x78 uint64 + var x79 uint64 + x78, x79 = bits.Add64(x73, x70, uint64(p224Uint1(x77))) + x80 := (uint64(p224Uint1(x79)) + x71) + var x82 uint64 + _, x82 = bits.Add64(x58, x68, uint64(0x0)) + var x83 uint64 + var x84 uint64 + x83, x84 = bits.Add64(x60, x74, uint64(p224Uint1(x82))) + var x85 uint64 + var x86 uint64 + x85, x86 = bits.Add64(x62, x76, uint64(p224Uint1(x84))) + var x87 uint64 + var x88 uint64 + x87, x88 = bits.Add64(x64, x78, uint64(p224Uint1(x86))) + var x89 uint64 + var x90 uint64 + x89, x90 = bits.Add64(x66, x80, uint64(p224Uint1(x88))) + x91 := (uint64(p224Uint1(x90)) + uint64(p224Uint1(x67))) + var x92 uint64 + var x93 uint64 + x93, x92 = bits.Mul64(x2, arg1[3]) + var x94 uint64 + var x95 uint64 + x95, x94 = bits.Mul64(x2, arg1[2]) + var x96 uint64 + var x97 uint64 + x97, x96 = bits.Mul64(x2, arg1[1]) + var x98 uint64 + var x99 uint64 + x99, x98 = bits.Mul64(x2, arg1[0]) + var x100 uint64 + var x101 uint64 + x100, x101 = bits.Add64(x99, x96, uint64(0x0)) + var x102 uint64 + var x103 uint64 + x102, x103 = bits.Add64(x97, x94, uint64(p224Uint1(x101))) + var x104 uint64 + var x105 uint64 + x104, x105 = bits.Add64(x95, x92, uint64(p224Uint1(x103))) + x106 := (uint64(p224Uint1(x105)) + x93) + var x107 uint64 + var x108 uint64 + x107, x108 = bits.Add64(x83, x98, uint64(0x0)) + var x109 uint64 + var x110 uint64 + x109, x110 = bits.Add64(x85, x100, uint64(p224Uint1(x108))) + var x111 uint64 + var x112 uint64 + x111, x112 = bits.Add64(x87, x102, uint64(p224Uint1(x110))) + var x113 uint64 + var x114 uint64 + x113, x114 = bits.Add64(x89, x104, uint64(p224Uint1(x112))) + var x115 uint64 + var x116 uint64 + x115, x116 = bits.Add64(x91, x106, uint64(p224Uint1(x114))) + var x117 uint64 + _, x117 = bits.Mul64(x107, 0xffffffffffffffff) + var x119 uint64 + var x120 uint64 + x120, x119 = bits.Mul64(x117, 0xffffffff) + var x121 uint64 + var x122 uint64 + x122, x121 = bits.Mul64(x117, 0xffffffffffffffff) + var x123 uint64 + var x124 uint64 + x124, x123 = bits.Mul64(x117, 0xffffffff00000000) + var x125 uint64 + var x126 uint64 + x125, x126 = bits.Add64(x124, x121, uint64(0x0)) + var x127 uint64 + var x128 uint64 + x127, x128 = bits.Add64(x122, x119, uint64(p224Uint1(x126))) + x129 := (uint64(p224Uint1(x128)) + x120) + var x131 uint64 + _, x131 = bits.Add64(x107, x117, uint64(0x0)) + var x132 uint64 + var x133 uint64 + x132, x133 = bits.Add64(x109, x123, uint64(p224Uint1(x131))) + var x134 uint64 + var x135 uint64 + x134, x135 = bits.Add64(x111, x125, uint64(p224Uint1(x133))) + var x136 uint64 + var x137 uint64 + x136, x137 = bits.Add64(x113, x127, uint64(p224Uint1(x135))) + var x138 uint64 + var x139 uint64 + x138, x139 = bits.Add64(x115, x129, uint64(p224Uint1(x137))) + x140 := (uint64(p224Uint1(x139)) + uint64(p224Uint1(x116))) + var x141 uint64 + var x142 uint64 + x142, x141 = bits.Mul64(x3, arg1[3]) + var x143 uint64 + var x144 uint64 + x144, x143 = bits.Mul64(x3, arg1[2]) + var x145 uint64 + var x146 uint64 + x146, x145 = bits.Mul64(x3, arg1[1]) + var x147 uint64 + var x148 uint64 + x148, x147 = bits.Mul64(x3, arg1[0]) + var x149 uint64 + var x150 uint64 + x149, x150 = bits.Add64(x148, x145, uint64(0x0)) + var x151 uint64 + var x152 uint64 + x151, x152 = bits.Add64(x146, x143, uint64(p224Uint1(x150))) + var x153 uint64 + var x154 uint64 + x153, x154 = bits.Add64(x144, x141, uint64(p224Uint1(x152))) + x155 := (uint64(p224Uint1(x154)) + x142) + var x156 uint64 + var x157 uint64 + x156, x157 = bits.Add64(x132, x147, uint64(0x0)) + var x158 uint64 + var x159 uint64 + x158, x159 = bits.Add64(x134, x149, uint64(p224Uint1(x157))) + var x160 uint64 + var x161 uint64 + x160, x161 = bits.Add64(x136, x151, uint64(p224Uint1(x159))) + var x162 uint64 + var x163 uint64 + x162, x163 = bits.Add64(x138, x153, uint64(p224Uint1(x161))) + var x164 uint64 + var x165 uint64 + x164, x165 = bits.Add64(x140, x155, uint64(p224Uint1(x163))) + var x166 uint64 + _, x166 = bits.Mul64(x156, 0xffffffffffffffff) + var x168 uint64 + var x169 uint64 + x169, x168 = bits.Mul64(x166, 0xffffffff) + var x170 uint64 + var x171 uint64 + x171, x170 = bits.Mul64(x166, 0xffffffffffffffff) + var x172 uint64 + var x173 uint64 + x173, x172 = bits.Mul64(x166, 0xffffffff00000000) + var x174 uint64 + var x175 uint64 + x174, x175 = bits.Add64(x173, x170, uint64(0x0)) + var x176 uint64 + var x177 uint64 + x176, x177 = bits.Add64(x171, x168, uint64(p224Uint1(x175))) + x178 := (uint64(p224Uint1(x177)) + x169) + var x180 uint64 + _, x180 = bits.Add64(x156, x166, uint64(0x0)) + var x181 uint64 + var x182 uint64 + x181, x182 = bits.Add64(x158, x172, uint64(p224Uint1(x180))) + var x183 uint64 + var x184 uint64 + x183, x184 = bits.Add64(x160, x174, uint64(p224Uint1(x182))) + var x185 uint64 + var x186 uint64 + x185, x186 = bits.Add64(x162, x176, uint64(p224Uint1(x184))) + var x187 uint64 + var x188 uint64 + x187, x188 = bits.Add64(x164, x178, uint64(p224Uint1(x186))) + x189 := (uint64(p224Uint1(x188)) + uint64(p224Uint1(x165))) + var x190 uint64 + var x191 uint64 + x190, x191 = bits.Sub64(x181, uint64(0x1), uint64(0x0)) + var x192 uint64 + var x193 uint64 + x192, x193 = bits.Sub64(x183, 0xffffffff00000000, uint64(p224Uint1(x191))) + var x194 uint64 + var x195 uint64 + x194, x195 = bits.Sub64(x185, 0xffffffffffffffff, uint64(p224Uint1(x193))) + var x196 uint64 + var x197 uint64 + x196, x197 = bits.Sub64(x187, 0xffffffff, uint64(p224Uint1(x195))) + var x199 uint64 + _, x199 = bits.Sub64(x189, uint64(0x0), uint64(p224Uint1(x197))) + var x200 uint64 + p224CmovznzU64(&x200, p224Uint1(x199), x190, x181) + var x201 uint64 + p224CmovznzU64(&x201, p224Uint1(x199), x192, x183) + var x202 uint64 + p224CmovznzU64(&x202, p224Uint1(x199), x194, x185) + var x203 uint64 + p224CmovznzU64(&x203, p224Uint1(x199), x196, x187) + out1[0] = x200 + out1[1] = x201 + out1[2] = x202 + out1[3] = x203 +} + +// p224Add adds two field elements in the Montgomery domain. +// +// Preconditions: +// 0 ≤ eval arg1 < m +// 0 ≤ eval arg2 < m +// Postconditions: +// eval (from_montgomery out1) mod m = (eval (from_montgomery arg1) + eval (from_montgomery arg2)) mod m +// 0 ≤ eval out1 < m +// +func p224Add(out1 *p224MontgomeryDomainFieldElement, arg1 *p224MontgomeryDomainFieldElement, arg2 *p224MontgomeryDomainFieldElement) { + var x1 uint64 + var x2 uint64 + x1, x2 = bits.Add64(arg1[0], arg2[0], uint64(0x0)) + var x3 uint64 + var x4 uint64 + x3, x4 = bits.Add64(arg1[1], arg2[1], uint64(p224Uint1(x2))) + var x5 uint64 + var x6 uint64 + x5, x6 = bits.Add64(arg1[2], arg2[2], uint64(p224Uint1(x4))) + var x7 uint64 + var x8 uint64 + x7, x8 = bits.Add64(arg1[3], arg2[3], uint64(p224Uint1(x6))) + var x9 uint64 + var x10 uint64 + x9, x10 = bits.Sub64(x1, uint64(0x1), uint64(0x0)) + var x11 uint64 + var x12 uint64 + x11, x12 = bits.Sub64(x3, 0xffffffff00000000, uint64(p224Uint1(x10))) + var x13 uint64 + var x14 uint64 + x13, x14 = bits.Sub64(x5, 0xffffffffffffffff, uint64(p224Uint1(x12))) + var x15 uint64 + var x16 uint64 + x15, x16 = bits.Sub64(x7, 0xffffffff, uint64(p224Uint1(x14))) + var x18 uint64 + _, x18 = bits.Sub64(uint64(p224Uint1(x8)), uint64(0x0), uint64(p224Uint1(x16))) + var x19 uint64 + p224CmovznzU64(&x19, p224Uint1(x18), x9, x1) + var x20 uint64 + p224CmovznzU64(&x20, p224Uint1(x18), x11, x3) + var x21 uint64 + p224CmovznzU64(&x21, p224Uint1(x18), x13, x5) + var x22 uint64 + p224CmovznzU64(&x22, p224Uint1(x18), x15, x7) + out1[0] = x19 + out1[1] = x20 + out1[2] = x21 + out1[3] = x22 +} + +// p224Sub subtracts two field elements in the Montgomery domain. +// +// Preconditions: +// 0 ≤ eval arg1 < m +// 0 ≤ eval arg2 < m +// Postconditions: +// eval (from_montgomery out1) mod m = (eval (from_montgomery arg1) - eval (from_montgomery arg2)) mod m +// 0 ≤ eval out1 < m +// +func p224Sub(out1 *p224MontgomeryDomainFieldElement, arg1 *p224MontgomeryDomainFieldElement, arg2 *p224MontgomeryDomainFieldElement) { + var x1 uint64 + var x2 uint64 + x1, x2 = bits.Sub64(arg1[0], arg2[0], uint64(0x0)) + var x3 uint64 + var x4 uint64 + x3, x4 = bits.Sub64(arg1[1], arg2[1], uint64(p224Uint1(x2))) + var x5 uint64 + var x6 uint64 + x5, x6 = bits.Sub64(arg1[2], arg2[2], uint64(p224Uint1(x4))) + var x7 uint64 + var x8 uint64 + x7, x8 = bits.Sub64(arg1[3], arg2[3], uint64(p224Uint1(x6))) + var x9 uint64 + p224CmovznzU64(&x9, p224Uint1(x8), uint64(0x0), 0xffffffffffffffff) + var x10 uint64 + var x11 uint64 + x10, x11 = bits.Add64(x1, uint64((p224Uint1(x9) & 0x1)), uint64(0x0)) + var x12 uint64 + var x13 uint64 + x12, x13 = bits.Add64(x3, (x9 & 0xffffffff00000000), uint64(p224Uint1(x11))) + var x14 uint64 + var x15 uint64 + x14, x15 = bits.Add64(x5, x9, uint64(p224Uint1(x13))) + var x16 uint64 + x16, _ = bits.Add64(x7, (x9 & 0xffffffff), uint64(p224Uint1(x15))) + out1[0] = x10 + out1[1] = x12 + out1[2] = x14 + out1[3] = x16 +} + +// p224SetOne returns the field element one in the Montgomery domain. +// +// Postconditions: +// eval (from_montgomery out1) mod m = 1 mod m +// 0 ≤ eval out1 < m +// +func p224SetOne(out1 *p224MontgomeryDomainFieldElement) { + out1[0] = 0xffffffff00000000 + out1[1] = 0xffffffffffffffff + out1[2] = uint64(0x0) + out1[3] = uint64(0x0) +} + +// p224FromMontgomery translates a field element out of the Montgomery domain. +// +// Preconditions: +// 0 ≤ eval arg1 < m +// Postconditions: +// eval out1 mod m = (eval arg1 * ((2^64)⁻¹ mod m)^4) mod m +// 0 ≤ eval out1 < m +// +func p224FromMontgomery(out1 *p224NonMontgomeryDomainFieldElement, arg1 *p224MontgomeryDomainFieldElement) { + x1 := arg1[0] + var x2 uint64 + _, x2 = bits.Mul64(x1, 0xffffffffffffffff) + var x4 uint64 + var x5 uint64 + x5, x4 = bits.Mul64(x2, 0xffffffff) + var x6 uint64 + var x7 uint64 + x7, x6 = bits.Mul64(x2, 0xffffffffffffffff) + var x8 uint64 + var x9 uint64 + x9, x8 = bits.Mul64(x2, 0xffffffff00000000) + var x10 uint64 + var x11 uint64 + x10, x11 = bits.Add64(x9, x6, uint64(0x0)) + var x12 uint64 + var x13 uint64 + x12, x13 = bits.Add64(x7, x4, uint64(p224Uint1(x11))) + var x15 uint64 + _, x15 = bits.Add64(x1, x2, uint64(0x0)) + var x16 uint64 + var x17 uint64 + x16, x17 = bits.Add64(uint64(0x0), x8, uint64(p224Uint1(x15))) + var x18 uint64 + var x19 uint64 + x18, x19 = bits.Add64(uint64(0x0), x10, uint64(p224Uint1(x17))) + var x20 uint64 + var x21 uint64 + x20, x21 = bits.Add64(uint64(0x0), x12, uint64(p224Uint1(x19))) + var x22 uint64 + var x23 uint64 + x22, x23 = bits.Add64(x16, arg1[1], uint64(0x0)) + var x24 uint64 + var x25 uint64 + x24, x25 = bits.Add64(x18, uint64(0x0), uint64(p224Uint1(x23))) + var x26 uint64 + var x27 uint64 + x26, x27 = bits.Add64(x20, uint64(0x0), uint64(p224Uint1(x25))) + var x28 uint64 + _, x28 = bits.Mul64(x22, 0xffffffffffffffff) + var x30 uint64 + var x31 uint64 + x31, x30 = bits.Mul64(x28, 0xffffffff) + var x32 uint64 + var x33 uint64 + x33, x32 = bits.Mul64(x28, 0xffffffffffffffff) + var x34 uint64 + var x35 uint64 + x35, x34 = bits.Mul64(x28, 0xffffffff00000000) + var x36 uint64 + var x37 uint64 + x36, x37 = bits.Add64(x35, x32, uint64(0x0)) + var x38 uint64 + var x39 uint64 + x38, x39 = bits.Add64(x33, x30, uint64(p224Uint1(x37))) + var x41 uint64 + _, x41 = bits.Add64(x22, x28, uint64(0x0)) + var x42 uint64 + var x43 uint64 + x42, x43 = bits.Add64(x24, x34, uint64(p224Uint1(x41))) + var x44 uint64 + var x45 uint64 + x44, x45 = bits.Add64(x26, x36, uint64(p224Uint1(x43))) + var x46 uint64 + var x47 uint64 + x46, x47 = bits.Add64((uint64(p224Uint1(x27)) + (uint64(p224Uint1(x21)) + (uint64(p224Uint1(x13)) + x5))), x38, uint64(p224Uint1(x45))) + var x48 uint64 + var x49 uint64 + x48, x49 = bits.Add64(x42, arg1[2], uint64(0x0)) + var x50 uint64 + var x51 uint64 + x50, x51 = bits.Add64(x44, uint64(0x0), uint64(p224Uint1(x49))) + var x52 uint64 + var x53 uint64 + x52, x53 = bits.Add64(x46, uint64(0x0), uint64(p224Uint1(x51))) + var x54 uint64 + _, x54 = bits.Mul64(x48, 0xffffffffffffffff) + var x56 uint64 + var x57 uint64 + x57, x56 = bits.Mul64(x54, 0xffffffff) + var x58 uint64 + var x59 uint64 + x59, x58 = bits.Mul64(x54, 0xffffffffffffffff) + var x60 uint64 + var x61 uint64 + x61, x60 = bits.Mul64(x54, 0xffffffff00000000) + var x62 uint64 + var x63 uint64 + x62, x63 = bits.Add64(x61, x58, uint64(0x0)) + var x64 uint64 + var x65 uint64 + x64, x65 = bits.Add64(x59, x56, uint64(p224Uint1(x63))) + var x67 uint64 + _, x67 = bits.Add64(x48, x54, uint64(0x0)) + var x68 uint64 + var x69 uint64 + x68, x69 = bits.Add64(x50, x60, uint64(p224Uint1(x67))) + var x70 uint64 + var x71 uint64 + x70, x71 = bits.Add64(x52, x62, uint64(p224Uint1(x69))) + var x72 uint64 + var x73 uint64 + x72, x73 = bits.Add64((uint64(p224Uint1(x53)) + (uint64(p224Uint1(x47)) + (uint64(p224Uint1(x39)) + x31))), x64, uint64(p224Uint1(x71))) + var x74 uint64 + var x75 uint64 + x74, x75 = bits.Add64(x68, arg1[3], uint64(0x0)) + var x76 uint64 + var x77 uint64 + x76, x77 = bits.Add64(x70, uint64(0x0), uint64(p224Uint1(x75))) + var x78 uint64 + var x79 uint64 + x78, x79 = bits.Add64(x72, uint64(0x0), uint64(p224Uint1(x77))) + var x80 uint64 + _, x80 = bits.Mul64(x74, 0xffffffffffffffff) + var x82 uint64 + var x83 uint64 + x83, x82 = bits.Mul64(x80, 0xffffffff) + var x84 uint64 + var x85 uint64 + x85, x84 = bits.Mul64(x80, 0xffffffffffffffff) + var x86 uint64 + var x87 uint64 + x87, x86 = bits.Mul64(x80, 0xffffffff00000000) + var x88 uint64 + var x89 uint64 + x88, x89 = bits.Add64(x87, x84, uint64(0x0)) + var x90 uint64 + var x91 uint64 + x90, x91 = bits.Add64(x85, x82, uint64(p224Uint1(x89))) + var x93 uint64 + _, x93 = bits.Add64(x74, x80, uint64(0x0)) + var x94 uint64 + var x95 uint64 + x94, x95 = bits.Add64(x76, x86, uint64(p224Uint1(x93))) + var x96 uint64 + var x97 uint64 + x96, x97 = bits.Add64(x78, x88, uint64(p224Uint1(x95))) + var x98 uint64 + var x99 uint64 + x98, x99 = bits.Add64((uint64(p224Uint1(x79)) + (uint64(p224Uint1(x73)) + (uint64(p224Uint1(x65)) + x57))), x90, uint64(p224Uint1(x97))) + x100 := (uint64(p224Uint1(x99)) + (uint64(p224Uint1(x91)) + x83)) + var x101 uint64 + var x102 uint64 + x101, x102 = bits.Sub64(x94, uint64(0x1), uint64(0x0)) + var x103 uint64 + var x104 uint64 + x103, x104 = bits.Sub64(x96, 0xffffffff00000000, uint64(p224Uint1(x102))) + var x105 uint64 + var x106 uint64 + x105, x106 = bits.Sub64(x98, 0xffffffffffffffff, uint64(p224Uint1(x104))) + var x107 uint64 + var x108 uint64 + x107, x108 = bits.Sub64(x100, 0xffffffff, uint64(p224Uint1(x106))) + var x110 uint64 + _, x110 = bits.Sub64(uint64(0x0), uint64(0x0), uint64(p224Uint1(x108))) + var x111 uint64 + p224CmovznzU64(&x111, p224Uint1(x110), x101, x94) + var x112 uint64 + p224CmovznzU64(&x112, p224Uint1(x110), x103, x96) + var x113 uint64 + p224CmovznzU64(&x113, p224Uint1(x110), x105, x98) + var x114 uint64 + p224CmovznzU64(&x114, p224Uint1(x110), x107, x100) + out1[0] = x111 + out1[1] = x112 + out1[2] = x113 + out1[3] = x114 +} + +// p224ToMontgomery translates a field element into the Montgomery domain. +// +// Preconditions: +// 0 ≤ eval arg1 < m +// Postconditions: +// eval (from_montgomery out1) mod m = eval arg1 mod m +// 0 ≤ eval out1 < m +// +func p224ToMontgomery(out1 *p224MontgomeryDomainFieldElement, arg1 *p224NonMontgomeryDomainFieldElement) { + x1 := arg1[1] + x2 := arg1[2] + x3 := arg1[3] + x4 := arg1[0] + var x5 uint64 + var x6 uint64 + x6, x5 = bits.Mul64(x4, 0xffffffff) + var x7 uint64 + var x8 uint64 + x8, x7 = bits.Mul64(x4, 0xfffffffe00000000) + var x9 uint64 + var x10 uint64 + x10, x9 = bits.Mul64(x4, 0xffffffff00000000) + var x11 uint64 + var x12 uint64 + x12, x11 = bits.Mul64(x4, 0xffffffff00000001) + var x13 uint64 + var x14 uint64 + x13, x14 = bits.Add64(x12, x9, uint64(0x0)) + var x15 uint64 + var x16 uint64 + x15, x16 = bits.Add64(x10, x7, uint64(p224Uint1(x14))) + var x17 uint64 + var x18 uint64 + x17, x18 = bits.Add64(x8, x5, uint64(p224Uint1(x16))) + var x19 uint64 + _, x19 = bits.Mul64(x11, 0xffffffffffffffff) + var x21 uint64 + var x22 uint64 + x22, x21 = bits.Mul64(x19, 0xffffffff) + var x23 uint64 + var x24 uint64 + x24, x23 = bits.Mul64(x19, 0xffffffffffffffff) + var x25 uint64 + var x26 uint64 + x26, x25 = bits.Mul64(x19, 0xffffffff00000000) + var x27 uint64 + var x28 uint64 + x27, x28 = bits.Add64(x26, x23, uint64(0x0)) + var x29 uint64 + var x30 uint64 + x29, x30 = bits.Add64(x24, x21, uint64(p224Uint1(x28))) + var x32 uint64 + _, x32 = bits.Add64(x11, x19, uint64(0x0)) + var x33 uint64 + var x34 uint64 + x33, x34 = bits.Add64(x13, x25, uint64(p224Uint1(x32))) + var x35 uint64 + var x36 uint64 + x35, x36 = bits.Add64(x15, x27, uint64(p224Uint1(x34))) + var x37 uint64 + var x38 uint64 + x37, x38 = bits.Add64(x17, x29, uint64(p224Uint1(x36))) + var x39 uint64 + var x40 uint64 + x40, x39 = bits.Mul64(x1, 0xffffffff) + var x41 uint64 + var x42 uint64 + x42, x41 = bits.Mul64(x1, 0xfffffffe00000000) + var x43 uint64 + var x44 uint64 + x44, x43 = bits.Mul64(x1, 0xffffffff00000000) + var x45 uint64 + var x46 uint64 + x46, x45 = bits.Mul64(x1, 0xffffffff00000001) + var x47 uint64 + var x48 uint64 + x47, x48 = bits.Add64(x46, x43, uint64(0x0)) + var x49 uint64 + var x50 uint64 + x49, x50 = bits.Add64(x44, x41, uint64(p224Uint1(x48))) + var x51 uint64 + var x52 uint64 + x51, x52 = bits.Add64(x42, x39, uint64(p224Uint1(x50))) + var x53 uint64 + var x54 uint64 + x53, x54 = bits.Add64(x33, x45, uint64(0x0)) + var x55 uint64 + var x56 uint64 + x55, x56 = bits.Add64(x35, x47, uint64(p224Uint1(x54))) + var x57 uint64 + var x58 uint64 + x57, x58 = bits.Add64(x37, x49, uint64(p224Uint1(x56))) + var x59 uint64 + var x60 uint64 + x59, x60 = bits.Add64(((uint64(p224Uint1(x38)) + (uint64(p224Uint1(x18)) + x6)) + (uint64(p224Uint1(x30)) + x22)), x51, uint64(p224Uint1(x58))) + var x61 uint64 + _, x61 = bits.Mul64(x53, 0xffffffffffffffff) + var x63 uint64 + var x64 uint64 + x64, x63 = bits.Mul64(x61, 0xffffffff) + var x65 uint64 + var x66 uint64 + x66, x65 = bits.Mul64(x61, 0xffffffffffffffff) + var x67 uint64 + var x68 uint64 + x68, x67 = bits.Mul64(x61, 0xffffffff00000000) + var x69 uint64 + var x70 uint64 + x69, x70 = bits.Add64(x68, x65, uint64(0x0)) + var x71 uint64 + var x72 uint64 + x71, x72 = bits.Add64(x66, x63, uint64(p224Uint1(x70))) + var x74 uint64 + _, x74 = bits.Add64(x53, x61, uint64(0x0)) + var x75 uint64 + var x76 uint64 + x75, x76 = bits.Add64(x55, x67, uint64(p224Uint1(x74))) + var x77 uint64 + var x78 uint64 + x77, x78 = bits.Add64(x57, x69, uint64(p224Uint1(x76))) + var x79 uint64 + var x80 uint64 + x79, x80 = bits.Add64(x59, x71, uint64(p224Uint1(x78))) + var x81 uint64 + var x82 uint64 + x82, x81 = bits.Mul64(x2, 0xffffffff) + var x83 uint64 + var x84 uint64 + x84, x83 = bits.Mul64(x2, 0xfffffffe00000000) + var x85 uint64 + var x86 uint64 + x86, x85 = bits.Mul64(x2, 0xffffffff00000000) + var x87 uint64 + var x88 uint64 + x88, x87 = bits.Mul64(x2, 0xffffffff00000001) + var x89 uint64 + var x90 uint64 + x89, x90 = bits.Add64(x88, x85, uint64(0x0)) + var x91 uint64 + var x92 uint64 + x91, x92 = bits.Add64(x86, x83, uint64(p224Uint1(x90))) + var x93 uint64 + var x94 uint64 + x93, x94 = bits.Add64(x84, x81, uint64(p224Uint1(x92))) + var x95 uint64 + var x96 uint64 + x95, x96 = bits.Add64(x75, x87, uint64(0x0)) + var x97 uint64 + var x98 uint64 + x97, x98 = bits.Add64(x77, x89, uint64(p224Uint1(x96))) + var x99 uint64 + var x100 uint64 + x99, x100 = bits.Add64(x79, x91, uint64(p224Uint1(x98))) + var x101 uint64 + var x102 uint64 + x101, x102 = bits.Add64(((uint64(p224Uint1(x80)) + (uint64(p224Uint1(x60)) + (uint64(p224Uint1(x52)) + x40))) + (uint64(p224Uint1(x72)) + x64)), x93, uint64(p224Uint1(x100))) + var x103 uint64 + _, x103 = bits.Mul64(x95, 0xffffffffffffffff) + var x105 uint64 + var x106 uint64 + x106, x105 = bits.Mul64(x103, 0xffffffff) + var x107 uint64 + var x108 uint64 + x108, x107 = bits.Mul64(x103, 0xffffffffffffffff) + var x109 uint64 + var x110 uint64 + x110, x109 = bits.Mul64(x103, 0xffffffff00000000) + var x111 uint64 + var x112 uint64 + x111, x112 = bits.Add64(x110, x107, uint64(0x0)) + var x113 uint64 + var x114 uint64 + x113, x114 = bits.Add64(x108, x105, uint64(p224Uint1(x112))) + var x116 uint64 + _, x116 = bits.Add64(x95, x103, uint64(0x0)) + var x117 uint64 + var x118 uint64 + x117, x118 = bits.Add64(x97, x109, uint64(p224Uint1(x116))) + var x119 uint64 + var x120 uint64 + x119, x120 = bits.Add64(x99, x111, uint64(p224Uint1(x118))) + var x121 uint64 + var x122 uint64 + x121, x122 = bits.Add64(x101, x113, uint64(p224Uint1(x120))) + var x123 uint64 + var x124 uint64 + x124, x123 = bits.Mul64(x3, 0xffffffff) + var x125 uint64 + var x126 uint64 + x126, x125 = bits.Mul64(x3, 0xfffffffe00000000) + var x127 uint64 + var x128 uint64 + x128, x127 = bits.Mul64(x3, 0xffffffff00000000) + var x129 uint64 + var x130 uint64 + x130, x129 = bits.Mul64(x3, 0xffffffff00000001) + var x131 uint64 + var x132 uint64 + x131, x132 = bits.Add64(x130, x127, uint64(0x0)) + var x133 uint64 + var x134 uint64 + x133, x134 = bits.Add64(x128, x125, uint64(p224Uint1(x132))) + var x135 uint64 + var x136 uint64 + x135, x136 = bits.Add64(x126, x123, uint64(p224Uint1(x134))) + var x137 uint64 + var x138 uint64 + x137, x138 = bits.Add64(x117, x129, uint64(0x0)) + var x139 uint64 + var x140 uint64 + x139, x140 = bits.Add64(x119, x131, uint64(p224Uint1(x138))) + var x141 uint64 + var x142 uint64 + x141, x142 = bits.Add64(x121, x133, uint64(p224Uint1(x140))) + var x143 uint64 + var x144 uint64 + x143, x144 = bits.Add64(((uint64(p224Uint1(x122)) + (uint64(p224Uint1(x102)) + (uint64(p224Uint1(x94)) + x82))) + (uint64(p224Uint1(x114)) + x106)), x135, uint64(p224Uint1(x142))) + var x145 uint64 + _, x145 = bits.Mul64(x137, 0xffffffffffffffff) + var x147 uint64 + var x148 uint64 + x148, x147 = bits.Mul64(x145, 0xffffffff) + var x149 uint64 + var x150 uint64 + x150, x149 = bits.Mul64(x145, 0xffffffffffffffff) + var x151 uint64 + var x152 uint64 + x152, x151 = bits.Mul64(x145, 0xffffffff00000000) + var x153 uint64 + var x154 uint64 + x153, x154 = bits.Add64(x152, x149, uint64(0x0)) + var x155 uint64 + var x156 uint64 + x155, x156 = bits.Add64(x150, x147, uint64(p224Uint1(x154))) + var x158 uint64 + _, x158 = bits.Add64(x137, x145, uint64(0x0)) + var x159 uint64 + var x160 uint64 + x159, x160 = bits.Add64(x139, x151, uint64(p224Uint1(x158))) + var x161 uint64 + var x162 uint64 + x161, x162 = bits.Add64(x141, x153, uint64(p224Uint1(x160))) + var x163 uint64 + var x164 uint64 + x163, x164 = bits.Add64(x143, x155, uint64(p224Uint1(x162))) + x165 := ((uint64(p224Uint1(x164)) + (uint64(p224Uint1(x144)) + (uint64(p224Uint1(x136)) + x124))) + (uint64(p224Uint1(x156)) + x148)) + var x166 uint64 + var x167 uint64 + x166, x167 = bits.Sub64(x159, uint64(0x1), uint64(0x0)) + var x168 uint64 + var x169 uint64 + x168, x169 = bits.Sub64(x161, 0xffffffff00000000, uint64(p224Uint1(x167))) + var x170 uint64 + var x171 uint64 + x170, x171 = bits.Sub64(x163, 0xffffffffffffffff, uint64(p224Uint1(x169))) + var x172 uint64 + var x173 uint64 + x172, x173 = bits.Sub64(x165, 0xffffffff, uint64(p224Uint1(x171))) + var x175 uint64 + _, x175 = bits.Sub64(uint64(0x0), uint64(0x0), uint64(p224Uint1(x173))) + var x176 uint64 + p224CmovznzU64(&x176, p224Uint1(x175), x166, x159) + var x177 uint64 + p224CmovznzU64(&x177, p224Uint1(x175), x168, x161) + var x178 uint64 + p224CmovznzU64(&x178, p224Uint1(x175), x170, x163) + var x179 uint64 + p224CmovznzU64(&x179, p224Uint1(x175), x172, x165) + out1[0] = x176 + out1[1] = x177 + out1[2] = x178 + out1[3] = x179 +} + +// p224Selectznz is a multi-limb conditional select. +// +// Postconditions: +// eval out1 = (if arg1 = 0 then eval arg2 else eval arg3) +// +// Input Bounds: +// arg1: [0x0 ~> 0x1] +// arg2: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]] +// arg3: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]] +// Output Bounds: +// out1: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]] +func p224Selectznz(out1 *[4]uint64, arg1 p224Uint1, arg2 *[4]uint64, arg3 *[4]uint64) { + var x1 uint64 + p224CmovznzU64(&x1, arg1, arg2[0], arg3[0]) + var x2 uint64 + p224CmovznzU64(&x2, arg1, arg2[1], arg3[1]) + var x3 uint64 + p224CmovznzU64(&x3, arg1, arg2[2], arg3[2]) + var x4 uint64 + p224CmovznzU64(&x4, arg1, arg2[3], arg3[3]) + out1[0] = x1 + out1[1] = x2 + out1[2] = x3 + out1[3] = x4 +} + +// p224ToBytes serializes a field element NOT in the Montgomery domain to bytes in little-endian order. +// +// Preconditions: +// 0 ≤ eval arg1 < m +// Postconditions: +// out1 = map (λ x, ⌊((eval arg1 mod m) mod 2^(8 * (x + 1))) / 2^(8 * x)⌋) [0..27] +// +// Input Bounds: +// arg1: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffff]] +// Output Bounds: +// out1: [[0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff]] +func p224ToBytes(out1 *[28]uint8, arg1 *[4]uint64) { + x1 := arg1[3] + x2 := arg1[2] + x3 := arg1[1] + x4 := arg1[0] + x5 := (uint8(x4) & 0xff) + x6 := (x4 >> 8) + x7 := (uint8(x6) & 0xff) + x8 := (x6 >> 8) + x9 := (uint8(x8) & 0xff) + x10 := (x8 >> 8) + x11 := (uint8(x10) & 0xff) + x12 := (x10 >> 8) + x13 := (uint8(x12) & 0xff) + x14 := (x12 >> 8) + x15 := (uint8(x14) & 0xff) + x16 := (x14 >> 8) + x17 := (uint8(x16) & 0xff) + x18 := uint8((x16 >> 8)) + x19 := (uint8(x3) & 0xff) + x20 := (x3 >> 8) + x21 := (uint8(x20) & 0xff) + x22 := (x20 >> 8) + x23 := (uint8(x22) & 0xff) + x24 := (x22 >> 8) + x25 := (uint8(x24) & 0xff) + x26 := (x24 >> 8) + x27 := (uint8(x26) & 0xff) + x28 := (x26 >> 8) + x29 := (uint8(x28) & 0xff) + x30 := (x28 >> 8) + x31 := (uint8(x30) & 0xff) + x32 := uint8((x30 >> 8)) + x33 := (uint8(x2) & 0xff) + x34 := (x2 >> 8) + x35 := (uint8(x34) & 0xff) + x36 := (x34 >> 8) + x37 := (uint8(x36) & 0xff) + x38 := (x36 >> 8) + x39 := (uint8(x38) & 0xff) + x40 := (x38 >> 8) + x41 := (uint8(x40) & 0xff) + x42 := (x40 >> 8) + x43 := (uint8(x42) & 0xff) + x44 := (x42 >> 8) + x45 := (uint8(x44) & 0xff) + x46 := uint8((x44 >> 8)) + x47 := (uint8(x1) & 0xff) + x48 := (x1 >> 8) + x49 := (uint8(x48) & 0xff) + x50 := (x48 >> 8) + x51 := (uint8(x50) & 0xff) + x52 := uint8((x50 >> 8)) + out1[0] = x5 + out1[1] = x7 + out1[2] = x9 + out1[3] = x11 + out1[4] = x13 + out1[5] = x15 + out1[6] = x17 + out1[7] = x18 + out1[8] = x19 + out1[9] = x21 + out1[10] = x23 + out1[11] = x25 + out1[12] = x27 + out1[13] = x29 + out1[14] = x31 + out1[15] = x32 + out1[16] = x33 + out1[17] = x35 + out1[18] = x37 + out1[19] = x39 + out1[20] = x41 + out1[21] = x43 + out1[22] = x45 + out1[23] = x46 + out1[24] = x47 + out1[25] = x49 + out1[26] = x51 + out1[27] = x52 +} + +// p224FromBytes deserializes a field element NOT in the Montgomery domain from bytes in little-endian order. +// +// Preconditions: +// 0 ≤ bytes_eval arg1 < m +// Postconditions: +// eval out1 mod m = bytes_eval arg1 mod m +// 0 ≤ eval out1 < m +// +// Input Bounds: +// arg1: [[0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff]] +// Output Bounds: +// out1: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffff]] +func p224FromBytes(out1 *[4]uint64, arg1 *[28]uint8) { + x1 := (uint64(arg1[27]) << 24) + x2 := (uint64(arg1[26]) << 16) + x3 := (uint64(arg1[25]) << 8) + x4 := arg1[24] + x5 := (uint64(arg1[23]) << 56) + x6 := (uint64(arg1[22]) << 48) + x7 := (uint64(arg1[21]) << 40) + x8 := (uint64(arg1[20]) << 32) + x9 := (uint64(arg1[19]) << 24) + x10 := (uint64(arg1[18]) << 16) + x11 := (uint64(arg1[17]) << 8) + x12 := arg1[16] + x13 := (uint64(arg1[15]) << 56) + x14 := (uint64(arg1[14]) << 48) + x15 := (uint64(arg1[13]) << 40) + x16 := (uint64(arg1[12]) << 32) + x17 := (uint64(arg1[11]) << 24) + x18 := (uint64(arg1[10]) << 16) + x19 := (uint64(arg1[9]) << 8) + x20 := arg1[8] + x21 := (uint64(arg1[7]) << 56) + x22 := (uint64(arg1[6]) << 48) + x23 := (uint64(arg1[5]) << 40) + x24 := (uint64(arg1[4]) << 32) + x25 := (uint64(arg1[3]) << 24) + x26 := (uint64(arg1[2]) << 16) + x27 := (uint64(arg1[1]) << 8) + x28 := arg1[0] + x29 := (x27 + uint64(x28)) + x30 := (x26 + x29) + x31 := (x25 + x30) + x32 := (x24 + x31) + x33 := (x23 + x32) + x34 := (x22 + x33) + x35 := (x21 + x34) + x36 := (x19 + uint64(x20)) + x37 := (x18 + x36) + x38 := (x17 + x37) + x39 := (x16 + x38) + x40 := (x15 + x39) + x41 := (x14 + x40) + x42 := (x13 + x41) + x43 := (x11 + uint64(x12)) + x44 := (x10 + x43) + x45 := (x9 + x44) + x46 := (x8 + x45) + x47 := (x7 + x46) + x48 := (x6 + x47) + x49 := (x5 + x48) + x50 := (x3 + uint64(x4)) + x51 := (x2 + x50) + x52 := (x1 + x51) + out1[0] = x35 + out1[1] = x42 + out1[2] = x49 + out1[3] = x52 +} diff --git a/libgo/go/crypto/elliptic/internal/fiat/p224_invert.go b/libgo/go/crypto/elliptic/internal/fiat/p224_invert.go new file mode 100644 index 0000000..4163ed0 --- /dev/null +++ b/libgo/go/crypto/elliptic/internal/fiat/p224_invert.go @@ -0,0 +1,87 @@ +// Copyright 2021 The Go Authors. All rights reserved. +// Use of this source code is governed by a BSD-style +// license that can be found in the LICENSE file. + +// Code generated by addchain. DO NOT EDIT. + +package fiat + +// Invert sets e = 1/x, and returns e. +// +// If x == 0, Invert returns e = 0. +func (e *P224Element) Invert(x *P224Element) *P224Element { + // Inversion is implemented as exponentiation with exponent p − 2. + // The sequence of 11 multiplications and 223 squarings is derived from the + // following addition chain generated with github.com/mmcloughlin/addchain v0.3.0. + // + // _10 = 2*1 + // _11 = 1 + _10 + // _110 = 2*_11 + // _111 = 1 + _110 + // _111000 = _111 << 3 + // _111111 = _111 + _111000 + // x12 = _111111 << 6 + _111111 + // x14 = x12 << 2 + _11 + // x17 = x14 << 3 + _111 + // x31 = x17 << 14 + x14 + // x48 = x31 << 17 + x17 + // x96 = x48 << 48 + x48 + // x127 = x96 << 31 + x31 + // return x127 << 97 + x96 + // + + var z = new(P224Element).Set(e) + var t0 = new(P224Element) + var t1 = new(P224Element) + var t2 = new(P224Element) + + z.Square(x) + t0.Mul(x, z) + z.Square(t0) + z.Mul(x, z) + t1.Square(z) + for s := 1; s < 3; s++ { + t1.Square(t1) + } + t1.Mul(z, t1) + t2.Square(t1) + for s := 1; s < 6; s++ { + t2.Square(t2) + } + t1.Mul(t1, t2) + for s := 0; s < 2; s++ { + t1.Square(t1) + } + t0.Mul(t0, t1) + t1.Square(t0) + for s := 1; s < 3; s++ { + t1.Square(t1) + } + z.Mul(z, t1) + t1.Square(z) + for s := 1; s < 14; s++ { + t1.Square(t1) + } + t0.Mul(t0, t1) + t1.Square(t0) + for s := 1; s < 17; s++ { + t1.Square(t1) + } + z.Mul(z, t1) + t1.Square(z) + for s := 1; s < 48; s++ { + t1.Square(t1) + } + z.Mul(z, t1) + t1.Square(z) + for s := 1; s < 31; s++ { + t1.Square(t1) + } + t0.Mul(t0, t1) + for s := 0; s < 97; s++ { + t0.Square(t0) + } + z.Mul(z, t0) + + return e.Set(z) +} diff --git a/libgo/go/crypto/elliptic/internal/fiat/p384.go b/libgo/go/crypto/elliptic/internal/fiat/p384.go new file mode 100644 index 0000000..5474d77 --- /dev/null +++ b/libgo/go/crypto/elliptic/internal/fiat/p384.go @@ -0,0 +1,135 @@ +// Copyright 2021 The Go Authors. All rights reserved. +// Use of this source code is governed by a BSD-style +// license that can be found in the LICENSE file. + +// Code generated by generate.go. DO NOT EDIT. + +package fiat + +import ( + "crypto/subtle" + "errors" +) + +// P384Element is an integer modulo 2^384 - 2^128 - 2^96 + 2^32 - 1. +// +// The zero value is a valid zero element. +type P384Element struct { + // Values are represented internally always in the Montgomery domain, and + // converted in Bytes and SetBytes. + x p384MontgomeryDomainFieldElement +} + +const p384ElementLen = 48 + +type p384UntypedFieldElement = [6]uint64 + +// One sets e = 1, and returns e. +func (e *P384Element) One() *P384Element { + p384SetOne(&e.x) + return e +} + +// Equal returns 1 if e == t, and zero otherwise. +func (e *P384Element) Equal(t *P384Element) int { + eBytes := e.Bytes() + tBytes := t.Bytes() + return subtle.ConstantTimeCompare(eBytes, tBytes) +} + +var p384ZeroEncoding = new(P384Element).Bytes() + +// IsZero returns 1 if e == 0, and zero otherwise. +func (e *P384Element) IsZero() int { + eBytes := e.Bytes() + return subtle.ConstantTimeCompare(eBytes, p384ZeroEncoding) +} + +// Set sets e = t, and returns e. +func (e *P384Element) Set(t *P384Element) *P384Element { + e.x = t.x + return e +} + +// Bytes returns the 48-byte big-endian encoding of e. +func (e *P384Element) Bytes() []byte { + // This function is outlined to make the allocations inline in the caller + // rather than happen on the heap. + var out [p384ElementLen]byte + return e.bytes(&out) +} + +func (e *P384Element) bytes(out *[p384ElementLen]byte) []byte { + var tmp p384NonMontgomeryDomainFieldElement + p384FromMontgomery(&tmp, &e.x) + p384ToBytes(out, (*p384UntypedFieldElement)(&tmp)) + p384InvertEndianness(out[:]) + return out[:] +} + +// p384MinusOneEncoding is the encoding of -1 mod p, so p - 1, the +// highest canonical encoding. It is used by SetBytes to check for non-canonical +// encodings such as p + k, 2p + k, etc. +var p384MinusOneEncoding = new(P384Element).Sub( + new(P384Element), new(P384Element).One()).Bytes() + +// SetBytes sets e = v, where v is a big-endian 48-byte encoding, and returns e. +// If v is not 48 bytes or it encodes a value higher than 2^384 - 2^128 - 2^96 + 2^32 - 1, +// SetBytes returns nil and an error, and e is unchanged. +func (e *P384Element) SetBytes(v []byte) (*P384Element, error) { + if len(v) != p384ElementLen { + return nil, errors.New("invalid P384Element encoding") + } + for i := range v { + if v[i] < p384MinusOneEncoding[i] { + break + } + if v[i] > p384MinusOneEncoding[i] { + return nil, errors.New("invalid P384Element encoding") + } + } + var in [p384ElementLen]byte + copy(in[:], v) + p384InvertEndianness(in[:]) + var tmp p384NonMontgomeryDomainFieldElement + p384FromBytes((*p384UntypedFieldElement)(&tmp), &in) + p384ToMontgomery(&e.x, &tmp) + return e, nil +} + +// Add sets e = t1 + t2, and returns e. +func (e *P384Element) Add(t1, t2 *P384Element) *P384Element { + p384Add(&e.x, &t1.x, &t2.x) + return e +} + +// Sub sets e = t1 - t2, and returns e. +func (e *P384Element) Sub(t1, t2 *P384Element) *P384Element { + p384Sub(&e.x, &t1.x, &t2.x) + return e +} + +// Mul sets e = t1 * t2, and returns e. +func (e *P384Element) Mul(t1, t2 *P384Element) *P384Element { + p384Mul(&e.x, &t1.x, &t2.x) + return e +} + +// Square sets e = t * t, and returns e. +func (e *P384Element) Square(t *P384Element) *P384Element { + p384Square(&e.x, &t.x) + return e +} + +// Select sets v to a if cond == 1, and to b if cond == 0. +func (v *P384Element) Select(a, b *P384Element, cond int) *P384Element { + p384Selectznz((*p384UntypedFieldElement)(&v.x), p384Uint1(cond), + (*p384UntypedFieldElement)(&b.x), (*p384UntypedFieldElement)(&a.x)) + return v +} + +func p384InvertEndianness(v []byte) { + for i := 0; i < len(v)/2; i++ { + v[i], v[len(v)-1-i] = v[len(v)-1-i], v[i] + } +} diff --git a/libgo/go/crypto/elliptic/internal/fiat/p384_fiat64.go b/libgo/go/crypto/elliptic/internal/fiat/p384_fiat64.go new file mode 100644 index 0000000..493bed4 --- /dev/null +++ b/libgo/go/crypto/elliptic/internal/fiat/p384_fiat64.go @@ -0,0 +1,3004 @@ +// Code generated by Fiat Cryptography. DO NOT EDIT. +// +// Autogenerated: word_by_word_montgomery --lang Go --no-wide-int --cmovznz-by-mul --relax-primitive-carry-to-bitwidth 32,64 --internal-static --public-function-case camelCase --public-type-case camelCase --private-function-case camelCase --private-type-case camelCase --doc-text-before-function-name '' --doc-newline-before-package-declaration --doc-prepend-header 'Code generated by Fiat Cryptography. DO NOT EDIT.' --package-name fiat --no-prefix-fiat p384 64 '2^384 - 2^128 - 2^96 + 2^32 - 1' mul square add sub one from_montgomery to_montgomery selectznz to_bytes from_bytes +// +// curve description: p384 +// +// machine_wordsize = 64 (from "64") +// +// requested operations: mul, square, add, sub, one, from_montgomery, to_montgomery, selectznz, to_bytes, from_bytes +// +// m = 0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffeffffffff0000000000000000ffffffff (from "2^384 - 2^128 - 2^96 + 2^32 - 1") +// +// +// +// NOTE: In addition to the bounds specified above each function, all +// +// functions synthesized for this Montgomery arithmetic require the +// +// input to be strictly less than the prime modulus (m), and also +// +// require the input to be in the unique saturated representation. +// +// All functions also ensure that these two properties are true of +// +// return values. +// +// +// +// Computed values: +// +// eval z = z[0] + (z[1] << 64) + (z[2] << 128) + (z[3] << 192) + (z[4] << 256) + (z[5] << 0x140) +// +// bytes_eval z = z[0] + (z[1] << 8) + (z[2] << 16) + (z[3] << 24) + (z[4] << 32) + (z[5] << 40) + (z[6] << 48) + (z[7] << 56) + (z[8] << 64) + (z[9] << 72) + (z[10] << 80) + (z[11] << 88) + (z[12] << 96) + (z[13] << 104) + (z[14] << 112) + (z[15] << 120) + (z[16] << 128) + (z[17] << 136) + (z[18] << 144) + (z[19] << 152) + (z[20] << 160) + (z[21] << 168) + (z[22] << 176) + (z[23] << 184) + (z[24] << 192) + (z[25] << 200) + (z[26] << 208) + (z[27] << 216) + (z[28] << 224) + (z[29] << 232) + (z[30] << 240) + (z[31] << 248) + (z[32] << 256) + (z[33] << 0x108) + (z[34] << 0x110) + (z[35] << 0x118) + (z[36] << 0x120) + (z[37] << 0x128) + (z[38] << 0x130) + (z[39] << 0x138) + (z[40] << 0x140) + (z[41] << 0x148) + (z[42] << 0x150) + (z[43] << 0x158) + (z[44] << 0x160) + (z[45] << 0x168) + (z[46] << 0x170) + (z[47] << 0x178) +// +// twos_complement_eval z = let x1 := z[0] + (z[1] << 64) + (z[2] << 128) + (z[3] << 192) + (z[4] << 256) + (z[5] << 0x140) in +// +// if x1 & (2^384-1) < 2^383 then x1 & (2^384-1) else (x1 & (2^384-1)) - 2^384 + +package fiat + +import "math/bits" + +type p384Uint1 uint64 // We use uint64 instead of a more narrow type for performance reasons; see https://github.com/mit-plv/fiat-crypto/pull/1006#issuecomment-892625927 +type p384Int1 int64 // We use uint64 instead of a more narrow type for performance reasons; see https://github.com/mit-plv/fiat-crypto/pull/1006#issuecomment-892625927 + +// The type p384MontgomeryDomainFieldElement is a field element in the Montgomery domain. +// +// Bounds: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]] +type p384MontgomeryDomainFieldElement [6]uint64 + +// The type p384NonMontgomeryDomainFieldElement is a field element NOT in the Montgomery domain. +// +// Bounds: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]] +type p384NonMontgomeryDomainFieldElement [6]uint64 + +// p384CmovznzU64 is a single-word conditional move. +// +// Postconditions: +// out1 = (if arg1 = 0 then arg2 else arg3) +// +// Input Bounds: +// arg1: [0x0 ~> 0x1] +// arg2: [0x0 ~> 0xffffffffffffffff] +// arg3: [0x0 ~> 0xffffffffffffffff] +// Output Bounds: +// out1: [0x0 ~> 0xffffffffffffffff] +func p384CmovznzU64(out1 *uint64, arg1 p384Uint1, arg2 uint64, arg3 uint64) { + x1 := (uint64(arg1) * 0xffffffffffffffff) + x2 := ((x1 & arg3) | ((^x1) & arg2)) + *out1 = x2 +} + +// p384Mul multiplies two field elements in the Montgomery domain. +// +// Preconditions: +// 0 ≤ eval arg1 < m +// 0 ≤ eval arg2 < m +// Postconditions: +// eval (from_montgomery out1) mod m = (eval (from_montgomery arg1) * eval (from_montgomery arg2)) mod m +// 0 ≤ eval out1 < m +// +func p384Mul(out1 *p384MontgomeryDomainFieldElement, arg1 *p384MontgomeryDomainFieldElement, arg2 *p384MontgomeryDomainFieldElement) { + x1 := arg1[1] + x2 := arg1[2] + x3 := arg1[3] + x4 := arg1[4] + x5 := arg1[5] + x6 := arg1[0] + var x7 uint64 + var x8 uint64 + x8, x7 = bits.Mul64(x6, arg2[5]) + var x9 uint64 + var x10 uint64 + x10, x9 = bits.Mul64(x6, arg2[4]) + var x11 uint64 + var x12 uint64 + x12, x11 = bits.Mul64(x6, arg2[3]) + var x13 uint64 + var x14 uint64 + x14, x13 = bits.Mul64(x6, arg2[2]) + var x15 uint64 + var x16 uint64 + x16, x15 = bits.Mul64(x6, arg2[1]) + var x17 uint64 + var x18 uint64 + x18, x17 = bits.Mul64(x6, arg2[0]) + var x19 uint64 + var x20 uint64 + x19, x20 = bits.Add64(x18, x15, uint64(0x0)) + var x21 uint64 + var x22 uint64 + x21, x22 = bits.Add64(x16, x13, uint64(p384Uint1(x20))) + var x23 uint64 + var x24 uint64 + x23, x24 = bits.Add64(x14, x11, uint64(p384Uint1(x22))) + var x25 uint64 + var x26 uint64 + x25, x26 = bits.Add64(x12, x9, uint64(p384Uint1(x24))) + var x27 uint64 + var x28 uint64 + x27, x28 = bits.Add64(x10, x7, uint64(p384Uint1(x26))) + x29 := (uint64(p384Uint1(x28)) + x8) + var x30 uint64 + _, x30 = bits.Mul64(x17, 0x100000001) + var x32 uint64 + var x33 uint64 + x33, x32 = bits.Mul64(x30, 0xffffffffffffffff) + var x34 uint64 + var x35 uint64 + x35, x34 = bits.Mul64(x30, 0xffffffffffffffff) + var x36 uint64 + var x37 uint64 + x37, x36 = bits.Mul64(x30, 0xffffffffffffffff) + var x38 uint64 + var x39 uint64 + x39, x38 = bits.Mul64(x30, 0xfffffffffffffffe) + var x40 uint64 + var x41 uint64 + x41, x40 = bits.Mul64(x30, 0xffffffff00000000) + var x42 uint64 + var x43 uint64 + x43, x42 = bits.Mul64(x30, 0xffffffff) + var x44 uint64 + var x45 uint64 + x44, x45 = bits.Add64(x43, x40, uint64(0x0)) + var x46 uint64 + var x47 uint64 + x46, x47 = bits.Add64(x41, x38, uint64(p384Uint1(x45))) + var x48 uint64 + var x49 uint64 + x48, x49 = bits.Add64(x39, x36, uint64(p384Uint1(x47))) + var x50 uint64 + var x51 uint64 + x50, x51 = bits.Add64(x37, x34, uint64(p384Uint1(x49))) + var x52 uint64 + var x53 uint64 + x52, x53 = bits.Add64(x35, x32, uint64(p384Uint1(x51))) + x54 := (uint64(p384Uint1(x53)) + x33) + var x56 uint64 + _, x56 = bits.Add64(x17, x42, uint64(0x0)) + var x57 uint64 + var x58 uint64 + x57, x58 = bits.Add64(x19, x44, uint64(p384Uint1(x56))) + var x59 uint64 + var x60 uint64 + x59, x60 = bits.Add64(x21, x46, uint64(p384Uint1(x58))) + var x61 uint64 + var x62 uint64 + x61, x62 = bits.Add64(x23, x48, uint64(p384Uint1(x60))) + var x63 uint64 + var x64 uint64 + x63, x64 = bits.Add64(x25, x50, uint64(p384Uint1(x62))) + var x65 uint64 + var x66 uint64 + x65, x66 = bits.Add64(x27, x52, uint64(p384Uint1(x64))) + var x67 uint64 + var x68 uint64 + x67, x68 = bits.Add64(x29, x54, uint64(p384Uint1(x66))) + var x69 uint64 + var x70 uint64 + x70, x69 = bits.Mul64(x1, arg2[5]) + var x71 uint64 + var x72 uint64 + x72, x71 = bits.Mul64(x1, arg2[4]) + var x73 uint64 + var x74 uint64 + x74, x73 = bits.Mul64(x1, arg2[3]) + var x75 uint64 + var x76 uint64 + x76, x75 = bits.Mul64(x1, arg2[2]) + var x77 uint64 + var x78 uint64 + x78, x77 = bits.Mul64(x1, arg2[1]) + var x79 uint64 + var x80 uint64 + x80, x79 = bits.Mul64(x1, arg2[0]) + var x81 uint64 + var x82 uint64 + x81, x82 = bits.Add64(x80, x77, uint64(0x0)) + var x83 uint64 + var x84 uint64 + x83, x84 = bits.Add64(x78, x75, uint64(p384Uint1(x82))) + var x85 uint64 + var x86 uint64 + x85, x86 = bits.Add64(x76, x73, uint64(p384Uint1(x84))) + var x87 uint64 + var x88 uint64 + x87, x88 = bits.Add64(x74, x71, uint64(p384Uint1(x86))) + var x89 uint64 + var x90 uint64 + x89, x90 = bits.Add64(x72, x69, uint64(p384Uint1(x88))) + x91 := (uint64(p384Uint1(x90)) + x70) + var x92 uint64 + var x93 uint64 + x92, x93 = bits.Add64(x57, x79, uint64(0x0)) + var x94 uint64 + var x95 uint64 + x94, x95 = bits.Add64(x59, x81, uint64(p384Uint1(x93))) + var x96 uint64 + var x97 uint64 + x96, x97 = bits.Add64(x61, x83, uint64(p384Uint1(x95))) + var x98 uint64 + var x99 uint64 + x98, x99 = bits.Add64(x63, x85, uint64(p384Uint1(x97))) + var x100 uint64 + var x101 uint64 + x100, x101 = bits.Add64(x65, x87, uint64(p384Uint1(x99))) + var x102 uint64 + var x103 uint64 + x102, x103 = bits.Add64(x67, x89, uint64(p384Uint1(x101))) + var x104 uint64 + var x105 uint64 + x104, x105 = bits.Add64(uint64(p384Uint1(x68)), x91, uint64(p384Uint1(x103))) + var x106 uint64 + _, x106 = bits.Mul64(x92, 0x100000001) + var x108 uint64 + var x109 uint64 + x109, x108 = bits.Mul64(x106, 0xffffffffffffffff) + var x110 uint64 + var x111 uint64 + x111, x110 = bits.Mul64(x106, 0xffffffffffffffff) + var x112 uint64 + var x113 uint64 + x113, x112 = bits.Mul64(x106, 0xffffffffffffffff) + var x114 uint64 + var x115 uint64 + x115, x114 = bits.Mul64(x106, 0xfffffffffffffffe) + var x116 uint64 + var x117 uint64 + x117, x116 = bits.Mul64(x106, 0xffffffff00000000) + var x118 uint64 + var x119 uint64 + x119, x118 = bits.Mul64(x106, 0xffffffff) + var x120 uint64 + var x121 uint64 + x120, x121 = bits.Add64(x119, x116, uint64(0x0)) + var x122 uint64 + var x123 uint64 + x122, x123 = bits.Add64(x117, x114, uint64(p384Uint1(x121))) + var x124 uint64 + var x125 uint64 + x124, x125 = bits.Add64(x115, x112, uint64(p384Uint1(x123))) + var x126 uint64 + var x127 uint64 + x126, x127 = bits.Add64(x113, x110, uint64(p384Uint1(x125))) + var x128 uint64 + var x129 uint64 + x128, x129 = bits.Add64(x111, x108, uint64(p384Uint1(x127))) + x130 := (uint64(p384Uint1(x129)) + x109) + var x132 uint64 + _, x132 = bits.Add64(x92, x118, uint64(0x0)) + var x133 uint64 + var x134 uint64 + x133, x134 = bits.Add64(x94, x120, uint64(p384Uint1(x132))) + var x135 uint64 + var x136 uint64 + x135, x136 = bits.Add64(x96, x122, uint64(p384Uint1(x134))) + var x137 uint64 + var x138 uint64 + x137, x138 = bits.Add64(x98, x124, uint64(p384Uint1(x136))) + var x139 uint64 + var x140 uint64 + x139, x140 = bits.Add64(x100, x126, uint64(p384Uint1(x138))) + var x141 uint64 + var x142 uint64 + x141, x142 = bits.Add64(x102, x128, uint64(p384Uint1(x140))) + var x143 uint64 + var x144 uint64 + x143, x144 = bits.Add64(x104, x130, uint64(p384Uint1(x142))) + x145 := (uint64(p384Uint1(x144)) + uint64(p384Uint1(x105))) + var x146 uint64 + var x147 uint64 + x147, x146 = bits.Mul64(x2, arg2[5]) + var x148 uint64 + var x149 uint64 + x149, x148 = bits.Mul64(x2, arg2[4]) + var x150 uint64 + var x151 uint64 + x151, x150 = bits.Mul64(x2, arg2[3]) + var x152 uint64 + var x153 uint64 + x153, x152 = bits.Mul64(x2, arg2[2]) + var x154 uint64 + var x155 uint64 + x155, x154 = bits.Mul64(x2, arg2[1]) + var x156 uint64 + var x157 uint64 + x157, x156 = bits.Mul64(x2, arg2[0]) + var x158 uint64 + var x159 uint64 + x158, x159 = bits.Add64(x157, x154, uint64(0x0)) + var x160 uint64 + var x161 uint64 + x160, x161 = bits.Add64(x155, x152, uint64(p384Uint1(x159))) + var x162 uint64 + var x163 uint64 + x162, x163 = bits.Add64(x153, x150, uint64(p384Uint1(x161))) + var x164 uint64 + var x165 uint64 + x164, x165 = bits.Add64(x151, x148, uint64(p384Uint1(x163))) + var x166 uint64 + var x167 uint64 + x166, x167 = bits.Add64(x149, x146, uint64(p384Uint1(x165))) + x168 := (uint64(p384Uint1(x167)) + x147) + var x169 uint64 + var x170 uint64 + x169, x170 = bits.Add64(x133, x156, uint64(0x0)) + var x171 uint64 + var x172 uint64 + x171, x172 = bits.Add64(x135, x158, uint64(p384Uint1(x170))) + var x173 uint64 + var x174 uint64 + x173, x174 = bits.Add64(x137, x160, uint64(p384Uint1(x172))) + var x175 uint64 + var x176 uint64 + x175, x176 = bits.Add64(x139, x162, uint64(p384Uint1(x174))) + var x177 uint64 + var x178 uint64 + x177, x178 = bits.Add64(x141, x164, uint64(p384Uint1(x176))) + var x179 uint64 + var x180 uint64 + x179, x180 = bits.Add64(x143, x166, uint64(p384Uint1(x178))) + var x181 uint64 + var x182 uint64 + x181, x182 = bits.Add64(x145, x168, uint64(p384Uint1(x180))) + var x183 uint64 + _, x183 = bits.Mul64(x169, 0x100000001) + var x185 uint64 + var x186 uint64 + x186, x185 = bits.Mul64(x183, 0xffffffffffffffff) + var x187 uint64 + var x188 uint64 + x188, x187 = bits.Mul64(x183, 0xffffffffffffffff) + var x189 uint64 + var x190 uint64 + x190, x189 = bits.Mul64(x183, 0xffffffffffffffff) + var x191 uint64 + var x192 uint64 + x192, x191 = bits.Mul64(x183, 0xfffffffffffffffe) + var x193 uint64 + var x194 uint64 + x194, x193 = bits.Mul64(x183, 0xffffffff00000000) + var x195 uint64 + var x196 uint64 + x196, x195 = bits.Mul64(x183, 0xffffffff) + var x197 uint64 + var x198 uint64 + x197, x198 = bits.Add64(x196, x193, uint64(0x0)) + var x199 uint64 + var x200 uint64 + x199, x200 = bits.Add64(x194, x191, uint64(p384Uint1(x198))) + var x201 uint64 + var x202 uint64 + x201, x202 = bits.Add64(x192, x189, uint64(p384Uint1(x200))) + var x203 uint64 + var x204 uint64 + x203, x204 = bits.Add64(x190, x187, uint64(p384Uint1(x202))) + var x205 uint64 + var x206 uint64 + x205, x206 = bits.Add64(x188, x185, uint64(p384Uint1(x204))) + x207 := (uint64(p384Uint1(x206)) + x186) + var x209 uint64 + _, x209 = bits.Add64(x169, x195, uint64(0x0)) + var x210 uint64 + var x211 uint64 + x210, x211 = bits.Add64(x171, x197, uint64(p384Uint1(x209))) + var x212 uint64 + var x213 uint64 + x212, x213 = bits.Add64(x173, x199, uint64(p384Uint1(x211))) + var x214 uint64 + var x215 uint64 + x214, x215 = bits.Add64(x175, x201, uint64(p384Uint1(x213))) + var x216 uint64 + var x217 uint64 + x216, x217 = bits.Add64(x177, x203, uint64(p384Uint1(x215))) + var x218 uint64 + var x219 uint64 + x218, x219 = bits.Add64(x179, x205, uint64(p384Uint1(x217))) + var x220 uint64 + var x221 uint64 + x220, x221 = bits.Add64(x181, x207, uint64(p384Uint1(x219))) + x222 := (uint64(p384Uint1(x221)) + uint64(p384Uint1(x182))) + var x223 uint64 + var x224 uint64 + x224, x223 = bits.Mul64(x3, arg2[5]) + var x225 uint64 + var x226 uint64 + x226, x225 = bits.Mul64(x3, arg2[4]) + var x227 uint64 + var x228 uint64 + x228, x227 = bits.Mul64(x3, arg2[3]) + var x229 uint64 + var x230 uint64 + x230, x229 = bits.Mul64(x3, arg2[2]) + var x231 uint64 + var x232 uint64 + x232, x231 = bits.Mul64(x3, arg2[1]) + var x233 uint64 + var x234 uint64 + x234, x233 = bits.Mul64(x3, arg2[0]) + var x235 uint64 + var x236 uint64 + x235, x236 = bits.Add64(x234, x231, uint64(0x0)) + var x237 uint64 + var x238 uint64 + x237, x238 = bits.Add64(x232, x229, uint64(p384Uint1(x236))) + var x239 uint64 + var x240 uint64 + x239, x240 = bits.Add64(x230, x227, uint64(p384Uint1(x238))) + var x241 uint64 + var x242 uint64 + x241, x242 = bits.Add64(x228, x225, uint64(p384Uint1(x240))) + var x243 uint64 + var x244 uint64 + x243, x244 = bits.Add64(x226, x223, uint64(p384Uint1(x242))) + x245 := (uint64(p384Uint1(x244)) + x224) + var x246 uint64 + var x247 uint64 + x246, x247 = bits.Add64(x210, x233, uint64(0x0)) + var x248 uint64 + var x249 uint64 + x248, x249 = bits.Add64(x212, x235, uint64(p384Uint1(x247))) + var x250 uint64 + var x251 uint64 + x250, x251 = bits.Add64(x214, x237, uint64(p384Uint1(x249))) + var x252 uint64 + var x253 uint64 + x252, x253 = bits.Add64(x216, x239, uint64(p384Uint1(x251))) + var x254 uint64 + var x255 uint64 + x254, x255 = bits.Add64(x218, x241, uint64(p384Uint1(x253))) + var x256 uint64 + var x257 uint64 + x256, x257 = bits.Add64(x220, x243, uint64(p384Uint1(x255))) + var x258 uint64 + var x259 uint64 + x258, x259 = bits.Add64(x222, x245, uint64(p384Uint1(x257))) + var x260 uint64 + _, x260 = bits.Mul64(x246, 0x100000001) + var x262 uint64 + var x263 uint64 + x263, x262 = bits.Mul64(x260, 0xffffffffffffffff) + var x264 uint64 + var x265 uint64 + x265, x264 = bits.Mul64(x260, 0xffffffffffffffff) + var x266 uint64 + var x267 uint64 + x267, x266 = bits.Mul64(x260, 0xffffffffffffffff) + var x268 uint64 + var x269 uint64 + x269, x268 = bits.Mul64(x260, 0xfffffffffffffffe) + var x270 uint64 + var x271 uint64 + x271, x270 = bits.Mul64(x260, 0xffffffff00000000) + var x272 uint64 + var x273 uint64 + x273, x272 = bits.Mul64(x260, 0xffffffff) + var x274 uint64 + var x275 uint64 + x274, x275 = bits.Add64(x273, x270, uint64(0x0)) + var x276 uint64 + var x277 uint64 + x276, x277 = bits.Add64(x271, x268, uint64(p384Uint1(x275))) + var x278 uint64 + var x279 uint64 + x278, x279 = bits.Add64(x269, x266, uint64(p384Uint1(x277))) + var x280 uint64 + var x281 uint64 + x280, x281 = bits.Add64(x267, x264, uint64(p384Uint1(x279))) + var x282 uint64 + var x283 uint64 + x282, x283 = bits.Add64(x265, x262, uint64(p384Uint1(x281))) + x284 := (uint64(p384Uint1(x283)) + x263) + var x286 uint64 + _, x286 = bits.Add64(x246, x272, uint64(0x0)) + var x287 uint64 + var x288 uint64 + x287, x288 = bits.Add64(x248, x274, uint64(p384Uint1(x286))) + var x289 uint64 + var x290 uint64 + x289, x290 = bits.Add64(x250, x276, uint64(p384Uint1(x288))) + var x291 uint64 + var x292 uint64 + x291, x292 = bits.Add64(x252, x278, uint64(p384Uint1(x290))) + var x293 uint64 + var x294 uint64 + x293, x294 = bits.Add64(x254, x280, uint64(p384Uint1(x292))) + var x295 uint64 + var x296 uint64 + x295, x296 = bits.Add64(x256, x282, uint64(p384Uint1(x294))) + var x297 uint64 + var x298 uint64 + x297, x298 = bits.Add64(x258, x284, uint64(p384Uint1(x296))) + x299 := (uint64(p384Uint1(x298)) + uint64(p384Uint1(x259))) + var x300 uint64 + var x301 uint64 + x301, x300 = bits.Mul64(x4, arg2[5]) + var x302 uint64 + var x303 uint64 + x303, x302 = bits.Mul64(x4, arg2[4]) + var x304 uint64 + var x305 uint64 + x305, x304 = bits.Mul64(x4, arg2[3]) + var x306 uint64 + var x307 uint64 + x307, x306 = bits.Mul64(x4, arg2[2]) + var x308 uint64 + var x309 uint64 + x309, x308 = bits.Mul64(x4, arg2[1]) + var x310 uint64 + var x311 uint64 + x311, x310 = bits.Mul64(x4, arg2[0]) + var x312 uint64 + var x313 uint64 + x312, x313 = bits.Add64(x311, x308, uint64(0x0)) + var x314 uint64 + var x315 uint64 + x314, x315 = bits.Add64(x309, x306, uint64(p384Uint1(x313))) + var x316 uint64 + var x317 uint64 + x316, x317 = bits.Add64(x307, x304, uint64(p384Uint1(x315))) + var x318 uint64 + var x319 uint64 + x318, x319 = bits.Add64(x305, x302, uint64(p384Uint1(x317))) + var x320 uint64 + var x321 uint64 + x320, x321 = bits.Add64(x303, x300, uint64(p384Uint1(x319))) + x322 := (uint64(p384Uint1(x321)) + x301) + var x323 uint64 + var x324 uint64 + x323, x324 = bits.Add64(x287, x310, uint64(0x0)) + var x325 uint64 + var x326 uint64 + x325, x326 = bits.Add64(x289, x312, uint64(p384Uint1(x324))) + var x327 uint64 + var x328 uint64 + x327, x328 = bits.Add64(x291, x314, uint64(p384Uint1(x326))) + var x329 uint64 + var x330 uint64 + x329, x330 = bits.Add64(x293, x316, uint64(p384Uint1(x328))) + var x331 uint64 + var x332 uint64 + x331, x332 = bits.Add64(x295, x318, uint64(p384Uint1(x330))) + var x333 uint64 + var x334 uint64 + x333, x334 = bits.Add64(x297, x320, uint64(p384Uint1(x332))) + var x335 uint64 + var x336 uint64 + x335, x336 = bits.Add64(x299, x322, uint64(p384Uint1(x334))) + var x337 uint64 + _, x337 = bits.Mul64(x323, 0x100000001) + var x339 uint64 + var x340 uint64 + x340, x339 = bits.Mul64(x337, 0xffffffffffffffff) + var x341 uint64 + var x342 uint64 + x342, x341 = bits.Mul64(x337, 0xffffffffffffffff) + var x343 uint64 + var x344 uint64 + x344, x343 = bits.Mul64(x337, 0xffffffffffffffff) + var x345 uint64 + var x346 uint64 + x346, x345 = bits.Mul64(x337, 0xfffffffffffffffe) + var x347 uint64 + var x348 uint64 + x348, x347 = bits.Mul64(x337, 0xffffffff00000000) + var x349 uint64 + var x350 uint64 + x350, x349 = bits.Mul64(x337, 0xffffffff) + var x351 uint64 + var x352 uint64 + x351, x352 = bits.Add64(x350, x347, uint64(0x0)) + var x353 uint64 + var x354 uint64 + x353, x354 = bits.Add64(x348, x345, uint64(p384Uint1(x352))) + var x355 uint64 + var x356 uint64 + x355, x356 = bits.Add64(x346, x343, uint64(p384Uint1(x354))) + var x357 uint64 + var x358 uint64 + x357, x358 = bits.Add64(x344, x341, uint64(p384Uint1(x356))) + var x359 uint64 + var x360 uint64 + x359, x360 = bits.Add64(x342, x339, uint64(p384Uint1(x358))) + x361 := (uint64(p384Uint1(x360)) + x340) + var x363 uint64 + _, x363 = bits.Add64(x323, x349, uint64(0x0)) + var x364 uint64 + var x365 uint64 + x364, x365 = bits.Add64(x325, x351, uint64(p384Uint1(x363))) + var x366 uint64 + var x367 uint64 + x366, x367 = bits.Add64(x327, x353, uint64(p384Uint1(x365))) + var x368 uint64 + var x369 uint64 + x368, x369 = bits.Add64(x329, x355, uint64(p384Uint1(x367))) + var x370 uint64 + var x371 uint64 + x370, x371 = bits.Add64(x331, x357, uint64(p384Uint1(x369))) + var x372 uint64 + var x373 uint64 + x372, x373 = bits.Add64(x333, x359, uint64(p384Uint1(x371))) + var x374 uint64 + var x375 uint64 + x374, x375 = bits.Add64(x335, x361, uint64(p384Uint1(x373))) + x376 := (uint64(p384Uint1(x375)) + uint64(p384Uint1(x336))) + var x377 uint64 + var x378 uint64 + x378, x377 = bits.Mul64(x5, arg2[5]) + var x379 uint64 + var x380 uint64 + x380, x379 = bits.Mul64(x5, arg2[4]) + var x381 uint64 + var x382 uint64 + x382, x381 = bits.Mul64(x5, arg2[3]) + var x383 uint64 + var x384 uint64 + x384, x383 = bits.Mul64(x5, arg2[2]) + var x385 uint64 + var x386 uint64 + x386, x385 = bits.Mul64(x5, arg2[1]) + var x387 uint64 + var x388 uint64 + x388, x387 = bits.Mul64(x5, arg2[0]) + var x389 uint64 + var x390 uint64 + x389, x390 = bits.Add64(x388, x385, uint64(0x0)) + var x391 uint64 + var x392 uint64 + x391, x392 = bits.Add64(x386, x383, uint64(p384Uint1(x390))) + var x393 uint64 + var x394 uint64 + x393, x394 = bits.Add64(x384, x381, uint64(p384Uint1(x392))) + var x395 uint64 + var x396 uint64 + x395, x396 = bits.Add64(x382, x379, uint64(p384Uint1(x394))) + var x397 uint64 + var x398 uint64 + x397, x398 = bits.Add64(x380, x377, uint64(p384Uint1(x396))) + x399 := (uint64(p384Uint1(x398)) + x378) + var x400 uint64 + var x401 uint64 + x400, x401 = bits.Add64(x364, x387, uint64(0x0)) + var x402 uint64 + var x403 uint64 + x402, x403 = bits.Add64(x366, x389, uint64(p384Uint1(x401))) + var x404 uint64 + var x405 uint64 + x404, x405 = bits.Add64(x368, x391, uint64(p384Uint1(x403))) + var x406 uint64 + var x407 uint64 + x406, x407 = bits.Add64(x370, x393, uint64(p384Uint1(x405))) + var x408 uint64 + var x409 uint64 + x408, x409 = bits.Add64(x372, x395, uint64(p384Uint1(x407))) + var x410 uint64 + var x411 uint64 + x410, x411 = bits.Add64(x374, x397, uint64(p384Uint1(x409))) + var x412 uint64 + var x413 uint64 + x412, x413 = bits.Add64(x376, x399, uint64(p384Uint1(x411))) + var x414 uint64 + _, x414 = bits.Mul64(x400, 0x100000001) + var x416 uint64 + var x417 uint64 + x417, x416 = bits.Mul64(x414, 0xffffffffffffffff) + var x418 uint64 + var x419 uint64 + x419, x418 = bits.Mul64(x414, 0xffffffffffffffff) + var x420 uint64 + var x421 uint64 + x421, x420 = bits.Mul64(x414, 0xffffffffffffffff) + var x422 uint64 + var x423 uint64 + x423, x422 = bits.Mul64(x414, 0xfffffffffffffffe) + var x424 uint64 + var x425 uint64 + x425, x424 = bits.Mul64(x414, 0xffffffff00000000) + var x426 uint64 + var x427 uint64 + x427, x426 = bits.Mul64(x414, 0xffffffff) + var x428 uint64 + var x429 uint64 + x428, x429 = bits.Add64(x427, x424, uint64(0x0)) + var x430 uint64 + var x431 uint64 + x430, x431 = bits.Add64(x425, x422, uint64(p384Uint1(x429))) + var x432 uint64 + var x433 uint64 + x432, x433 = bits.Add64(x423, x420, uint64(p384Uint1(x431))) + var x434 uint64 + var x435 uint64 + x434, x435 = bits.Add64(x421, x418, uint64(p384Uint1(x433))) + var x436 uint64 + var x437 uint64 + x436, x437 = bits.Add64(x419, x416, uint64(p384Uint1(x435))) + x438 := (uint64(p384Uint1(x437)) + x417) + var x440 uint64 + _, x440 = bits.Add64(x400, x426, uint64(0x0)) + var x441 uint64 + var x442 uint64 + x441, x442 = bits.Add64(x402, x428, uint64(p384Uint1(x440))) + var x443 uint64 + var x444 uint64 + x443, x444 = bits.Add64(x404, x430, uint64(p384Uint1(x442))) + var x445 uint64 + var x446 uint64 + x445, x446 = bits.Add64(x406, x432, uint64(p384Uint1(x444))) + var x447 uint64 + var x448 uint64 + x447, x448 = bits.Add64(x408, x434, uint64(p384Uint1(x446))) + var x449 uint64 + var x450 uint64 + x449, x450 = bits.Add64(x410, x436, uint64(p384Uint1(x448))) + var x451 uint64 + var x452 uint64 + x451, x452 = bits.Add64(x412, x438, uint64(p384Uint1(x450))) + x453 := (uint64(p384Uint1(x452)) + uint64(p384Uint1(x413))) + var x454 uint64 + var x455 uint64 + x454, x455 = bits.Sub64(x441, 0xffffffff, uint64(0x0)) + var x456 uint64 + var x457 uint64 + x456, x457 = bits.Sub64(x443, 0xffffffff00000000, uint64(p384Uint1(x455))) + var x458 uint64 + var x459 uint64 + x458, x459 = bits.Sub64(x445, 0xfffffffffffffffe, uint64(p384Uint1(x457))) + var x460 uint64 + var x461 uint64 + x460, x461 = bits.Sub64(x447, 0xffffffffffffffff, uint64(p384Uint1(x459))) + var x462 uint64 + var x463 uint64 + x462, x463 = bits.Sub64(x449, 0xffffffffffffffff, uint64(p384Uint1(x461))) + var x464 uint64 + var x465 uint64 + x464, x465 = bits.Sub64(x451, 0xffffffffffffffff, uint64(p384Uint1(x463))) + var x467 uint64 + _, x467 = bits.Sub64(x453, uint64(0x0), uint64(p384Uint1(x465))) + var x468 uint64 + p384CmovznzU64(&x468, p384Uint1(x467), x454, x441) + var x469 uint64 + p384CmovznzU64(&x469, p384Uint1(x467), x456, x443) + var x470 uint64 + p384CmovznzU64(&x470, p384Uint1(x467), x458, x445) + var x471 uint64 + p384CmovznzU64(&x471, p384Uint1(x467), x460, x447) + var x472 uint64 + p384CmovznzU64(&x472, p384Uint1(x467), x462, x449) + var x473 uint64 + p384CmovznzU64(&x473, p384Uint1(x467), x464, x451) + out1[0] = x468 + out1[1] = x469 + out1[2] = x470 + out1[3] = x471 + out1[4] = x472 + out1[5] = x473 +} + +// p384Square squares a field element in the Montgomery domain. +// +// Preconditions: +// 0 ≤ eval arg1 < m +// Postconditions: +// eval (from_montgomery out1) mod m = (eval (from_montgomery arg1) * eval (from_montgomery arg1)) mod m +// 0 ≤ eval out1 < m +// +func p384Square(out1 *p384MontgomeryDomainFieldElement, arg1 *p384MontgomeryDomainFieldElement) { + x1 := arg1[1] + x2 := arg1[2] + x3 := arg1[3] + x4 := arg1[4] + x5 := arg1[5] + x6 := arg1[0] + var x7 uint64 + var x8 uint64 + x8, x7 = bits.Mul64(x6, arg1[5]) + var x9 uint64 + var x10 uint64 + x10, x9 = bits.Mul64(x6, arg1[4]) + var x11 uint64 + var x12 uint64 + x12, x11 = bits.Mul64(x6, arg1[3]) + var x13 uint64 + var x14 uint64 + x14, x13 = bits.Mul64(x6, arg1[2]) + var x15 uint64 + var x16 uint64 + x16, x15 = bits.Mul64(x6, arg1[1]) + var x17 uint64 + var x18 uint64 + x18, x17 = bits.Mul64(x6, arg1[0]) + var x19 uint64 + var x20 uint64 + x19, x20 = bits.Add64(x18, x15, uint64(0x0)) + var x21 uint64 + var x22 uint64 + x21, x22 = bits.Add64(x16, x13, uint64(p384Uint1(x20))) + var x23 uint64 + var x24 uint64 + x23, x24 = bits.Add64(x14, x11, uint64(p384Uint1(x22))) + var x25 uint64 + var x26 uint64 + x25, x26 = bits.Add64(x12, x9, uint64(p384Uint1(x24))) + var x27 uint64 + var x28 uint64 + x27, x28 = bits.Add64(x10, x7, uint64(p384Uint1(x26))) + x29 := (uint64(p384Uint1(x28)) + x8) + var x30 uint64 + _, x30 = bits.Mul64(x17, 0x100000001) + var x32 uint64 + var x33 uint64 + x33, x32 = bits.Mul64(x30, 0xffffffffffffffff) + var x34 uint64 + var x35 uint64 + x35, x34 = bits.Mul64(x30, 0xffffffffffffffff) + var x36 uint64 + var x37 uint64 + x37, x36 = bits.Mul64(x30, 0xffffffffffffffff) + var x38 uint64 + var x39 uint64 + x39, x38 = bits.Mul64(x30, 0xfffffffffffffffe) + var x40 uint64 + var x41 uint64 + x41, x40 = bits.Mul64(x30, 0xffffffff00000000) + var x42 uint64 + var x43 uint64 + x43, x42 = bits.Mul64(x30, 0xffffffff) + var x44 uint64 + var x45 uint64 + x44, x45 = bits.Add64(x43, x40, uint64(0x0)) + var x46 uint64 + var x47 uint64 + x46, x47 = bits.Add64(x41, x38, uint64(p384Uint1(x45))) + var x48 uint64 + var x49 uint64 + x48, x49 = bits.Add64(x39, x36, uint64(p384Uint1(x47))) + var x50 uint64 + var x51 uint64 + x50, x51 = bits.Add64(x37, x34, uint64(p384Uint1(x49))) + var x52 uint64 + var x53 uint64 + x52, x53 = bits.Add64(x35, x32, uint64(p384Uint1(x51))) + x54 := (uint64(p384Uint1(x53)) + x33) + var x56 uint64 + _, x56 = bits.Add64(x17, x42, uint64(0x0)) + var x57 uint64 + var x58 uint64 + x57, x58 = bits.Add64(x19, x44, uint64(p384Uint1(x56))) + var x59 uint64 + var x60 uint64 + x59, x60 = bits.Add64(x21, x46, uint64(p384Uint1(x58))) + var x61 uint64 + var x62 uint64 + x61, x62 = bits.Add64(x23, x48, uint64(p384Uint1(x60))) + var x63 uint64 + var x64 uint64 + x63, x64 = bits.Add64(x25, x50, uint64(p384Uint1(x62))) + var x65 uint64 + var x66 uint64 + x65, x66 = bits.Add64(x27, x52, uint64(p384Uint1(x64))) + var x67 uint64 + var x68 uint64 + x67, x68 = bits.Add64(x29, x54, uint64(p384Uint1(x66))) + var x69 uint64 + var x70 uint64 + x70, x69 = bits.Mul64(x1, arg1[5]) + var x71 uint64 + var x72 uint64 + x72, x71 = bits.Mul64(x1, arg1[4]) + var x73 uint64 + var x74 uint64 + x74, x73 = bits.Mul64(x1, arg1[3]) + var x75 uint64 + var x76 uint64 + x76, x75 = bits.Mul64(x1, arg1[2]) + var x77 uint64 + var x78 uint64 + x78, x77 = bits.Mul64(x1, arg1[1]) + var x79 uint64 + var x80 uint64 + x80, x79 = bits.Mul64(x1, arg1[0]) + var x81 uint64 + var x82 uint64 + x81, x82 = bits.Add64(x80, x77, uint64(0x0)) + var x83 uint64 + var x84 uint64 + x83, x84 = bits.Add64(x78, x75, uint64(p384Uint1(x82))) + var x85 uint64 + var x86 uint64 + x85, x86 = bits.Add64(x76, x73, uint64(p384Uint1(x84))) + var x87 uint64 + var x88 uint64 + x87, x88 = bits.Add64(x74, x71, uint64(p384Uint1(x86))) + var x89 uint64 + var x90 uint64 + x89, x90 = bits.Add64(x72, x69, uint64(p384Uint1(x88))) + x91 := (uint64(p384Uint1(x90)) + x70) + var x92 uint64 + var x93 uint64 + x92, x93 = bits.Add64(x57, x79, uint64(0x0)) + var x94 uint64 + var x95 uint64 + x94, x95 = bits.Add64(x59, x81, uint64(p384Uint1(x93))) + var x96 uint64 + var x97 uint64 + x96, x97 = bits.Add64(x61, x83, uint64(p384Uint1(x95))) + var x98 uint64 + var x99 uint64 + x98, x99 = bits.Add64(x63, x85, uint64(p384Uint1(x97))) + var x100 uint64 + var x101 uint64 + x100, x101 = bits.Add64(x65, x87, uint64(p384Uint1(x99))) + var x102 uint64 + var x103 uint64 + x102, x103 = bits.Add64(x67, x89, uint64(p384Uint1(x101))) + var x104 uint64 + var x105 uint64 + x104, x105 = bits.Add64(uint64(p384Uint1(x68)), x91, uint64(p384Uint1(x103))) + var x106 uint64 + _, x106 = bits.Mul64(x92, 0x100000001) + var x108 uint64 + var x109 uint64 + x109, x108 = bits.Mul64(x106, 0xffffffffffffffff) + var x110 uint64 + var x111 uint64 + x111, x110 = bits.Mul64(x106, 0xffffffffffffffff) + var x112 uint64 + var x113 uint64 + x113, x112 = bits.Mul64(x106, 0xffffffffffffffff) + var x114 uint64 + var x115 uint64 + x115, x114 = bits.Mul64(x106, 0xfffffffffffffffe) + var x116 uint64 + var x117 uint64 + x117, x116 = bits.Mul64(x106, 0xffffffff00000000) + var x118 uint64 + var x119 uint64 + x119, x118 = bits.Mul64(x106, 0xffffffff) + var x120 uint64 + var x121 uint64 + x120, x121 = bits.Add64(x119, x116, uint64(0x0)) + var x122 uint64 + var x123 uint64 + x122, x123 = bits.Add64(x117, x114, uint64(p384Uint1(x121))) + var x124 uint64 + var x125 uint64 + x124, x125 = bits.Add64(x115, x112, uint64(p384Uint1(x123))) + var x126 uint64 + var x127 uint64 + x126, x127 = bits.Add64(x113, x110, uint64(p384Uint1(x125))) + var x128 uint64 + var x129 uint64 + x128, x129 = bits.Add64(x111, x108, uint64(p384Uint1(x127))) + x130 := (uint64(p384Uint1(x129)) + x109) + var x132 uint64 + _, x132 = bits.Add64(x92, x118, uint64(0x0)) + var x133 uint64 + var x134 uint64 + x133, x134 = bits.Add64(x94, x120, uint64(p384Uint1(x132))) + var x135 uint64 + var x136 uint64 + x135, x136 = bits.Add64(x96, x122, uint64(p384Uint1(x134))) + var x137 uint64 + var x138 uint64 + x137, x138 = bits.Add64(x98, x124, uint64(p384Uint1(x136))) + var x139 uint64 + var x140 uint64 + x139, x140 = bits.Add64(x100, x126, uint64(p384Uint1(x138))) + var x141 uint64 + var x142 uint64 + x141, x142 = bits.Add64(x102, x128, uint64(p384Uint1(x140))) + var x143 uint64 + var x144 uint64 + x143, x144 = bits.Add64(x104, x130, uint64(p384Uint1(x142))) + x145 := (uint64(p384Uint1(x144)) + uint64(p384Uint1(x105))) + var x146 uint64 + var x147 uint64 + x147, x146 = bits.Mul64(x2, arg1[5]) + var x148 uint64 + var x149 uint64 + x149, x148 = bits.Mul64(x2, arg1[4]) + var x150 uint64 + var x151 uint64 + x151, x150 = bits.Mul64(x2, arg1[3]) + var x152 uint64 + var x153 uint64 + x153, x152 = bits.Mul64(x2, arg1[2]) + var x154 uint64 + var x155 uint64 + x155, x154 = bits.Mul64(x2, arg1[1]) + var x156 uint64 + var x157 uint64 + x157, x156 = bits.Mul64(x2, arg1[0]) + var x158 uint64 + var x159 uint64 + x158, x159 = bits.Add64(x157, x154, uint64(0x0)) + var x160 uint64 + var x161 uint64 + x160, x161 = bits.Add64(x155, x152, uint64(p384Uint1(x159))) + var x162 uint64 + var x163 uint64 + x162, x163 = bits.Add64(x153, x150, uint64(p384Uint1(x161))) + var x164 uint64 + var x165 uint64 + x164, x165 = bits.Add64(x151, x148, uint64(p384Uint1(x163))) + var x166 uint64 + var x167 uint64 + x166, x167 = bits.Add64(x149, x146, uint64(p384Uint1(x165))) + x168 := (uint64(p384Uint1(x167)) + x147) + var x169 uint64 + var x170 uint64 + x169, x170 = bits.Add64(x133, x156, uint64(0x0)) + var x171 uint64 + var x172 uint64 + x171, x172 = bits.Add64(x135, x158, uint64(p384Uint1(x170))) + var x173 uint64 + var x174 uint64 + x173, x174 = bits.Add64(x137, x160, uint64(p384Uint1(x172))) + var x175 uint64 + var x176 uint64 + x175, x176 = bits.Add64(x139, x162, uint64(p384Uint1(x174))) + var x177 uint64 + var x178 uint64 + x177, x178 = bits.Add64(x141, x164, uint64(p384Uint1(x176))) + var x179 uint64 + var x180 uint64 + x179, x180 = bits.Add64(x143, x166, uint64(p384Uint1(x178))) + var x181 uint64 + var x182 uint64 + x181, x182 = bits.Add64(x145, x168, uint64(p384Uint1(x180))) + var x183 uint64 + _, x183 = bits.Mul64(x169, 0x100000001) + var x185 uint64 + var x186 uint64 + x186, x185 = bits.Mul64(x183, 0xffffffffffffffff) + var x187 uint64 + var x188 uint64 + x188, x187 = bits.Mul64(x183, 0xffffffffffffffff) + var x189 uint64 + var x190 uint64 + x190, x189 = bits.Mul64(x183, 0xffffffffffffffff) + var x191 uint64 + var x192 uint64 + x192, x191 = bits.Mul64(x183, 0xfffffffffffffffe) + var x193 uint64 + var x194 uint64 + x194, x193 = bits.Mul64(x183, 0xffffffff00000000) + var x195 uint64 + var x196 uint64 + x196, x195 = bits.Mul64(x183, 0xffffffff) + var x197 uint64 + var x198 uint64 + x197, x198 = bits.Add64(x196, x193, uint64(0x0)) + var x199 uint64 + var x200 uint64 + x199, x200 = bits.Add64(x194, x191, uint64(p384Uint1(x198))) + var x201 uint64 + var x202 uint64 + x201, x202 = bits.Add64(x192, x189, uint64(p384Uint1(x200))) + var x203 uint64 + var x204 uint64 + x203, x204 = bits.Add64(x190, x187, uint64(p384Uint1(x202))) + var x205 uint64 + var x206 uint64 + x205, x206 = bits.Add64(x188, x185, uint64(p384Uint1(x204))) + x207 := (uint64(p384Uint1(x206)) + x186) + var x209 uint64 + _, x209 = bits.Add64(x169, x195, uint64(0x0)) + var x210 uint64 + var x211 uint64 + x210, x211 = bits.Add64(x171, x197, uint64(p384Uint1(x209))) + var x212 uint64 + var x213 uint64 + x212, x213 = bits.Add64(x173, x199, uint64(p384Uint1(x211))) + var x214 uint64 + var x215 uint64 + x214, x215 = bits.Add64(x175, x201, uint64(p384Uint1(x213))) + var x216 uint64 + var x217 uint64 + x216, x217 = bits.Add64(x177, x203, uint64(p384Uint1(x215))) + var x218 uint64 + var x219 uint64 + x218, x219 = bits.Add64(x179, x205, uint64(p384Uint1(x217))) + var x220 uint64 + var x221 uint64 + x220, x221 = bits.Add64(x181, x207, uint64(p384Uint1(x219))) + x222 := (uint64(p384Uint1(x221)) + uint64(p384Uint1(x182))) + var x223 uint64 + var x224 uint64 + x224, x223 = bits.Mul64(x3, arg1[5]) + var x225 uint64 + var x226 uint64 + x226, x225 = bits.Mul64(x3, arg1[4]) + var x227 uint64 + var x228 uint64 + x228, x227 = bits.Mul64(x3, arg1[3]) + var x229 uint64 + var x230 uint64 + x230, x229 = bits.Mul64(x3, arg1[2]) + var x231 uint64 + var x232 uint64 + x232, x231 = bits.Mul64(x3, arg1[1]) + var x233 uint64 + var x234 uint64 + x234, x233 = bits.Mul64(x3, arg1[0]) + var x235 uint64 + var x236 uint64 + x235, x236 = bits.Add64(x234, x231, uint64(0x0)) + var x237 uint64 + var x238 uint64 + x237, x238 = bits.Add64(x232, x229, uint64(p384Uint1(x236))) + var x239 uint64 + var x240 uint64 + x239, x240 = bits.Add64(x230, x227, uint64(p384Uint1(x238))) + var x241 uint64 + var x242 uint64 + x241, x242 = bits.Add64(x228, x225, uint64(p384Uint1(x240))) + var x243 uint64 + var x244 uint64 + x243, x244 = bits.Add64(x226, x223, uint64(p384Uint1(x242))) + x245 := (uint64(p384Uint1(x244)) + x224) + var x246 uint64 + var x247 uint64 + x246, x247 = bits.Add64(x210, x233, uint64(0x0)) + var x248 uint64 + var x249 uint64 + x248, x249 = bits.Add64(x212, x235, uint64(p384Uint1(x247))) + var x250 uint64 + var x251 uint64 + x250, x251 = bits.Add64(x214, x237, uint64(p384Uint1(x249))) + var x252 uint64 + var x253 uint64 + x252, x253 = bits.Add64(x216, x239, uint64(p384Uint1(x251))) + var x254 uint64 + var x255 uint64 + x254, x255 = bits.Add64(x218, x241, uint64(p384Uint1(x253))) + var x256 uint64 + var x257 uint64 + x256, x257 = bits.Add64(x220, x243, uint64(p384Uint1(x255))) + var x258 uint64 + var x259 uint64 + x258, x259 = bits.Add64(x222, x245, uint64(p384Uint1(x257))) + var x260 uint64 + _, x260 = bits.Mul64(x246, 0x100000001) + var x262 uint64 + var x263 uint64 + x263, x262 = bits.Mul64(x260, 0xffffffffffffffff) + var x264 uint64 + var x265 uint64 + x265, x264 = bits.Mul64(x260, 0xffffffffffffffff) + var x266 uint64 + var x267 uint64 + x267, x266 = bits.Mul64(x260, 0xffffffffffffffff) + var x268 uint64 + var x269 uint64 + x269, x268 = bits.Mul64(x260, 0xfffffffffffffffe) + var x270 uint64 + var x271 uint64 + x271, x270 = bits.Mul64(x260, 0xffffffff00000000) + var x272 uint64 + var x273 uint64 + x273, x272 = bits.Mul64(x260, 0xffffffff) + var x274 uint64 + var x275 uint64 + x274, x275 = bits.Add64(x273, x270, uint64(0x0)) + var x276 uint64 + var x277 uint64 + x276, x277 = bits.Add64(x271, x268, uint64(p384Uint1(x275))) + var x278 uint64 + var x279 uint64 + x278, x279 = bits.Add64(x269, x266, uint64(p384Uint1(x277))) + var x280 uint64 + var x281 uint64 + x280, x281 = bits.Add64(x267, x264, uint64(p384Uint1(x279))) + var x282 uint64 + var x283 uint64 + x282, x283 = bits.Add64(x265, x262, uint64(p384Uint1(x281))) + x284 := (uint64(p384Uint1(x283)) + x263) + var x286 uint64 + _, x286 = bits.Add64(x246, x272, uint64(0x0)) + var x287 uint64 + var x288 uint64 + x287, x288 = bits.Add64(x248, x274, uint64(p384Uint1(x286))) + var x289 uint64 + var x290 uint64 + x289, x290 = bits.Add64(x250, x276, uint64(p384Uint1(x288))) + var x291 uint64 + var x292 uint64 + x291, x292 = bits.Add64(x252, x278, uint64(p384Uint1(x290))) + var x293 uint64 + var x294 uint64 + x293, x294 = bits.Add64(x254, x280, uint64(p384Uint1(x292))) + var x295 uint64 + var x296 uint64 + x295, x296 = bits.Add64(x256, x282, uint64(p384Uint1(x294))) + var x297 uint64 + var x298 uint64 + x297, x298 = bits.Add64(x258, x284, uint64(p384Uint1(x296))) + x299 := (uint64(p384Uint1(x298)) + uint64(p384Uint1(x259))) + var x300 uint64 + var x301 uint64 + x301, x300 = bits.Mul64(x4, arg1[5]) + var x302 uint64 + var x303 uint64 + x303, x302 = bits.Mul64(x4, arg1[4]) + var x304 uint64 + var x305 uint64 + x305, x304 = bits.Mul64(x4, arg1[3]) + var x306 uint64 + var x307 uint64 + x307, x306 = bits.Mul64(x4, arg1[2]) + var x308 uint64 + var x309 uint64 + x309, x308 = bits.Mul64(x4, arg1[1]) + var x310 uint64 + var x311 uint64 + x311, x310 = bits.Mul64(x4, arg1[0]) + var x312 uint64 + var x313 uint64 + x312, x313 = bits.Add64(x311, x308, uint64(0x0)) + var x314 uint64 + var x315 uint64 + x314, x315 = bits.Add64(x309, x306, uint64(p384Uint1(x313))) + var x316 uint64 + var x317 uint64 + x316, x317 = bits.Add64(x307, x304, uint64(p384Uint1(x315))) + var x318 uint64 + var x319 uint64 + x318, x319 = bits.Add64(x305, x302, uint64(p384Uint1(x317))) + var x320 uint64 + var x321 uint64 + x320, x321 = bits.Add64(x303, x300, uint64(p384Uint1(x319))) + x322 := (uint64(p384Uint1(x321)) + x301) + var x323 uint64 + var x324 uint64 + x323, x324 = bits.Add64(x287, x310, uint64(0x0)) + var x325 uint64 + var x326 uint64 + x325, x326 = bits.Add64(x289, x312, uint64(p384Uint1(x324))) + var x327 uint64 + var x328 uint64 + x327, x328 = bits.Add64(x291, x314, uint64(p384Uint1(x326))) + var x329 uint64 + var x330 uint64 + x329, x330 = bits.Add64(x293, x316, uint64(p384Uint1(x328))) + var x331 uint64 + var x332 uint64 + x331, x332 = bits.Add64(x295, x318, uint64(p384Uint1(x330))) + var x333 uint64 + var x334 uint64 + x333, x334 = bits.Add64(x297, x320, uint64(p384Uint1(x332))) + var x335 uint64 + var x336 uint64 + x335, x336 = bits.Add64(x299, x322, uint64(p384Uint1(x334))) + var x337 uint64 + _, x337 = bits.Mul64(x323, 0x100000001) + var x339 uint64 + var x340 uint64 + x340, x339 = bits.Mul64(x337, 0xffffffffffffffff) + var x341 uint64 + var x342 uint64 + x342, x341 = bits.Mul64(x337, 0xffffffffffffffff) + var x343 uint64 + var x344 uint64 + x344, x343 = bits.Mul64(x337, 0xffffffffffffffff) + var x345 uint64 + var x346 uint64 + x346, x345 = bits.Mul64(x337, 0xfffffffffffffffe) + var x347 uint64 + var x348 uint64 + x348, x347 = bits.Mul64(x337, 0xffffffff00000000) + var x349 uint64 + var x350 uint64 + x350, x349 = bits.Mul64(x337, 0xffffffff) + var x351 uint64 + var x352 uint64 + x351, x352 = bits.Add64(x350, x347, uint64(0x0)) + var x353 uint64 + var x354 uint64 + x353, x354 = bits.Add64(x348, x345, uint64(p384Uint1(x352))) + var x355 uint64 + var x356 uint64 + x355, x356 = bits.Add64(x346, x343, uint64(p384Uint1(x354))) + var x357 uint64 + var x358 uint64 + x357, x358 = bits.Add64(x344, x341, uint64(p384Uint1(x356))) + var x359 uint64 + var x360 uint64 + x359, x360 = bits.Add64(x342, x339, uint64(p384Uint1(x358))) + x361 := (uint64(p384Uint1(x360)) + x340) + var x363 uint64 + _, x363 = bits.Add64(x323, x349, uint64(0x0)) + var x364 uint64 + var x365 uint64 + x364, x365 = bits.Add64(x325, x351, uint64(p384Uint1(x363))) + var x366 uint64 + var x367 uint64 + x366, x367 = bits.Add64(x327, x353, uint64(p384Uint1(x365))) + var x368 uint64 + var x369 uint64 + x368, x369 = bits.Add64(x329, x355, uint64(p384Uint1(x367))) + var x370 uint64 + var x371 uint64 + x370, x371 = bits.Add64(x331, x357, uint64(p384Uint1(x369))) + var x372 uint64 + var x373 uint64 + x372, x373 = bits.Add64(x333, x359, uint64(p384Uint1(x371))) + var x374 uint64 + var x375 uint64 + x374, x375 = bits.Add64(x335, x361, uint64(p384Uint1(x373))) + x376 := (uint64(p384Uint1(x375)) + uint64(p384Uint1(x336))) + var x377 uint64 + var x378 uint64 + x378, x377 = bits.Mul64(x5, arg1[5]) + var x379 uint64 + var x380 uint64 + x380, x379 = bits.Mul64(x5, arg1[4]) + var x381 uint64 + var x382 uint64 + x382, x381 = bits.Mul64(x5, arg1[3]) + var x383 uint64 + var x384 uint64 + x384, x383 = bits.Mul64(x5, arg1[2]) + var x385 uint64 + var x386 uint64 + x386, x385 = bits.Mul64(x5, arg1[1]) + var x387 uint64 + var x388 uint64 + x388, x387 = bits.Mul64(x5, arg1[0]) + var x389 uint64 + var x390 uint64 + x389, x390 = bits.Add64(x388, x385, uint64(0x0)) + var x391 uint64 + var x392 uint64 + x391, x392 = bits.Add64(x386, x383, uint64(p384Uint1(x390))) + var x393 uint64 + var x394 uint64 + x393, x394 = bits.Add64(x384, x381, uint64(p384Uint1(x392))) + var x395 uint64 + var x396 uint64 + x395, x396 = bits.Add64(x382, x379, uint64(p384Uint1(x394))) + var x397 uint64 + var x398 uint64 + x397, x398 = bits.Add64(x380, x377, uint64(p384Uint1(x396))) + x399 := (uint64(p384Uint1(x398)) + x378) + var x400 uint64 + var x401 uint64 + x400, x401 = bits.Add64(x364, x387, uint64(0x0)) + var x402 uint64 + var x403 uint64 + x402, x403 = bits.Add64(x366, x389, uint64(p384Uint1(x401))) + var x404 uint64 + var x405 uint64 + x404, x405 = bits.Add64(x368, x391, uint64(p384Uint1(x403))) + var x406 uint64 + var x407 uint64 + x406, x407 = bits.Add64(x370, x393, uint64(p384Uint1(x405))) + var x408 uint64 + var x409 uint64 + x408, x409 = bits.Add64(x372, x395, uint64(p384Uint1(x407))) + var x410 uint64 + var x411 uint64 + x410, x411 = bits.Add64(x374, x397, uint64(p384Uint1(x409))) + var x412 uint64 + var x413 uint64 + x412, x413 = bits.Add64(x376, x399, uint64(p384Uint1(x411))) + var x414 uint64 + _, x414 = bits.Mul64(x400, 0x100000001) + var x416 uint64 + var x417 uint64 + x417, x416 = bits.Mul64(x414, 0xffffffffffffffff) + var x418 uint64 + var x419 uint64 + x419, x418 = bits.Mul64(x414, 0xffffffffffffffff) + var x420 uint64 + var x421 uint64 + x421, x420 = bits.Mul64(x414, 0xffffffffffffffff) + var x422 uint64 + var x423 uint64 + x423, x422 = bits.Mul64(x414, 0xfffffffffffffffe) + var x424 uint64 + var x425 uint64 + x425, x424 = bits.Mul64(x414, 0xffffffff00000000) + var x426 uint64 + var x427 uint64 + x427, x426 = bits.Mul64(x414, 0xffffffff) + var x428 uint64 + var x429 uint64 + x428, x429 = bits.Add64(x427, x424, uint64(0x0)) + var x430 uint64 + var x431 uint64 + x430, x431 = bits.Add64(x425, x422, uint64(p384Uint1(x429))) + var x432 uint64 + var x433 uint64 + x432, x433 = bits.Add64(x423, x420, uint64(p384Uint1(x431))) + var x434 uint64 + var x435 uint64 + x434, x435 = bits.Add64(x421, x418, uint64(p384Uint1(x433))) + var x436 uint64 + var x437 uint64 + x436, x437 = bits.Add64(x419, x416, uint64(p384Uint1(x435))) + x438 := (uint64(p384Uint1(x437)) + x417) + var x440 uint64 + _, x440 = bits.Add64(x400, x426, uint64(0x0)) + var x441 uint64 + var x442 uint64 + x441, x442 = bits.Add64(x402, x428, uint64(p384Uint1(x440))) + var x443 uint64 + var x444 uint64 + x443, x444 = bits.Add64(x404, x430, uint64(p384Uint1(x442))) + var x445 uint64 + var x446 uint64 + x445, x446 = bits.Add64(x406, x432, uint64(p384Uint1(x444))) + var x447 uint64 + var x448 uint64 + x447, x448 = bits.Add64(x408, x434, uint64(p384Uint1(x446))) + var x449 uint64 + var x450 uint64 + x449, x450 = bits.Add64(x410, x436, uint64(p384Uint1(x448))) + var x451 uint64 + var x452 uint64 + x451, x452 = bits.Add64(x412, x438, uint64(p384Uint1(x450))) + x453 := (uint64(p384Uint1(x452)) + uint64(p384Uint1(x413))) + var x454 uint64 + var x455 uint64 + x454, x455 = bits.Sub64(x441, 0xffffffff, uint64(0x0)) + var x456 uint64 + var x457 uint64 + x456, x457 = bits.Sub64(x443, 0xffffffff00000000, uint64(p384Uint1(x455))) + var x458 uint64 + var x459 uint64 + x458, x459 = bits.Sub64(x445, 0xfffffffffffffffe, uint64(p384Uint1(x457))) + var x460 uint64 + var x461 uint64 + x460, x461 = bits.Sub64(x447, 0xffffffffffffffff, uint64(p384Uint1(x459))) + var x462 uint64 + var x463 uint64 + x462, x463 = bits.Sub64(x449, 0xffffffffffffffff, uint64(p384Uint1(x461))) + var x464 uint64 + var x465 uint64 + x464, x465 = bits.Sub64(x451, 0xffffffffffffffff, uint64(p384Uint1(x463))) + var x467 uint64 + _, x467 = bits.Sub64(x453, uint64(0x0), uint64(p384Uint1(x465))) + var x468 uint64 + p384CmovznzU64(&x468, p384Uint1(x467), x454, x441) + var x469 uint64 + p384CmovznzU64(&x469, p384Uint1(x467), x456, x443) + var x470 uint64 + p384CmovznzU64(&x470, p384Uint1(x467), x458, x445) + var x471 uint64 + p384CmovznzU64(&x471, p384Uint1(x467), x460, x447) + var x472 uint64 + p384CmovznzU64(&x472, p384Uint1(x467), x462, x449) + var x473 uint64 + p384CmovznzU64(&x473, p384Uint1(x467), x464, x451) + out1[0] = x468 + out1[1] = x469 + out1[2] = x470 + out1[3] = x471 + out1[4] = x472 + out1[5] = x473 +} + +// p384Add adds two field elements in the Montgomery domain. +// +// Preconditions: +// 0 ≤ eval arg1 < m +// 0 ≤ eval arg2 < m +// Postconditions: +// eval (from_montgomery out1) mod m = (eval (from_montgomery arg1) + eval (from_montgomery arg2)) mod m +// 0 ≤ eval out1 < m +// +func p384Add(out1 *p384MontgomeryDomainFieldElement, arg1 *p384MontgomeryDomainFieldElement, arg2 *p384MontgomeryDomainFieldElement) { + var x1 uint64 + var x2 uint64 + x1, x2 = bits.Add64(arg1[0], arg2[0], uint64(0x0)) + var x3 uint64 + var x4 uint64 + x3, x4 = bits.Add64(arg1[1], arg2[1], uint64(p384Uint1(x2))) + var x5 uint64 + var x6 uint64 + x5, x6 = bits.Add64(arg1[2], arg2[2], uint64(p384Uint1(x4))) + var x7 uint64 + var x8 uint64 + x7, x8 = bits.Add64(arg1[3], arg2[3], uint64(p384Uint1(x6))) + var x9 uint64 + var x10 uint64 + x9, x10 = bits.Add64(arg1[4], arg2[4], uint64(p384Uint1(x8))) + var x11 uint64 + var x12 uint64 + x11, x12 = bits.Add64(arg1[5], arg2[5], uint64(p384Uint1(x10))) + var x13 uint64 + var x14 uint64 + x13, x14 = bits.Sub64(x1, 0xffffffff, uint64(0x0)) + var x15 uint64 + var x16 uint64 + x15, x16 = bits.Sub64(x3, 0xffffffff00000000, uint64(p384Uint1(x14))) + var x17 uint64 + var x18 uint64 + x17, x18 = bits.Sub64(x5, 0xfffffffffffffffe, uint64(p384Uint1(x16))) + var x19 uint64 + var x20 uint64 + x19, x20 = bits.Sub64(x7, 0xffffffffffffffff, uint64(p384Uint1(x18))) + var x21 uint64 + var x22 uint64 + x21, x22 = bits.Sub64(x9, 0xffffffffffffffff, uint64(p384Uint1(x20))) + var x23 uint64 + var x24 uint64 + x23, x24 = bits.Sub64(x11, 0xffffffffffffffff, uint64(p384Uint1(x22))) + var x26 uint64 + _, x26 = bits.Sub64(uint64(p384Uint1(x12)), uint64(0x0), uint64(p384Uint1(x24))) + var x27 uint64 + p384CmovznzU64(&x27, p384Uint1(x26), x13, x1) + var x28 uint64 + p384CmovznzU64(&x28, p384Uint1(x26), x15, x3) + var x29 uint64 + p384CmovznzU64(&x29, p384Uint1(x26), x17, x5) + var x30 uint64 + p384CmovznzU64(&x30, p384Uint1(x26), x19, x7) + var x31 uint64 + p384CmovznzU64(&x31, p384Uint1(x26), x21, x9) + var x32 uint64 + p384CmovznzU64(&x32, p384Uint1(x26), x23, x11) + out1[0] = x27 + out1[1] = x28 + out1[2] = x29 + out1[3] = x30 + out1[4] = x31 + out1[5] = x32 +} + +// p384Sub subtracts two field elements in the Montgomery domain. +// +// Preconditions: +// 0 ≤ eval arg1 < m +// 0 ≤ eval arg2 < m +// Postconditions: +// eval (from_montgomery out1) mod m = (eval (from_montgomery arg1) - eval (from_montgomery arg2)) mod m +// 0 ≤ eval out1 < m +// +func p384Sub(out1 *p384MontgomeryDomainFieldElement, arg1 *p384MontgomeryDomainFieldElement, arg2 *p384MontgomeryDomainFieldElement) { + var x1 uint64 + var x2 uint64 + x1, x2 = bits.Sub64(arg1[0], arg2[0], uint64(0x0)) + var x3 uint64 + var x4 uint64 + x3, x4 = bits.Sub64(arg1[1], arg2[1], uint64(p384Uint1(x2))) + var x5 uint64 + var x6 uint64 + x5, x6 = bits.Sub64(arg1[2], arg2[2], uint64(p384Uint1(x4))) + var x7 uint64 + var x8 uint64 + x7, x8 = bits.Sub64(arg1[3], arg2[3], uint64(p384Uint1(x6))) + var x9 uint64 + var x10 uint64 + x9, x10 = bits.Sub64(arg1[4], arg2[4], uint64(p384Uint1(x8))) + var x11 uint64 + var x12 uint64 + x11, x12 = bits.Sub64(arg1[5], arg2[5], uint64(p384Uint1(x10))) + var x13 uint64 + p384CmovznzU64(&x13, p384Uint1(x12), uint64(0x0), 0xffffffffffffffff) + var x14 uint64 + var x15 uint64 + x14, x15 = bits.Add64(x1, (x13 & 0xffffffff), uint64(0x0)) + var x16 uint64 + var x17 uint64 + x16, x17 = bits.Add64(x3, (x13 & 0xffffffff00000000), uint64(p384Uint1(x15))) + var x18 uint64 + var x19 uint64 + x18, x19 = bits.Add64(x5, (x13 & 0xfffffffffffffffe), uint64(p384Uint1(x17))) + var x20 uint64 + var x21 uint64 + x20, x21 = bits.Add64(x7, x13, uint64(p384Uint1(x19))) + var x22 uint64 + var x23 uint64 + x22, x23 = bits.Add64(x9, x13, uint64(p384Uint1(x21))) + var x24 uint64 + x24, _ = bits.Add64(x11, x13, uint64(p384Uint1(x23))) + out1[0] = x14 + out1[1] = x16 + out1[2] = x18 + out1[3] = x20 + out1[4] = x22 + out1[5] = x24 +} + +// p384SetOne returns the field element one in the Montgomery domain. +// +// Postconditions: +// eval (from_montgomery out1) mod m = 1 mod m +// 0 ≤ eval out1 < m +// +func p384SetOne(out1 *p384MontgomeryDomainFieldElement) { + out1[0] = 0xffffffff00000001 + out1[1] = 0xffffffff + out1[2] = uint64(0x1) + out1[3] = uint64(0x0) + out1[4] = uint64(0x0) + out1[5] = uint64(0x0) +} + +// p384FromMontgomery translates a field element out of the Montgomery domain. +// +// Preconditions: +// 0 ≤ eval arg1 < m +// Postconditions: +// eval out1 mod m = (eval arg1 * ((2^64)⁻¹ mod m)^6) mod m +// 0 ≤ eval out1 < m +// +func p384FromMontgomery(out1 *p384NonMontgomeryDomainFieldElement, arg1 *p384MontgomeryDomainFieldElement) { + x1 := arg1[0] + var x2 uint64 + _, x2 = bits.Mul64(x1, 0x100000001) + var x4 uint64 + var x5 uint64 + x5, x4 = bits.Mul64(x2, 0xffffffffffffffff) + var x6 uint64 + var x7 uint64 + x7, x6 = bits.Mul64(x2, 0xffffffffffffffff) + var x8 uint64 + var x9 uint64 + x9, x8 = bits.Mul64(x2, 0xffffffffffffffff) + var x10 uint64 + var x11 uint64 + x11, x10 = bits.Mul64(x2, 0xfffffffffffffffe) + var x12 uint64 + var x13 uint64 + x13, x12 = bits.Mul64(x2, 0xffffffff00000000) + var x14 uint64 + var x15 uint64 + x15, x14 = bits.Mul64(x2, 0xffffffff) + var x16 uint64 + var x17 uint64 + x16, x17 = bits.Add64(x15, x12, uint64(0x0)) + var x18 uint64 + var x19 uint64 + x18, x19 = bits.Add64(x13, x10, uint64(p384Uint1(x17))) + var x20 uint64 + var x21 uint64 + x20, x21 = bits.Add64(x11, x8, uint64(p384Uint1(x19))) + var x22 uint64 + var x23 uint64 + x22, x23 = bits.Add64(x9, x6, uint64(p384Uint1(x21))) + var x24 uint64 + var x25 uint64 + x24, x25 = bits.Add64(x7, x4, uint64(p384Uint1(x23))) + var x27 uint64 + _, x27 = bits.Add64(x1, x14, uint64(0x0)) + var x28 uint64 + var x29 uint64 + x28, x29 = bits.Add64(uint64(0x0), x16, uint64(p384Uint1(x27))) + var x30 uint64 + var x31 uint64 + x30, x31 = bits.Add64(uint64(0x0), x18, uint64(p384Uint1(x29))) + var x32 uint64 + var x33 uint64 + x32, x33 = bits.Add64(uint64(0x0), x20, uint64(p384Uint1(x31))) + var x34 uint64 + var x35 uint64 + x34, x35 = bits.Add64(uint64(0x0), x22, uint64(p384Uint1(x33))) + var x36 uint64 + var x37 uint64 + x36, x37 = bits.Add64(uint64(0x0), x24, uint64(p384Uint1(x35))) + var x38 uint64 + var x39 uint64 + x38, x39 = bits.Add64(uint64(0x0), (uint64(p384Uint1(x25)) + x5), uint64(p384Uint1(x37))) + var x40 uint64 + var x41 uint64 + x40, x41 = bits.Add64(x28, arg1[1], uint64(0x0)) + var x42 uint64 + var x43 uint64 + x42, x43 = bits.Add64(x30, uint64(0x0), uint64(p384Uint1(x41))) + var x44 uint64 + var x45 uint64 + x44, x45 = bits.Add64(x32, uint64(0x0), uint64(p384Uint1(x43))) + var x46 uint64 + var x47 uint64 + x46, x47 = bits.Add64(x34, uint64(0x0), uint64(p384Uint1(x45))) + var x48 uint64 + var x49 uint64 + x48, x49 = bits.Add64(x36, uint64(0x0), uint64(p384Uint1(x47))) + var x50 uint64 + var x51 uint64 + x50, x51 = bits.Add64(x38, uint64(0x0), uint64(p384Uint1(x49))) + var x52 uint64 + _, x52 = bits.Mul64(x40, 0x100000001) + var x54 uint64 + var x55 uint64 + x55, x54 = bits.Mul64(x52, 0xffffffffffffffff) + var x56 uint64 + var x57 uint64 + x57, x56 = bits.Mul64(x52, 0xffffffffffffffff) + var x58 uint64 + var x59 uint64 + x59, x58 = bits.Mul64(x52, 0xffffffffffffffff) + var x60 uint64 + var x61 uint64 + x61, x60 = bits.Mul64(x52, 0xfffffffffffffffe) + var x62 uint64 + var x63 uint64 + x63, x62 = bits.Mul64(x52, 0xffffffff00000000) + var x64 uint64 + var x65 uint64 + x65, x64 = bits.Mul64(x52, 0xffffffff) + var x66 uint64 + var x67 uint64 + x66, x67 = bits.Add64(x65, x62, uint64(0x0)) + var x68 uint64 + var x69 uint64 + x68, x69 = bits.Add64(x63, x60, uint64(p384Uint1(x67))) + var x70 uint64 + var x71 uint64 + x70, x71 = bits.Add64(x61, x58, uint64(p384Uint1(x69))) + var x72 uint64 + var x73 uint64 + x72, x73 = bits.Add64(x59, x56, uint64(p384Uint1(x71))) + var x74 uint64 + var x75 uint64 + x74, x75 = bits.Add64(x57, x54, uint64(p384Uint1(x73))) + var x77 uint64 + _, x77 = bits.Add64(x40, x64, uint64(0x0)) + var x78 uint64 + var x79 uint64 + x78, x79 = bits.Add64(x42, x66, uint64(p384Uint1(x77))) + var x80 uint64 + var x81 uint64 + x80, x81 = bits.Add64(x44, x68, uint64(p384Uint1(x79))) + var x82 uint64 + var x83 uint64 + x82, x83 = bits.Add64(x46, x70, uint64(p384Uint1(x81))) + var x84 uint64 + var x85 uint64 + x84, x85 = bits.Add64(x48, x72, uint64(p384Uint1(x83))) + var x86 uint64 + var x87 uint64 + x86, x87 = bits.Add64(x50, x74, uint64(p384Uint1(x85))) + var x88 uint64 + var x89 uint64 + x88, x89 = bits.Add64((uint64(p384Uint1(x51)) + uint64(p384Uint1(x39))), (uint64(p384Uint1(x75)) + x55), uint64(p384Uint1(x87))) + var x90 uint64 + var x91 uint64 + x90, x91 = bits.Add64(x78, arg1[2], uint64(0x0)) + var x92 uint64 + var x93 uint64 + x92, x93 = bits.Add64(x80, uint64(0x0), uint64(p384Uint1(x91))) + var x94 uint64 + var x95 uint64 + x94, x95 = bits.Add64(x82, uint64(0x0), uint64(p384Uint1(x93))) + var x96 uint64 + var x97 uint64 + x96, x97 = bits.Add64(x84, uint64(0x0), uint64(p384Uint1(x95))) + var x98 uint64 + var x99 uint64 + x98, x99 = bits.Add64(x86, uint64(0x0), uint64(p384Uint1(x97))) + var x100 uint64 + var x101 uint64 + x100, x101 = bits.Add64(x88, uint64(0x0), uint64(p384Uint1(x99))) + var x102 uint64 + _, x102 = bits.Mul64(x90, 0x100000001) + var x104 uint64 + var x105 uint64 + x105, x104 = bits.Mul64(x102, 0xffffffffffffffff) + var x106 uint64 + var x107 uint64 + x107, x106 = bits.Mul64(x102, 0xffffffffffffffff) + var x108 uint64 + var x109 uint64 + x109, x108 = bits.Mul64(x102, 0xffffffffffffffff) + var x110 uint64 + var x111 uint64 + x111, x110 = bits.Mul64(x102, 0xfffffffffffffffe) + var x112 uint64 + var x113 uint64 + x113, x112 = bits.Mul64(x102, 0xffffffff00000000) + var x114 uint64 + var x115 uint64 + x115, x114 = bits.Mul64(x102, 0xffffffff) + var x116 uint64 + var x117 uint64 + x116, x117 = bits.Add64(x115, x112, uint64(0x0)) + var x118 uint64 + var x119 uint64 + x118, x119 = bits.Add64(x113, x110, uint64(p384Uint1(x117))) + var x120 uint64 + var x121 uint64 + x120, x121 = bits.Add64(x111, x108, uint64(p384Uint1(x119))) + var x122 uint64 + var x123 uint64 + x122, x123 = bits.Add64(x109, x106, uint64(p384Uint1(x121))) + var x124 uint64 + var x125 uint64 + x124, x125 = bits.Add64(x107, x104, uint64(p384Uint1(x123))) + var x127 uint64 + _, x127 = bits.Add64(x90, x114, uint64(0x0)) + var x128 uint64 + var x129 uint64 + x128, x129 = bits.Add64(x92, x116, uint64(p384Uint1(x127))) + var x130 uint64 + var x131 uint64 + x130, x131 = bits.Add64(x94, x118, uint64(p384Uint1(x129))) + var x132 uint64 + var x133 uint64 + x132, x133 = bits.Add64(x96, x120, uint64(p384Uint1(x131))) + var x134 uint64 + var x135 uint64 + x134, x135 = bits.Add64(x98, x122, uint64(p384Uint1(x133))) + var x136 uint64 + var x137 uint64 + x136, x137 = bits.Add64(x100, x124, uint64(p384Uint1(x135))) + var x138 uint64 + var x139 uint64 + x138, x139 = bits.Add64((uint64(p384Uint1(x101)) + uint64(p384Uint1(x89))), (uint64(p384Uint1(x125)) + x105), uint64(p384Uint1(x137))) + var x140 uint64 + var x141 uint64 + x140, x141 = bits.Add64(x128, arg1[3], uint64(0x0)) + var x142 uint64 + var x143 uint64 + x142, x143 = bits.Add64(x130, uint64(0x0), uint64(p384Uint1(x141))) + var x144 uint64 + var x145 uint64 + x144, x145 = bits.Add64(x132, uint64(0x0), uint64(p384Uint1(x143))) + var x146 uint64 + var x147 uint64 + x146, x147 = bits.Add64(x134, uint64(0x0), uint64(p384Uint1(x145))) + var x148 uint64 + var x149 uint64 + x148, x149 = bits.Add64(x136, uint64(0x0), uint64(p384Uint1(x147))) + var x150 uint64 + var x151 uint64 + x150, x151 = bits.Add64(x138, uint64(0x0), uint64(p384Uint1(x149))) + var x152 uint64 + _, x152 = bits.Mul64(x140, 0x100000001) + var x154 uint64 + var x155 uint64 + x155, x154 = bits.Mul64(x152, 0xffffffffffffffff) + var x156 uint64 + var x157 uint64 + x157, x156 = bits.Mul64(x152, 0xffffffffffffffff) + var x158 uint64 + var x159 uint64 + x159, x158 = bits.Mul64(x152, 0xffffffffffffffff) + var x160 uint64 + var x161 uint64 + x161, x160 = bits.Mul64(x152, 0xfffffffffffffffe) + var x162 uint64 + var x163 uint64 + x163, x162 = bits.Mul64(x152, 0xffffffff00000000) + var x164 uint64 + var x165 uint64 + x165, x164 = bits.Mul64(x152, 0xffffffff) + var x166 uint64 + var x167 uint64 + x166, x167 = bits.Add64(x165, x162, uint64(0x0)) + var x168 uint64 + var x169 uint64 + x168, x169 = bits.Add64(x163, x160, uint64(p384Uint1(x167))) + var x170 uint64 + var x171 uint64 + x170, x171 = bits.Add64(x161, x158, uint64(p384Uint1(x169))) + var x172 uint64 + var x173 uint64 + x172, x173 = bits.Add64(x159, x156, uint64(p384Uint1(x171))) + var x174 uint64 + var x175 uint64 + x174, x175 = bits.Add64(x157, x154, uint64(p384Uint1(x173))) + var x177 uint64 + _, x177 = bits.Add64(x140, x164, uint64(0x0)) + var x178 uint64 + var x179 uint64 + x178, x179 = bits.Add64(x142, x166, uint64(p384Uint1(x177))) + var x180 uint64 + var x181 uint64 + x180, x181 = bits.Add64(x144, x168, uint64(p384Uint1(x179))) + var x182 uint64 + var x183 uint64 + x182, x183 = bits.Add64(x146, x170, uint64(p384Uint1(x181))) + var x184 uint64 + var x185 uint64 + x184, x185 = bits.Add64(x148, x172, uint64(p384Uint1(x183))) + var x186 uint64 + var x187 uint64 + x186, x187 = bits.Add64(x150, x174, uint64(p384Uint1(x185))) + var x188 uint64 + var x189 uint64 + x188, x189 = bits.Add64((uint64(p384Uint1(x151)) + uint64(p384Uint1(x139))), (uint64(p384Uint1(x175)) + x155), uint64(p384Uint1(x187))) + var x190 uint64 + var x191 uint64 + x190, x191 = bits.Add64(x178, arg1[4], uint64(0x0)) + var x192 uint64 + var x193 uint64 + x192, x193 = bits.Add64(x180, uint64(0x0), uint64(p384Uint1(x191))) + var x194 uint64 + var x195 uint64 + x194, x195 = bits.Add64(x182, uint64(0x0), uint64(p384Uint1(x193))) + var x196 uint64 + var x197 uint64 + x196, x197 = bits.Add64(x184, uint64(0x0), uint64(p384Uint1(x195))) + var x198 uint64 + var x199 uint64 + x198, x199 = bits.Add64(x186, uint64(0x0), uint64(p384Uint1(x197))) + var x200 uint64 + var x201 uint64 + x200, x201 = bits.Add64(x188, uint64(0x0), uint64(p384Uint1(x199))) + var x202 uint64 + _, x202 = bits.Mul64(x190, 0x100000001) + var x204 uint64 + var x205 uint64 + x205, x204 = bits.Mul64(x202, 0xffffffffffffffff) + var x206 uint64 + var x207 uint64 + x207, x206 = bits.Mul64(x202, 0xffffffffffffffff) + var x208 uint64 + var x209 uint64 + x209, x208 = bits.Mul64(x202, 0xffffffffffffffff) + var x210 uint64 + var x211 uint64 + x211, x210 = bits.Mul64(x202, 0xfffffffffffffffe) + var x212 uint64 + var x213 uint64 + x213, x212 = bits.Mul64(x202, 0xffffffff00000000) + var x214 uint64 + var x215 uint64 + x215, x214 = bits.Mul64(x202, 0xffffffff) + var x216 uint64 + var x217 uint64 + x216, x217 = bits.Add64(x215, x212, uint64(0x0)) + var x218 uint64 + var x219 uint64 + x218, x219 = bits.Add64(x213, x210, uint64(p384Uint1(x217))) + var x220 uint64 + var x221 uint64 + x220, x221 = bits.Add64(x211, x208, uint64(p384Uint1(x219))) + var x222 uint64 + var x223 uint64 + x222, x223 = bits.Add64(x209, x206, uint64(p384Uint1(x221))) + var x224 uint64 + var x225 uint64 + x224, x225 = bits.Add64(x207, x204, uint64(p384Uint1(x223))) + var x227 uint64 + _, x227 = bits.Add64(x190, x214, uint64(0x0)) + var x228 uint64 + var x229 uint64 + x228, x229 = bits.Add64(x192, x216, uint64(p384Uint1(x227))) + var x230 uint64 + var x231 uint64 + x230, x231 = bits.Add64(x194, x218, uint64(p384Uint1(x229))) + var x232 uint64 + var x233 uint64 + x232, x233 = bits.Add64(x196, x220, uint64(p384Uint1(x231))) + var x234 uint64 + var x235 uint64 + x234, x235 = bits.Add64(x198, x222, uint64(p384Uint1(x233))) + var x236 uint64 + var x237 uint64 + x236, x237 = bits.Add64(x200, x224, uint64(p384Uint1(x235))) + var x238 uint64 + var x239 uint64 + x238, x239 = bits.Add64((uint64(p384Uint1(x201)) + uint64(p384Uint1(x189))), (uint64(p384Uint1(x225)) + x205), uint64(p384Uint1(x237))) + var x240 uint64 + var x241 uint64 + x240, x241 = bits.Add64(x228, arg1[5], uint64(0x0)) + var x242 uint64 + var x243 uint64 + x242, x243 = bits.Add64(x230, uint64(0x0), uint64(p384Uint1(x241))) + var x244 uint64 + var x245 uint64 + x244, x245 = bits.Add64(x232, uint64(0x0), uint64(p384Uint1(x243))) + var x246 uint64 + var x247 uint64 + x246, x247 = bits.Add64(x234, uint64(0x0), uint64(p384Uint1(x245))) + var x248 uint64 + var x249 uint64 + x248, x249 = bits.Add64(x236, uint64(0x0), uint64(p384Uint1(x247))) + var x250 uint64 + var x251 uint64 + x250, x251 = bits.Add64(x238, uint64(0x0), uint64(p384Uint1(x249))) + var x252 uint64 + _, x252 = bits.Mul64(x240, 0x100000001) + var x254 uint64 + var x255 uint64 + x255, x254 = bits.Mul64(x252, 0xffffffffffffffff) + var x256 uint64 + var x257 uint64 + x257, x256 = bits.Mul64(x252, 0xffffffffffffffff) + var x258 uint64 + var x259 uint64 + x259, x258 = bits.Mul64(x252, 0xffffffffffffffff) + var x260 uint64 + var x261 uint64 + x261, x260 = bits.Mul64(x252, 0xfffffffffffffffe) + var x262 uint64 + var x263 uint64 + x263, x262 = bits.Mul64(x252, 0xffffffff00000000) + var x264 uint64 + var x265 uint64 + x265, x264 = bits.Mul64(x252, 0xffffffff) + var x266 uint64 + var x267 uint64 + x266, x267 = bits.Add64(x265, x262, uint64(0x0)) + var x268 uint64 + var x269 uint64 + x268, x269 = bits.Add64(x263, x260, uint64(p384Uint1(x267))) + var x270 uint64 + var x271 uint64 + x270, x271 = bits.Add64(x261, x258, uint64(p384Uint1(x269))) + var x272 uint64 + var x273 uint64 + x272, x273 = bits.Add64(x259, x256, uint64(p384Uint1(x271))) + var x274 uint64 + var x275 uint64 + x274, x275 = bits.Add64(x257, x254, uint64(p384Uint1(x273))) + var x277 uint64 + _, x277 = bits.Add64(x240, x264, uint64(0x0)) + var x278 uint64 + var x279 uint64 + x278, x279 = bits.Add64(x242, x266, uint64(p384Uint1(x277))) + var x280 uint64 + var x281 uint64 + x280, x281 = bits.Add64(x244, x268, uint64(p384Uint1(x279))) + var x282 uint64 + var x283 uint64 + x282, x283 = bits.Add64(x246, x270, uint64(p384Uint1(x281))) + var x284 uint64 + var x285 uint64 + x284, x285 = bits.Add64(x248, x272, uint64(p384Uint1(x283))) + var x286 uint64 + var x287 uint64 + x286, x287 = bits.Add64(x250, x274, uint64(p384Uint1(x285))) + var x288 uint64 + var x289 uint64 + x288, x289 = bits.Add64((uint64(p384Uint1(x251)) + uint64(p384Uint1(x239))), (uint64(p384Uint1(x275)) + x255), uint64(p384Uint1(x287))) + var x290 uint64 + var x291 uint64 + x290, x291 = bits.Sub64(x278, 0xffffffff, uint64(0x0)) + var x292 uint64 + var x293 uint64 + x292, x293 = bits.Sub64(x280, 0xffffffff00000000, uint64(p384Uint1(x291))) + var x294 uint64 + var x295 uint64 + x294, x295 = bits.Sub64(x282, 0xfffffffffffffffe, uint64(p384Uint1(x293))) + var x296 uint64 + var x297 uint64 + x296, x297 = bits.Sub64(x284, 0xffffffffffffffff, uint64(p384Uint1(x295))) + var x298 uint64 + var x299 uint64 + x298, x299 = bits.Sub64(x286, 0xffffffffffffffff, uint64(p384Uint1(x297))) + var x300 uint64 + var x301 uint64 + x300, x301 = bits.Sub64(x288, 0xffffffffffffffff, uint64(p384Uint1(x299))) + var x303 uint64 + _, x303 = bits.Sub64(uint64(p384Uint1(x289)), uint64(0x0), uint64(p384Uint1(x301))) + var x304 uint64 + p384CmovznzU64(&x304, p384Uint1(x303), x290, x278) + var x305 uint64 + p384CmovznzU64(&x305, p384Uint1(x303), x292, x280) + var x306 uint64 + p384CmovznzU64(&x306, p384Uint1(x303), x294, x282) + var x307 uint64 + p384CmovznzU64(&x307, p384Uint1(x303), x296, x284) + var x308 uint64 + p384CmovznzU64(&x308, p384Uint1(x303), x298, x286) + var x309 uint64 + p384CmovznzU64(&x309, p384Uint1(x303), x300, x288) + out1[0] = x304 + out1[1] = x305 + out1[2] = x306 + out1[3] = x307 + out1[4] = x308 + out1[5] = x309 +} + +// p384ToMontgomery translates a field element into the Montgomery domain. +// +// Preconditions: +// 0 ≤ eval arg1 < m +// Postconditions: +// eval (from_montgomery out1) mod m = eval arg1 mod m +// 0 ≤ eval out1 < m +// +func p384ToMontgomery(out1 *p384MontgomeryDomainFieldElement, arg1 *p384NonMontgomeryDomainFieldElement) { + x1 := arg1[1] + x2 := arg1[2] + x3 := arg1[3] + x4 := arg1[4] + x5 := arg1[5] + x6 := arg1[0] + var x7 uint64 + var x8 uint64 + x8, x7 = bits.Mul64(x6, 0x200000000) + var x9 uint64 + var x10 uint64 + x10, x9 = bits.Mul64(x6, 0xfffffffe00000000) + var x11 uint64 + var x12 uint64 + x12, x11 = bits.Mul64(x6, 0x200000000) + var x13 uint64 + var x14 uint64 + x14, x13 = bits.Mul64(x6, 0xfffffffe00000001) + var x15 uint64 + var x16 uint64 + x15, x16 = bits.Add64(x14, x11, uint64(0x0)) + var x17 uint64 + var x18 uint64 + x17, x18 = bits.Add64(x12, x9, uint64(p384Uint1(x16))) + var x19 uint64 + var x20 uint64 + x19, x20 = bits.Add64(x10, x7, uint64(p384Uint1(x18))) + var x21 uint64 + var x22 uint64 + x21, x22 = bits.Add64(x8, x6, uint64(p384Uint1(x20))) + var x23 uint64 + _, x23 = bits.Mul64(x13, 0x100000001) + var x25 uint64 + var x26 uint64 + x26, x25 = bits.Mul64(x23, 0xffffffffffffffff) + var x27 uint64 + var x28 uint64 + x28, x27 = bits.Mul64(x23, 0xffffffffffffffff) + var x29 uint64 + var x30 uint64 + x30, x29 = bits.Mul64(x23, 0xffffffffffffffff) + var x31 uint64 + var x32 uint64 + x32, x31 = bits.Mul64(x23, 0xfffffffffffffffe) + var x33 uint64 + var x34 uint64 + x34, x33 = bits.Mul64(x23, 0xffffffff00000000) + var x35 uint64 + var x36 uint64 + x36, x35 = bits.Mul64(x23, 0xffffffff) + var x37 uint64 + var x38 uint64 + x37, x38 = bits.Add64(x36, x33, uint64(0x0)) + var x39 uint64 + var x40 uint64 + x39, x40 = bits.Add64(x34, x31, uint64(p384Uint1(x38))) + var x41 uint64 + var x42 uint64 + x41, x42 = bits.Add64(x32, x29, uint64(p384Uint1(x40))) + var x43 uint64 + var x44 uint64 + x43, x44 = bits.Add64(x30, x27, uint64(p384Uint1(x42))) + var x45 uint64 + var x46 uint64 + x45, x46 = bits.Add64(x28, x25, uint64(p384Uint1(x44))) + var x48 uint64 + _, x48 = bits.Add64(x13, x35, uint64(0x0)) + var x49 uint64 + var x50 uint64 + x49, x50 = bits.Add64(x15, x37, uint64(p384Uint1(x48))) + var x51 uint64 + var x52 uint64 + x51, x52 = bits.Add64(x17, x39, uint64(p384Uint1(x50))) + var x53 uint64 + var x54 uint64 + x53, x54 = bits.Add64(x19, x41, uint64(p384Uint1(x52))) + var x55 uint64 + var x56 uint64 + x55, x56 = bits.Add64(x21, x43, uint64(p384Uint1(x54))) + var x57 uint64 + var x58 uint64 + x57, x58 = bits.Add64(uint64(p384Uint1(x22)), x45, uint64(p384Uint1(x56))) + var x59 uint64 + var x60 uint64 + x59, x60 = bits.Add64(uint64(0x0), (uint64(p384Uint1(x46)) + x26), uint64(p384Uint1(x58))) + var x61 uint64 + var x62 uint64 + x62, x61 = bits.Mul64(x1, 0x200000000) + var x63 uint64 + var x64 uint64 + x64, x63 = bits.Mul64(x1, 0xfffffffe00000000) + var x65 uint64 + var x66 uint64 + x66, x65 = bits.Mul64(x1, 0x200000000) + var x67 uint64 + var x68 uint64 + x68, x67 = bits.Mul64(x1, 0xfffffffe00000001) + var x69 uint64 + var x70 uint64 + x69, x70 = bits.Add64(x68, x65, uint64(0x0)) + var x71 uint64 + var x72 uint64 + x71, x72 = bits.Add64(x66, x63, uint64(p384Uint1(x70))) + var x73 uint64 + var x74 uint64 + x73, x74 = bits.Add64(x64, x61, uint64(p384Uint1(x72))) + var x75 uint64 + var x76 uint64 + x75, x76 = bits.Add64(x62, x1, uint64(p384Uint1(x74))) + var x77 uint64 + var x78 uint64 + x77, x78 = bits.Add64(x49, x67, uint64(0x0)) + var x79 uint64 + var x80 uint64 + x79, x80 = bits.Add64(x51, x69, uint64(p384Uint1(x78))) + var x81 uint64 + var x82 uint64 + x81, x82 = bits.Add64(x53, x71, uint64(p384Uint1(x80))) + var x83 uint64 + var x84 uint64 + x83, x84 = bits.Add64(x55, x73, uint64(p384Uint1(x82))) + var x85 uint64 + var x86 uint64 + x85, x86 = bits.Add64(x57, x75, uint64(p384Uint1(x84))) + var x87 uint64 + var x88 uint64 + x87, x88 = bits.Add64(x59, uint64(p384Uint1(x76)), uint64(p384Uint1(x86))) + var x89 uint64 + _, x89 = bits.Mul64(x77, 0x100000001) + var x91 uint64 + var x92 uint64 + x92, x91 = bits.Mul64(x89, 0xffffffffffffffff) + var x93 uint64 + var x94 uint64 + x94, x93 = bits.Mul64(x89, 0xffffffffffffffff) + var x95 uint64 + var x96 uint64 + x96, x95 = bits.Mul64(x89, 0xffffffffffffffff) + var x97 uint64 + var x98 uint64 + x98, x97 = bits.Mul64(x89, 0xfffffffffffffffe) + var x99 uint64 + var x100 uint64 + x100, x99 = bits.Mul64(x89, 0xffffffff00000000) + var x101 uint64 + var x102 uint64 + x102, x101 = bits.Mul64(x89, 0xffffffff) + var x103 uint64 + var x104 uint64 + x103, x104 = bits.Add64(x102, x99, uint64(0x0)) + var x105 uint64 + var x106 uint64 + x105, x106 = bits.Add64(x100, x97, uint64(p384Uint1(x104))) + var x107 uint64 + var x108 uint64 + x107, x108 = bits.Add64(x98, x95, uint64(p384Uint1(x106))) + var x109 uint64 + var x110 uint64 + x109, x110 = bits.Add64(x96, x93, uint64(p384Uint1(x108))) + var x111 uint64 + var x112 uint64 + x111, x112 = bits.Add64(x94, x91, uint64(p384Uint1(x110))) + var x114 uint64 + _, x114 = bits.Add64(x77, x101, uint64(0x0)) + var x115 uint64 + var x116 uint64 + x115, x116 = bits.Add64(x79, x103, uint64(p384Uint1(x114))) + var x117 uint64 + var x118 uint64 + x117, x118 = bits.Add64(x81, x105, uint64(p384Uint1(x116))) + var x119 uint64 + var x120 uint64 + x119, x120 = bits.Add64(x83, x107, uint64(p384Uint1(x118))) + var x121 uint64 + var x122 uint64 + x121, x122 = bits.Add64(x85, x109, uint64(p384Uint1(x120))) + var x123 uint64 + var x124 uint64 + x123, x124 = bits.Add64(x87, x111, uint64(p384Uint1(x122))) + var x125 uint64 + var x126 uint64 + x125, x126 = bits.Add64((uint64(p384Uint1(x88)) + uint64(p384Uint1(x60))), (uint64(p384Uint1(x112)) + x92), uint64(p384Uint1(x124))) + var x127 uint64 + var x128 uint64 + x128, x127 = bits.Mul64(x2, 0x200000000) + var x129 uint64 + var x130 uint64 + x130, x129 = bits.Mul64(x2, 0xfffffffe00000000) + var x131 uint64 + var x132 uint64 + x132, x131 = bits.Mul64(x2, 0x200000000) + var x133 uint64 + var x134 uint64 + x134, x133 = bits.Mul64(x2, 0xfffffffe00000001) + var x135 uint64 + var x136 uint64 + x135, x136 = bits.Add64(x134, x131, uint64(0x0)) + var x137 uint64 + var x138 uint64 + x137, x138 = bits.Add64(x132, x129, uint64(p384Uint1(x136))) + var x139 uint64 + var x140 uint64 + x139, x140 = bits.Add64(x130, x127, uint64(p384Uint1(x138))) + var x141 uint64 + var x142 uint64 + x141, x142 = bits.Add64(x128, x2, uint64(p384Uint1(x140))) + var x143 uint64 + var x144 uint64 + x143, x144 = bits.Add64(x115, x133, uint64(0x0)) + var x145 uint64 + var x146 uint64 + x145, x146 = bits.Add64(x117, x135, uint64(p384Uint1(x144))) + var x147 uint64 + var x148 uint64 + x147, x148 = bits.Add64(x119, x137, uint64(p384Uint1(x146))) + var x149 uint64 + var x150 uint64 + x149, x150 = bits.Add64(x121, x139, uint64(p384Uint1(x148))) + var x151 uint64 + var x152 uint64 + x151, x152 = bits.Add64(x123, x141, uint64(p384Uint1(x150))) + var x153 uint64 + var x154 uint64 + x153, x154 = bits.Add64(x125, uint64(p384Uint1(x142)), uint64(p384Uint1(x152))) + var x155 uint64 + _, x155 = bits.Mul64(x143, 0x100000001) + var x157 uint64 + var x158 uint64 + x158, x157 = bits.Mul64(x155, 0xffffffffffffffff) + var x159 uint64 + var x160 uint64 + x160, x159 = bits.Mul64(x155, 0xffffffffffffffff) + var x161 uint64 + var x162 uint64 + x162, x161 = bits.Mul64(x155, 0xffffffffffffffff) + var x163 uint64 + var x164 uint64 + x164, x163 = bits.Mul64(x155, 0xfffffffffffffffe) + var x165 uint64 + var x166 uint64 + x166, x165 = bits.Mul64(x155, 0xffffffff00000000) + var x167 uint64 + var x168 uint64 + x168, x167 = bits.Mul64(x155, 0xffffffff) + var x169 uint64 + var x170 uint64 + x169, x170 = bits.Add64(x168, x165, uint64(0x0)) + var x171 uint64 + var x172 uint64 + x171, x172 = bits.Add64(x166, x163, uint64(p384Uint1(x170))) + var x173 uint64 + var x174 uint64 + x173, x174 = bits.Add64(x164, x161, uint64(p384Uint1(x172))) + var x175 uint64 + var x176 uint64 + x175, x176 = bits.Add64(x162, x159, uint64(p384Uint1(x174))) + var x177 uint64 + var x178 uint64 + x177, x178 = bits.Add64(x160, x157, uint64(p384Uint1(x176))) + var x180 uint64 + _, x180 = bits.Add64(x143, x167, uint64(0x0)) + var x181 uint64 + var x182 uint64 + x181, x182 = bits.Add64(x145, x169, uint64(p384Uint1(x180))) + var x183 uint64 + var x184 uint64 + x183, x184 = bits.Add64(x147, x171, uint64(p384Uint1(x182))) + var x185 uint64 + var x186 uint64 + x185, x186 = bits.Add64(x149, x173, uint64(p384Uint1(x184))) + var x187 uint64 + var x188 uint64 + x187, x188 = bits.Add64(x151, x175, uint64(p384Uint1(x186))) + var x189 uint64 + var x190 uint64 + x189, x190 = bits.Add64(x153, x177, uint64(p384Uint1(x188))) + var x191 uint64 + var x192 uint64 + x191, x192 = bits.Add64((uint64(p384Uint1(x154)) + uint64(p384Uint1(x126))), (uint64(p384Uint1(x178)) + x158), uint64(p384Uint1(x190))) + var x193 uint64 + var x194 uint64 + x194, x193 = bits.Mul64(x3, 0x200000000) + var x195 uint64 + var x196 uint64 + x196, x195 = bits.Mul64(x3, 0xfffffffe00000000) + var x197 uint64 + var x198 uint64 + x198, x197 = bits.Mul64(x3, 0x200000000) + var x199 uint64 + var x200 uint64 + x200, x199 = bits.Mul64(x3, 0xfffffffe00000001) + var x201 uint64 + var x202 uint64 + x201, x202 = bits.Add64(x200, x197, uint64(0x0)) + var x203 uint64 + var x204 uint64 + x203, x204 = bits.Add64(x198, x195, uint64(p384Uint1(x202))) + var x205 uint64 + var x206 uint64 + x205, x206 = bits.Add64(x196, x193, uint64(p384Uint1(x204))) + var x207 uint64 + var x208 uint64 + x207, x208 = bits.Add64(x194, x3, uint64(p384Uint1(x206))) + var x209 uint64 + var x210 uint64 + x209, x210 = bits.Add64(x181, x199, uint64(0x0)) + var x211 uint64 + var x212 uint64 + x211, x212 = bits.Add64(x183, x201, uint64(p384Uint1(x210))) + var x213 uint64 + var x214 uint64 + x213, x214 = bits.Add64(x185, x203, uint64(p384Uint1(x212))) + var x215 uint64 + var x216 uint64 + x215, x216 = bits.Add64(x187, x205, uint64(p384Uint1(x214))) + var x217 uint64 + var x218 uint64 + x217, x218 = bits.Add64(x189, x207, uint64(p384Uint1(x216))) + var x219 uint64 + var x220 uint64 + x219, x220 = bits.Add64(x191, uint64(p384Uint1(x208)), uint64(p384Uint1(x218))) + var x221 uint64 + _, x221 = bits.Mul64(x209, 0x100000001) + var x223 uint64 + var x224 uint64 + x224, x223 = bits.Mul64(x221, 0xffffffffffffffff) + var x225 uint64 + var x226 uint64 + x226, x225 = bits.Mul64(x221, 0xffffffffffffffff) + var x227 uint64 + var x228 uint64 + x228, x227 = bits.Mul64(x221, 0xffffffffffffffff) + var x229 uint64 + var x230 uint64 + x230, x229 = bits.Mul64(x221, 0xfffffffffffffffe) + var x231 uint64 + var x232 uint64 + x232, x231 = bits.Mul64(x221, 0xffffffff00000000) + var x233 uint64 + var x234 uint64 + x234, x233 = bits.Mul64(x221, 0xffffffff) + var x235 uint64 + var x236 uint64 + x235, x236 = bits.Add64(x234, x231, uint64(0x0)) + var x237 uint64 + var x238 uint64 + x237, x238 = bits.Add64(x232, x229, uint64(p384Uint1(x236))) + var x239 uint64 + var x240 uint64 + x239, x240 = bits.Add64(x230, x227, uint64(p384Uint1(x238))) + var x241 uint64 + var x242 uint64 + x241, x242 = bits.Add64(x228, x225, uint64(p384Uint1(x240))) + var x243 uint64 + var x244 uint64 + x243, x244 = bits.Add64(x226, x223, uint64(p384Uint1(x242))) + var x246 uint64 + _, x246 = bits.Add64(x209, x233, uint64(0x0)) + var x247 uint64 + var x248 uint64 + x247, x248 = bits.Add64(x211, x235, uint64(p384Uint1(x246))) + var x249 uint64 + var x250 uint64 + x249, x250 = bits.Add64(x213, x237, uint64(p384Uint1(x248))) + var x251 uint64 + var x252 uint64 + x251, x252 = bits.Add64(x215, x239, uint64(p384Uint1(x250))) + var x253 uint64 + var x254 uint64 + x253, x254 = bits.Add64(x217, x241, uint64(p384Uint1(x252))) + var x255 uint64 + var x256 uint64 + x255, x256 = bits.Add64(x219, x243, uint64(p384Uint1(x254))) + var x257 uint64 + var x258 uint64 + x257, x258 = bits.Add64((uint64(p384Uint1(x220)) + uint64(p384Uint1(x192))), (uint64(p384Uint1(x244)) + x224), uint64(p384Uint1(x256))) + var x259 uint64 + var x260 uint64 + x260, x259 = bits.Mul64(x4, 0x200000000) + var x261 uint64 + var x262 uint64 + x262, x261 = bits.Mul64(x4, 0xfffffffe00000000) + var x263 uint64 + var x264 uint64 + x264, x263 = bits.Mul64(x4, 0x200000000) + var x265 uint64 + var x266 uint64 + x266, x265 = bits.Mul64(x4, 0xfffffffe00000001) + var x267 uint64 + var x268 uint64 + x267, x268 = bits.Add64(x266, x263, uint64(0x0)) + var x269 uint64 + var x270 uint64 + x269, x270 = bits.Add64(x264, x261, uint64(p384Uint1(x268))) + var x271 uint64 + var x272 uint64 + x271, x272 = bits.Add64(x262, x259, uint64(p384Uint1(x270))) + var x273 uint64 + var x274 uint64 + x273, x274 = bits.Add64(x260, x4, uint64(p384Uint1(x272))) + var x275 uint64 + var x276 uint64 + x275, x276 = bits.Add64(x247, x265, uint64(0x0)) + var x277 uint64 + var x278 uint64 + x277, x278 = bits.Add64(x249, x267, uint64(p384Uint1(x276))) + var x279 uint64 + var x280 uint64 + x279, x280 = bits.Add64(x251, x269, uint64(p384Uint1(x278))) + var x281 uint64 + var x282 uint64 + x281, x282 = bits.Add64(x253, x271, uint64(p384Uint1(x280))) + var x283 uint64 + var x284 uint64 + x283, x284 = bits.Add64(x255, x273, uint64(p384Uint1(x282))) + var x285 uint64 + var x286 uint64 + x285, x286 = bits.Add64(x257, uint64(p384Uint1(x274)), uint64(p384Uint1(x284))) + var x287 uint64 + _, x287 = bits.Mul64(x275, 0x100000001) + var x289 uint64 + var x290 uint64 + x290, x289 = bits.Mul64(x287, 0xffffffffffffffff) + var x291 uint64 + var x292 uint64 + x292, x291 = bits.Mul64(x287, 0xffffffffffffffff) + var x293 uint64 + var x294 uint64 + x294, x293 = bits.Mul64(x287, 0xffffffffffffffff) + var x295 uint64 + var x296 uint64 + x296, x295 = bits.Mul64(x287, 0xfffffffffffffffe) + var x297 uint64 + var x298 uint64 + x298, x297 = bits.Mul64(x287, 0xffffffff00000000) + var x299 uint64 + var x300 uint64 + x300, x299 = bits.Mul64(x287, 0xffffffff) + var x301 uint64 + var x302 uint64 + x301, x302 = bits.Add64(x300, x297, uint64(0x0)) + var x303 uint64 + var x304 uint64 + x303, x304 = bits.Add64(x298, x295, uint64(p384Uint1(x302))) + var x305 uint64 + var x306 uint64 + x305, x306 = bits.Add64(x296, x293, uint64(p384Uint1(x304))) + var x307 uint64 + var x308 uint64 + x307, x308 = bits.Add64(x294, x291, uint64(p384Uint1(x306))) + var x309 uint64 + var x310 uint64 + x309, x310 = bits.Add64(x292, x289, uint64(p384Uint1(x308))) + var x312 uint64 + _, x312 = bits.Add64(x275, x299, uint64(0x0)) + var x313 uint64 + var x314 uint64 + x313, x314 = bits.Add64(x277, x301, uint64(p384Uint1(x312))) + var x315 uint64 + var x316 uint64 + x315, x316 = bits.Add64(x279, x303, uint64(p384Uint1(x314))) + var x317 uint64 + var x318 uint64 + x317, x318 = bits.Add64(x281, x305, uint64(p384Uint1(x316))) + var x319 uint64 + var x320 uint64 + x319, x320 = bits.Add64(x283, x307, uint64(p384Uint1(x318))) + var x321 uint64 + var x322 uint64 + x321, x322 = bits.Add64(x285, x309, uint64(p384Uint1(x320))) + var x323 uint64 + var x324 uint64 + x323, x324 = bits.Add64((uint64(p384Uint1(x286)) + uint64(p384Uint1(x258))), (uint64(p384Uint1(x310)) + x290), uint64(p384Uint1(x322))) + var x325 uint64 + var x326 uint64 + x326, x325 = bits.Mul64(x5, 0x200000000) + var x327 uint64 + var x328 uint64 + x328, x327 = bits.Mul64(x5, 0xfffffffe00000000) + var x329 uint64 + var x330 uint64 + x330, x329 = bits.Mul64(x5, 0x200000000) + var x331 uint64 + var x332 uint64 + x332, x331 = bits.Mul64(x5, 0xfffffffe00000001) + var x333 uint64 + var x334 uint64 + x333, x334 = bits.Add64(x332, x329, uint64(0x0)) + var x335 uint64 + var x336 uint64 + x335, x336 = bits.Add64(x330, x327, uint64(p384Uint1(x334))) + var x337 uint64 + var x338 uint64 + x337, x338 = bits.Add64(x328, x325, uint64(p384Uint1(x336))) + var x339 uint64 + var x340 uint64 + x339, x340 = bits.Add64(x326, x5, uint64(p384Uint1(x338))) + var x341 uint64 + var x342 uint64 + x341, x342 = bits.Add64(x313, x331, uint64(0x0)) + var x343 uint64 + var x344 uint64 + x343, x344 = bits.Add64(x315, x333, uint64(p384Uint1(x342))) + var x345 uint64 + var x346 uint64 + x345, x346 = bits.Add64(x317, x335, uint64(p384Uint1(x344))) + var x347 uint64 + var x348 uint64 + x347, x348 = bits.Add64(x319, x337, uint64(p384Uint1(x346))) + var x349 uint64 + var x350 uint64 + x349, x350 = bits.Add64(x321, x339, uint64(p384Uint1(x348))) + var x351 uint64 + var x352 uint64 + x351, x352 = bits.Add64(x323, uint64(p384Uint1(x340)), uint64(p384Uint1(x350))) + var x353 uint64 + _, x353 = bits.Mul64(x341, 0x100000001) + var x355 uint64 + var x356 uint64 + x356, x355 = bits.Mul64(x353, 0xffffffffffffffff) + var x357 uint64 + var x358 uint64 + x358, x357 = bits.Mul64(x353, 0xffffffffffffffff) + var x359 uint64 + var x360 uint64 + x360, x359 = bits.Mul64(x353, 0xffffffffffffffff) + var x361 uint64 + var x362 uint64 + x362, x361 = bits.Mul64(x353, 0xfffffffffffffffe) + var x363 uint64 + var x364 uint64 + x364, x363 = bits.Mul64(x353, 0xffffffff00000000) + var x365 uint64 + var x366 uint64 + x366, x365 = bits.Mul64(x353, 0xffffffff) + var x367 uint64 + var x368 uint64 + x367, x368 = bits.Add64(x366, x363, uint64(0x0)) + var x369 uint64 + var x370 uint64 + x369, x370 = bits.Add64(x364, x361, uint64(p384Uint1(x368))) + var x371 uint64 + var x372 uint64 + x371, x372 = bits.Add64(x362, x359, uint64(p384Uint1(x370))) + var x373 uint64 + var x374 uint64 + x373, x374 = bits.Add64(x360, x357, uint64(p384Uint1(x372))) + var x375 uint64 + var x376 uint64 + x375, x376 = bits.Add64(x358, x355, uint64(p384Uint1(x374))) + var x378 uint64 + _, x378 = bits.Add64(x341, x365, uint64(0x0)) + var x379 uint64 + var x380 uint64 + x379, x380 = bits.Add64(x343, x367, uint64(p384Uint1(x378))) + var x381 uint64 + var x382 uint64 + x381, x382 = bits.Add64(x345, x369, uint64(p384Uint1(x380))) + var x383 uint64 + var x384 uint64 + x383, x384 = bits.Add64(x347, x371, uint64(p384Uint1(x382))) + var x385 uint64 + var x386 uint64 + x385, x386 = bits.Add64(x349, x373, uint64(p384Uint1(x384))) + var x387 uint64 + var x388 uint64 + x387, x388 = bits.Add64(x351, x375, uint64(p384Uint1(x386))) + var x389 uint64 + var x390 uint64 + x389, x390 = bits.Add64((uint64(p384Uint1(x352)) + uint64(p384Uint1(x324))), (uint64(p384Uint1(x376)) + x356), uint64(p384Uint1(x388))) + var x391 uint64 + var x392 uint64 + x391, x392 = bits.Sub64(x379, 0xffffffff, uint64(0x0)) + var x393 uint64 + var x394 uint64 + x393, x394 = bits.Sub64(x381, 0xffffffff00000000, uint64(p384Uint1(x392))) + var x395 uint64 + var x396 uint64 + x395, x396 = bits.Sub64(x383, 0xfffffffffffffffe, uint64(p384Uint1(x394))) + var x397 uint64 + var x398 uint64 + x397, x398 = bits.Sub64(x385, 0xffffffffffffffff, uint64(p384Uint1(x396))) + var x399 uint64 + var x400 uint64 + x399, x400 = bits.Sub64(x387, 0xffffffffffffffff, uint64(p384Uint1(x398))) + var x401 uint64 + var x402 uint64 + x401, x402 = bits.Sub64(x389, 0xffffffffffffffff, uint64(p384Uint1(x400))) + var x404 uint64 + _, x404 = bits.Sub64(uint64(p384Uint1(x390)), uint64(0x0), uint64(p384Uint1(x402))) + var x405 uint64 + p384CmovznzU64(&x405, p384Uint1(x404), x391, x379) + var x406 uint64 + p384CmovznzU64(&x406, p384Uint1(x404), x393, x381) + var x407 uint64 + p384CmovznzU64(&x407, p384Uint1(x404), x395, x383) + var x408 uint64 + p384CmovznzU64(&x408, p384Uint1(x404), x397, x385) + var x409 uint64 + p384CmovznzU64(&x409, p384Uint1(x404), x399, x387) + var x410 uint64 + p384CmovznzU64(&x410, p384Uint1(x404), x401, x389) + out1[0] = x405 + out1[1] = x406 + out1[2] = x407 + out1[3] = x408 + out1[4] = x409 + out1[5] = x410 +} + +// p384Selectznz is a multi-limb conditional select. +// +// Postconditions: +// eval out1 = (if arg1 = 0 then eval arg2 else eval arg3) +// +// Input Bounds: +// arg1: [0x0 ~> 0x1] +// arg2: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]] +// arg3: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]] +// Output Bounds: +// out1: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]] +func p384Selectznz(out1 *[6]uint64, arg1 p384Uint1, arg2 *[6]uint64, arg3 *[6]uint64) { + var x1 uint64 + p384CmovznzU64(&x1, arg1, arg2[0], arg3[0]) + var x2 uint64 + p384CmovznzU64(&x2, arg1, arg2[1], arg3[1]) + var x3 uint64 + p384CmovznzU64(&x3, arg1, arg2[2], arg3[2]) + var x4 uint64 + p384CmovznzU64(&x4, arg1, arg2[3], arg3[3]) + var x5 uint64 + p384CmovznzU64(&x5, arg1, arg2[4], arg3[4]) + var x6 uint64 + p384CmovznzU64(&x6, arg1, arg2[5], arg3[5]) + out1[0] = x1 + out1[1] = x2 + out1[2] = x3 + out1[3] = x4 + out1[4] = x5 + out1[5] = x6 +} + +// p384ToBytes serializes a field element NOT in the Montgomery domain to bytes in little-endian order. +// +// Preconditions: +// 0 ≤ eval arg1 < m +// Postconditions: +// out1 = map (λ x, ⌊((eval arg1 mod m) mod 2^(8 * (x + 1))) / 2^(8 * x)⌋) [0..47] +// +// Input Bounds: +// arg1: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]] +// Output Bounds: +// out1: [[0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff]] +func p384ToBytes(out1 *[48]uint8, arg1 *[6]uint64) { + x1 := arg1[5] + x2 := arg1[4] + x3 := arg1[3] + x4 := arg1[2] + x5 := arg1[1] + x6 := arg1[0] + x7 := (uint8(x6) & 0xff) + x8 := (x6 >> 8) + x9 := (uint8(x8) & 0xff) + x10 := (x8 >> 8) + x11 := (uint8(x10) & 0xff) + x12 := (x10 >> 8) + x13 := (uint8(x12) & 0xff) + x14 := (x12 >> 8) + x15 := (uint8(x14) & 0xff) + x16 := (x14 >> 8) + x17 := (uint8(x16) & 0xff) + x18 := (x16 >> 8) + x19 := (uint8(x18) & 0xff) + x20 := uint8((x18 >> 8)) + x21 := (uint8(x5) & 0xff) + x22 := (x5 >> 8) + x23 := (uint8(x22) & 0xff) + x24 := (x22 >> 8) + x25 := (uint8(x24) & 0xff) + x26 := (x24 >> 8) + x27 := (uint8(x26) & 0xff) + x28 := (x26 >> 8) + x29 := (uint8(x28) & 0xff) + x30 := (x28 >> 8) + x31 := (uint8(x30) & 0xff) + x32 := (x30 >> 8) + x33 := (uint8(x32) & 0xff) + x34 := uint8((x32 >> 8)) + x35 := (uint8(x4) & 0xff) + x36 := (x4 >> 8) + x37 := (uint8(x36) & 0xff) + x38 := (x36 >> 8) + x39 := (uint8(x38) & 0xff) + x40 := (x38 >> 8) + x41 := (uint8(x40) & 0xff) + x42 := (x40 >> 8) + x43 := (uint8(x42) & 0xff) + x44 := (x42 >> 8) + x45 := (uint8(x44) & 0xff) + x46 := (x44 >> 8) + x47 := (uint8(x46) & 0xff) + x48 := uint8((x46 >> 8)) + x49 := (uint8(x3) & 0xff) + x50 := (x3 >> 8) + x51 := (uint8(x50) & 0xff) + x52 := (x50 >> 8) + x53 := (uint8(x52) & 0xff) + x54 := (x52 >> 8) + x55 := (uint8(x54) & 0xff) + x56 := (x54 >> 8) + x57 := (uint8(x56) & 0xff) + x58 := (x56 >> 8) + x59 := (uint8(x58) & 0xff) + x60 := (x58 >> 8) + x61 := (uint8(x60) & 0xff) + x62 := uint8((x60 >> 8)) + x63 := (uint8(x2) & 0xff) + x64 := (x2 >> 8) + x65 := (uint8(x64) & 0xff) + x66 := (x64 >> 8) + x67 := (uint8(x66) & 0xff) + x68 := (x66 >> 8) + x69 := (uint8(x68) & 0xff) + x70 := (x68 >> 8) + x71 := (uint8(x70) & 0xff) + x72 := (x70 >> 8) + x73 := (uint8(x72) & 0xff) + x74 := (x72 >> 8) + x75 := (uint8(x74) & 0xff) + x76 := uint8((x74 >> 8)) + x77 := (uint8(x1) & 0xff) + x78 := (x1 >> 8) + x79 := (uint8(x78) & 0xff) + x80 := (x78 >> 8) + x81 := (uint8(x80) & 0xff) + x82 := (x80 >> 8) + x83 := (uint8(x82) & 0xff) + x84 := (x82 >> 8) + x85 := (uint8(x84) & 0xff) + x86 := (x84 >> 8) + x87 := (uint8(x86) & 0xff) + x88 := (x86 >> 8) + x89 := (uint8(x88) & 0xff) + x90 := uint8((x88 >> 8)) + out1[0] = x7 + out1[1] = x9 + out1[2] = x11 + out1[3] = x13 + out1[4] = x15 + out1[5] = x17 + out1[6] = x19 + out1[7] = x20 + out1[8] = x21 + out1[9] = x23 + out1[10] = x25 + out1[11] = x27 + out1[12] = x29 + out1[13] = x31 + out1[14] = x33 + out1[15] = x34 + out1[16] = x35 + out1[17] = x37 + out1[18] = x39 + out1[19] = x41 + out1[20] = x43 + out1[21] = x45 + out1[22] = x47 + out1[23] = x48 + out1[24] = x49 + out1[25] = x51 + out1[26] = x53 + out1[27] = x55 + out1[28] = x57 + out1[29] = x59 + out1[30] = x61 + out1[31] = x62 + out1[32] = x63 + out1[33] = x65 + out1[34] = x67 + out1[35] = x69 + out1[36] = x71 + out1[37] = x73 + out1[38] = x75 + out1[39] = x76 + out1[40] = x77 + out1[41] = x79 + out1[42] = x81 + out1[43] = x83 + out1[44] = x85 + out1[45] = x87 + out1[46] = x89 + out1[47] = x90 +} + +// p384FromBytes deserializes a field element NOT in the Montgomery domain from bytes in little-endian order. +// +// Preconditions: +// 0 ≤ bytes_eval arg1 < m +// Postconditions: +// eval out1 mod m = bytes_eval arg1 mod m +// 0 ≤ eval out1 < m +// +// Input Bounds: +// arg1: [[0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff]] +// Output Bounds: +// out1: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]] +func p384FromBytes(out1 *[6]uint64, arg1 *[48]uint8) { + x1 := (uint64(arg1[47]) << 56) + x2 := (uint64(arg1[46]) << 48) + x3 := (uint64(arg1[45]) << 40) + x4 := (uint64(arg1[44]) << 32) + x5 := (uint64(arg1[43]) << 24) + x6 := (uint64(arg1[42]) << 16) + x7 := (uint64(arg1[41]) << 8) + x8 := arg1[40] + x9 := (uint64(arg1[39]) << 56) + x10 := (uint64(arg1[38]) << 48) + x11 := (uint64(arg1[37]) << 40) + x12 := (uint64(arg1[36]) << 32) + x13 := (uint64(arg1[35]) << 24) + x14 := (uint64(arg1[34]) << 16) + x15 := (uint64(arg1[33]) << 8) + x16 := arg1[32] + x17 := (uint64(arg1[31]) << 56) + x18 := (uint64(arg1[30]) << 48) + x19 := (uint64(arg1[29]) << 40) + x20 := (uint64(arg1[28]) << 32) + x21 := (uint64(arg1[27]) << 24) + x22 := (uint64(arg1[26]) << 16) + x23 := (uint64(arg1[25]) << 8) + x24 := arg1[24] + x25 := (uint64(arg1[23]) << 56) + x26 := (uint64(arg1[22]) << 48) + x27 := (uint64(arg1[21]) << 40) + x28 := (uint64(arg1[20]) << 32) + x29 := (uint64(arg1[19]) << 24) + x30 := (uint64(arg1[18]) << 16) + x31 := (uint64(arg1[17]) << 8) + x32 := arg1[16] + x33 := (uint64(arg1[15]) << 56) + x34 := (uint64(arg1[14]) << 48) + x35 := (uint64(arg1[13]) << 40) + x36 := (uint64(arg1[12]) << 32) + x37 := (uint64(arg1[11]) << 24) + x38 := (uint64(arg1[10]) << 16) + x39 := (uint64(arg1[9]) << 8) + x40 := arg1[8] + x41 := (uint64(arg1[7]) << 56) + x42 := (uint64(arg1[6]) << 48) + x43 := (uint64(arg1[5]) << 40) + x44 := (uint64(arg1[4]) << 32) + x45 := (uint64(arg1[3]) << 24) + x46 := (uint64(arg1[2]) << 16) + x47 := (uint64(arg1[1]) << 8) + x48 := arg1[0] + x49 := (x47 + uint64(x48)) + x50 := (x46 + x49) + x51 := (x45 + x50) + x52 := (x44 + x51) + x53 := (x43 + x52) + x54 := (x42 + x53) + x55 := (x41 + x54) + x56 := (x39 + uint64(x40)) + x57 := (x38 + x56) + x58 := (x37 + x57) + x59 := (x36 + x58) + x60 := (x35 + x59) + x61 := (x34 + x60) + x62 := (x33 + x61) + x63 := (x31 + uint64(x32)) + x64 := (x30 + x63) + x65 := (x29 + x64) + x66 := (x28 + x65) + x67 := (x27 + x66) + x68 := (x26 + x67) + x69 := (x25 + x68) + x70 := (x23 + uint64(x24)) + x71 := (x22 + x70) + x72 := (x21 + x71) + x73 := (x20 + x72) + x74 := (x19 + x73) + x75 := (x18 + x74) + x76 := (x17 + x75) + x77 := (x15 + uint64(x16)) + x78 := (x14 + x77) + x79 := (x13 + x78) + x80 := (x12 + x79) + x81 := (x11 + x80) + x82 := (x10 + x81) + x83 := (x9 + x82) + x84 := (x7 + uint64(x8)) + x85 := (x6 + x84) + x86 := (x5 + x85) + x87 := (x4 + x86) + x88 := (x3 + x87) + x89 := (x2 + x88) + x90 := (x1 + x89) + out1[0] = x55 + out1[1] = x62 + out1[2] = x69 + out1[3] = x76 + out1[4] = x83 + out1[5] = x90 +} diff --git a/libgo/go/crypto/elliptic/internal/fiat/p384_invert.go b/libgo/go/crypto/elliptic/internal/fiat/p384_invert.go new file mode 100644 index 0000000..24169e9 --- /dev/null +++ b/libgo/go/crypto/elliptic/internal/fiat/p384_invert.go @@ -0,0 +1,102 @@ +// Copyright 2021 The Go Authors. All rights reserved. +// Use of this source code is governed by a BSD-style +// license that can be found in the LICENSE file. + +// Code generated by addchain. DO NOT EDIT. + +package fiat + +// Invert sets e = 1/x, and returns e. +// +// If x == 0, Invert returns e = 0. +func (e *P384Element) Invert(x *P384Element) *P384Element { + // Inversion is implemented as exponentiation with exponent p − 2. + // The sequence of 15 multiplications and 383 squarings is derived from the + // following addition chain generated with github.com/mmcloughlin/addchain v0.3.0. + // + // _10 = 2*1 + // _11 = 1 + _10 + // _110 = 2*_11 + // _111 = 1 + _110 + // _111000 = _111 << 3 + // _111111 = _111 + _111000 + // x12 = _111111 << 6 + _111111 + // x24 = x12 << 12 + x12 + // x30 = x24 << 6 + _111111 + // x31 = 2*x30 + 1 + // x32 = 2*x31 + 1 + // x63 = x32 << 31 + x31 + // x126 = x63 << 63 + x63 + // x252 = x126 << 126 + x126 + // x255 = x252 << 3 + _111 + // i397 = ((x255 << 33 + x32) << 94 + x30) << 2 + // return 1 + i397 + // + + var z = new(P384Element).Set(e) + var t0 = new(P384Element) + var t1 = new(P384Element) + var t2 = new(P384Element) + var t3 = new(P384Element) + + z.Square(x) + z.Mul(x, z) + z.Square(z) + t1.Mul(x, z) + z.Square(t1) + for s := 1; s < 3; s++ { + z.Square(z) + } + z.Mul(t1, z) + t0.Square(z) + for s := 1; s < 6; s++ { + t0.Square(t0) + } + t0.Mul(z, t0) + t2.Square(t0) + for s := 1; s < 12; s++ { + t2.Square(t2) + } + t0.Mul(t0, t2) + for s := 0; s < 6; s++ { + t0.Square(t0) + } + z.Mul(z, t0) + t0.Square(z) + t2.Mul(x, t0) + t0.Square(t2) + t0.Mul(x, t0) + t3.Square(t0) + for s := 1; s < 31; s++ { + t3.Square(t3) + } + t2.Mul(t2, t3) + t3.Square(t2) + for s := 1; s < 63; s++ { + t3.Square(t3) + } + t2.Mul(t2, t3) + t3.Square(t2) + for s := 1; s < 126; s++ { + t3.Square(t3) + } + t2.Mul(t2, t3) + for s := 0; s < 3; s++ { + t2.Square(t2) + } + t1.Mul(t1, t2) + for s := 0; s < 33; s++ { + t1.Square(t1) + } + t0.Mul(t0, t1) + for s := 0; s < 94; s++ { + t0.Square(t0) + } + z.Mul(z, t0) + for s := 0; s < 2; s++ { + z.Square(z) + } + z.Mul(x, z) + + return e.Set(z) +} diff --git a/libgo/go/crypto/elliptic/internal/fiat/p521.go b/libgo/go/crypto/elliptic/internal/fiat/p521.go index dc67732..3d12117 100644 --- a/libgo/go/crypto/elliptic/internal/fiat/p521.go +++ b/libgo/go/crypto/elliptic/internal/fiat/p521.go @@ -2,8 +2,8 @@ // Use of this source code is governed by a BSD-style // license that can be found in the LICENSE file. -// Package fiat implements prime order fields using formally verified algorithms -// from the Fiat Cryptography project. +// Code generated by generate.go. DO NOT EDIT. + package fiat import ( @@ -15,20 +15,18 @@ import ( // // The zero value is a valid zero element. type P521Element struct { - // This element has the following bounds, which are tighter than - // the output bounds of some operations. Those operations must be - // followed by a carry. - // - // [0x0 ~> 0x400000000000000], [0x0 ~> 0x400000000000000], [0x0 ~> 0x400000000000000], - // [0x0 ~> 0x400000000000000], [0x0 ~> 0x400000000000000], [0x0 ~> 0x400000000000000], - // [0x0 ~> 0x400000000000000], [0x0 ~> 0x400000000000000], [0x0 ~> 0x200000000000000] - x [9]uint64 + // Values are represented internally always in the Montgomery domain, and + // converted in Bytes and SetBytes. + x p521MontgomeryDomainFieldElement } +const p521ElementLen = 66 + +type p521UntypedFieldElement = [9]uint64 + // One sets e = 1, and returns e. func (e *P521Element) One() *P521Element { - *e = P521Element{} - e.x[0] = 1 + p521SetOne(&e.x) return e } @@ -53,145 +51,85 @@ func (e *P521Element) Set(t *P521Element) *P521Element { return e } -// Bytes returns the 66-byte little-endian encoding of e. +// Bytes returns the 66-byte big-endian encoding of e. func (e *P521Element) Bytes() []byte { - // This function must be inlined to move the allocation to the parent and - // save it from escaping to the heap. - var out [66]byte - p521ToBytes(&out, &e.x) + // This function is outlined to make the allocations inline in the caller + // rather than happen on the heap. + var out [p521ElementLen]byte + return e.bytes(&out) +} + +func (e *P521Element) bytes(out *[p521ElementLen]byte) []byte { + var tmp p521NonMontgomeryDomainFieldElement + p521FromMontgomery(&tmp, &e.x) + p521ToBytes(out, (*p521UntypedFieldElement)(&tmp)) + p521InvertEndianness(out[:]) return out[:] } -// SetBytes sets e = v, where v is a little-endian 66-byte encoding, and returns -// e. If v is not 66 bytes or it encodes a value higher than 2^521 - 1, SetBytes -// returns nil and an error, and e is unchanged. +// p521MinusOneEncoding is the encoding of -1 mod p, so p - 1, the +// highest canonical encoding. It is used by SetBytes to check for non-canonical +// encodings such as p + k, 2p + k, etc. +var p521MinusOneEncoding = new(P521Element).Sub( + new(P521Element), new(P521Element).One()).Bytes() + +// SetBytes sets e = v, where v is a big-endian 66-byte encoding, and returns e. +// If v is not 66 bytes or it encodes a value higher than 2^521 - 1, +// SetBytes returns nil and an error, and e is unchanged. func (e *P521Element) SetBytes(v []byte) (*P521Element, error) { - if len(v) != 66 || v[65] > 1 { - return nil, errors.New("invalid P-521 field encoding") + if len(v) != p521ElementLen { + return nil, errors.New("invalid P521Element encoding") } - var in [66]byte + for i := range v { + if v[i] < p521MinusOneEncoding[i] { + break + } + if v[i] > p521MinusOneEncoding[i] { + return nil, errors.New("invalid P521Element encoding") + } + } + var in [p521ElementLen]byte copy(in[:], v) - p521FromBytes(&e.x, &in) + p521InvertEndianness(in[:]) + var tmp p521NonMontgomeryDomainFieldElement + p521FromBytes((*p521UntypedFieldElement)(&tmp), &in) + p521ToMontgomery(&e.x, &tmp) return e, nil } // Add sets e = t1 + t2, and returns e. func (e *P521Element) Add(t1, t2 *P521Element) *P521Element { p521Add(&e.x, &t1.x, &t2.x) - p521Carry(&e.x, &e.x) return e } // Sub sets e = t1 - t2, and returns e. func (e *P521Element) Sub(t1, t2 *P521Element) *P521Element { p521Sub(&e.x, &t1.x, &t2.x) - p521Carry(&e.x, &e.x) return e } // Mul sets e = t1 * t2, and returns e. func (e *P521Element) Mul(t1, t2 *P521Element) *P521Element { - p521CarryMul(&e.x, &t1.x, &t2.x) + p521Mul(&e.x, &t1.x, &t2.x) return e } // Square sets e = t * t, and returns e. func (e *P521Element) Square(t *P521Element) *P521Element { - p521CarrySquare(&e.x, &t.x) + p521Square(&e.x, &t.x) return e } -// Select sets e to a if cond == 1, and to b if cond == 0. +// Select sets v to a if cond == 1, and to b if cond == 0. func (v *P521Element) Select(a, b *P521Element, cond int) *P521Element { - p521Selectznz(&v.x, p521Uint1(cond), &b.x, &a.x) + p521Selectznz((*p521UntypedFieldElement)(&v.x), p521Uint1(cond), + (*p521UntypedFieldElement)(&b.x), (*p521UntypedFieldElement)(&a.x)) return v } -// Invert sets e = 1/t, and returns e. -// -// If t == 0, Invert returns e = 0. -func (e *P521Element) Invert(t *P521Element) *P521Element { - // Inversion is implemented as exponentiation with exponent p − 2. - // The sequence of multiplications and squarings was generated with - // github.com/mmcloughlin/addchain v0.2.0. - - var t1, t2 = new(P521Element), new(P521Element) - - // _10 = 2 * 1 - t1.Square(t) - - // _11 = 1 + _10 - t1.Mul(t, t1) - - // _1100 = _11 << 2 - t2.Square(t1) - t2.Square(t2) - - // _1111 = _11 + _1100 - t1.Mul(t1, t2) - - // _11110000 = _1111 << 4 - t2.Square(t1) - for i := 0; i < 3; i++ { - t2.Square(t2) +func p521InvertEndianness(v []byte) { + for i := 0; i < len(v)/2; i++ { + v[i], v[len(v)-1-i] = v[len(v)-1-i], v[i] } - - // _11111111 = _1111 + _11110000 - t1.Mul(t1, t2) - - // x16 = _11111111<<8 + _11111111 - t2.Square(t1) - for i := 0; i < 7; i++ { - t2.Square(t2) - } - t1.Mul(t1, t2) - - // x32 = x16<<16 + x16 - t2.Square(t1) - for i := 0; i < 15; i++ { - t2.Square(t2) - } - t1.Mul(t1, t2) - - // x64 = x32<<32 + x32 - t2.Square(t1) - for i := 0; i < 31; i++ { - t2.Square(t2) - } - t1.Mul(t1, t2) - - // x65 = 2*x64 + 1 - t2.Square(t1) - t2.Mul(t2, t) - - // x129 = x65<<64 + x64 - for i := 0; i < 64; i++ { - t2.Square(t2) - } - t1.Mul(t1, t2) - - // x130 = 2*x129 + 1 - t2.Square(t1) - t2.Mul(t2, t) - - // x259 = x130<<129 + x129 - for i := 0; i < 129; i++ { - t2.Square(t2) - } - t1.Mul(t1, t2) - - // x260 = 2*x259 + 1 - t2.Square(t1) - t2.Mul(t2, t) - - // x519 = x260<<259 + x259 - for i := 0; i < 259; i++ { - t2.Square(t2) - } - t1.Mul(t1, t2) - - // return x519<<2 + 1 - t1.Square(t1) - t1.Square(t1) - return e.Mul(t1, t) } diff --git a/libgo/go/crypto/elliptic/internal/fiat/p521_fiat64.go b/libgo/go/crypto/elliptic/internal/fiat/p521_fiat64.go index f86283b..9f4f290 100644 --- a/libgo/go/crypto/elliptic/internal/fiat/p521_fiat64.go +++ b/libgo/go/crypto/elliptic/internal/fiat/p521_fiat64.go @@ -1,1374 +1,5152 @@ // Code generated by Fiat Cryptography. DO NOT EDIT. // -// Autogenerated: 'fiat-crypto/src/ExtractionOCaml/unsaturated_solinas' --lang Go --no-wide-int --cmovznz-by-mul --internal-static --public-function-case camelCase --public-type-case camelCase --private-function-case camelCase --private-type-case camelCase --no-prefix-fiat --package-name fiat --doc-text-before-function-name '' --doc-prepend-header 'Code generated by Fiat Cryptography. DO NOT EDIT.' --doc-newline-before-package-declaration p521 64 9 '2^521 - 1' carry_mul carry_square carry add sub to_bytes from_bytes selectznz +// Autogenerated: word_by_word_montgomery --lang Go --no-wide-int --cmovznz-by-mul --relax-primitive-carry-to-bitwidth 32,64 --internal-static --public-function-case camelCase --public-type-case camelCase --private-function-case camelCase --private-type-case camelCase --doc-text-before-function-name '' --doc-newline-before-package-declaration --doc-prepend-header 'Code generated by Fiat Cryptography. DO NOT EDIT.' --package-name fiat --no-prefix-fiat p521 64 '2^521 - 1' mul square add sub one from_montgomery to_montgomery selectznz to_bytes from_bytes // // curve description: p521 // // machine_wordsize = 64 (from "64") // -// requested operations: carry_mul, carry_square, carry, add, sub, to_bytes, from_bytes, selectznz +// requested operations: mul, square, add, sub, one, from_montgomery, to_montgomery, selectznz, to_bytes, from_bytes // -// n = 9 (from "9") +// m = 0x1ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff (from "2^521 - 1") // -// s-c = 2^521 - [(1, 1)] (from "2^521 - 1") // -// tight_bounds_multiplier = 1 (from "") // +// NOTE: In addition to the bounds specified above each function, all // +// functions synthesized for this Montgomery arithmetic require the // -// Computed values: +// input to be strictly less than the prime modulus (m), and also +// +// require the input to be in the unique saturated representation. +// +// All functions also ensure that these two properties are true of // -// carry_chain = [0, 1, 2, 3, 4, 5, 6, 7, 8, 0, 1] +// return values. // -// eval z = z[0] + (z[1] << 58) + (z[2] << 116) + (z[3] << 174) + (z[4] << 232) + (z[5] << 0x122) + (z[6] << 0x15c) + (z[7] << 0x196) + (z[8] << 0x1d0) +// +// +// Computed values: +// +// eval z = z[0] + (z[1] << 64) + (z[2] << 128) + (z[3] << 192) + (z[4] << 256) + (z[5] << 0x140) + (z[6] << 0x180) + (z[7] << 0x1c0) + (z[8] << 2^9) // // bytes_eval z = z[0] + (z[1] << 8) + (z[2] << 16) + (z[3] << 24) + (z[4] << 32) + (z[5] << 40) + (z[6] << 48) + (z[7] << 56) + (z[8] << 64) + (z[9] << 72) + (z[10] << 80) + (z[11] << 88) + (z[12] << 96) + (z[13] << 104) + (z[14] << 112) + (z[15] << 120) + (z[16] << 128) + (z[17] << 136) + (z[18] << 144) + (z[19] << 152) + (z[20] << 160) + (z[21] << 168) + (z[22] << 176) + (z[23] << 184) + (z[24] << 192) + (z[25] << 200) + (z[26] << 208) + (z[27] << 216) + (z[28] << 224) + (z[29] << 232) + (z[30] << 240) + (z[31] << 248) + (z[32] << 256) + (z[33] << 0x108) + (z[34] << 0x110) + (z[35] << 0x118) + (z[36] << 0x120) + (z[37] << 0x128) + (z[38] << 0x130) + (z[39] << 0x138) + (z[40] << 0x140) + (z[41] << 0x148) + (z[42] << 0x150) + (z[43] << 0x158) + (z[44] << 0x160) + (z[45] << 0x168) + (z[46] << 0x170) + (z[47] << 0x178) + (z[48] << 0x180) + (z[49] << 0x188) + (z[50] << 0x190) + (z[51] << 0x198) + (z[52] << 0x1a0) + (z[53] << 0x1a8) + (z[54] << 0x1b0) + (z[55] << 0x1b8) + (z[56] << 0x1c0) + (z[57] << 0x1c8) + (z[58] << 0x1d0) + (z[59] << 0x1d8) + (z[60] << 0x1e0) + (z[61] << 0x1e8) + (z[62] << 0x1f0) + (z[63] << 0x1f8) + (z[64] << 2^9) + (z[65] << 0x208) // -// balance = [0x7fffffffffffffe, 0x7fffffffffffffe, 0x7fffffffffffffe, 0x7fffffffffffffe, 0x7fffffffffffffe, 0x7fffffffffffffe, 0x7fffffffffffffe, 0x7fffffffffffffe, 0x3fffffffffffffe] +// twos_complement_eval z = let x1 := z[0] + (z[1] << 64) + (z[2] << 128) + (z[3] << 192) + (z[4] << 256) + (z[5] << 0x140) + (z[6] << 0x180) + (z[7] << 0x1c0) + (z[8] << 2^9) in +// +// if x1 & (2^576-1) < 2^575 then x1 & (2^576-1) else (x1 & (2^576-1)) - 2^576 package fiat import "math/bits" -type p521Uint1 uint8 -type p521Int1 int8 +type p521Uint1 uint64 // We use uint64 instead of a more narrow type for performance reasons; see https://github.com/mit-plv/fiat-crypto/pull/1006#issuecomment-892625927 +type p521Int1 int64 // We use uint64 instead of a more narrow type for performance reasons; see https://github.com/mit-plv/fiat-crypto/pull/1006#issuecomment-892625927 -// p521AddcarryxU64 is a thin wrapper around bits.Add64 that uses p521Uint1 rather than uint64 -func p521AddcarryxU64(x uint64, y uint64, carry p521Uint1) (uint64, p521Uint1) { - sum, carryOut := bits.Add64(x, y, uint64(carry)) - return sum, p521Uint1(carryOut) -} +// The type p521MontgomeryDomainFieldElement is a field element in the Montgomery domain. +// +// Bounds: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]] +type p521MontgomeryDomainFieldElement [9]uint64 -// p521SubborrowxU64 is a thin wrapper around bits.Sub64 that uses p521Uint1 rather than uint64 -func p521SubborrowxU64(x uint64, y uint64, carry p521Uint1) (uint64, p521Uint1) { - sum, carryOut := bits.Sub64(x, y, uint64(carry)) - return sum, p521Uint1(carryOut) -} +// The type p521NonMontgomeryDomainFieldElement is a field element NOT in the Montgomery domain. +// +// Bounds: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]] +type p521NonMontgomeryDomainFieldElement [9]uint64 -// p521AddcarryxU58 is an addition with carry. +// p521CmovznzU64 is a single-word conditional move. // // Postconditions: -// out1 = (arg1 + arg2 + arg3) mod 2^58 -// out2 = ⌊(arg1 + arg2 + arg3) / 2^58⌋ +// out1 = (if arg1 = 0 then arg2 else arg3) // // Input Bounds: // arg1: [0x0 ~> 0x1] -// arg2: [0x0 ~> 0x3ffffffffffffff] -// arg3: [0x0 ~> 0x3ffffffffffffff] +// arg2: [0x0 ~> 0xffffffffffffffff] +// arg3: [0x0 ~> 0xffffffffffffffff] // Output Bounds: -// out1: [0x0 ~> 0x3ffffffffffffff] -// out2: [0x0 ~> 0x1] -func p521AddcarryxU58(out1 *uint64, out2 *p521Uint1, arg1 p521Uint1, arg2 uint64, arg3 uint64) { - x1 := ((uint64(arg1) + arg2) + arg3) - x2 := (x1 & 0x3ffffffffffffff) - x3 := p521Uint1((x1 >> 58)) +// out1: [0x0 ~> 0xffffffffffffffff] +func p521CmovznzU64(out1 *uint64, arg1 p521Uint1, arg2 uint64, arg3 uint64) { + x1 := (uint64(arg1) * 0xffffffffffffffff) + x2 := ((x1 & arg3) | ((^x1) & arg2)) *out1 = x2 - *out2 = x3 } -// p521SubborrowxU58 is a subtraction with borrow. +// p521Mul multiplies two field elements in the Montgomery domain. // +// Preconditions: +// 0 ≤ eval arg1 < m +// 0 ≤ eval arg2 < m // Postconditions: -// out1 = (-arg1 + arg2 + -arg3) mod 2^58 -// out2 = -⌊(-arg1 + arg2 + -arg3) / 2^58⌋ +// eval (from_montgomery out1) mod m = (eval (from_montgomery arg1) * eval (from_montgomery arg2)) mod m +// 0 ≤ eval out1 < m // -// Input Bounds: -// arg1: [0x0 ~> 0x1] -// arg2: [0x0 ~> 0x3ffffffffffffff] -// arg3: [0x0 ~> 0x3ffffffffffffff] -// Output Bounds: -// out1: [0x0 ~> 0x3ffffffffffffff] -// out2: [0x0 ~> 0x1] -func p521SubborrowxU58(out1 *uint64, out2 *p521Uint1, arg1 p521Uint1, arg2 uint64, arg3 uint64) { - x1 := ((int64(arg2) - int64(arg1)) - int64(arg3)) - x2 := p521Int1((x1 >> 58)) - x3 := (uint64(x1) & 0x3ffffffffffffff) - *out1 = x3 - *out2 = (0x0 - p521Uint1(x2)) +func p521Mul(out1 *p521MontgomeryDomainFieldElement, arg1 *p521MontgomeryDomainFieldElement, arg2 *p521MontgomeryDomainFieldElement) { + x1 := arg1[1] + x2 := arg1[2] + x3 := arg1[3] + x4 := arg1[4] + x5 := arg1[5] + x6 := arg1[6] + x7 := arg1[7] + x8 := arg1[8] + x9 := arg1[0] + var x10 uint64 + var x11 uint64 + x11, x10 = bits.Mul64(x9, arg2[8]) + var x12 uint64 + var x13 uint64 + x13, x12 = bits.Mul64(x9, arg2[7]) + var x14 uint64 + var x15 uint64 + x15, x14 = bits.Mul64(x9, arg2[6]) + var x16 uint64 + var x17 uint64 + x17, x16 = bits.Mul64(x9, arg2[5]) + var x18 uint64 + var x19 uint64 + x19, x18 = bits.Mul64(x9, arg2[4]) + var x20 uint64 + var x21 uint64 + x21, x20 = bits.Mul64(x9, arg2[3]) + var x22 uint64 + var x23 uint64 + x23, x22 = bits.Mul64(x9, arg2[2]) + var x24 uint64 + var x25 uint64 + x25, x24 = bits.Mul64(x9, arg2[1]) + var x26 uint64 + var x27 uint64 + x27, x26 = bits.Mul64(x9, arg2[0]) + var x28 uint64 + var x29 uint64 + x28, x29 = bits.Add64(x27, x24, uint64(0x0)) + var x30 uint64 + var x31 uint64 + x30, x31 = bits.Add64(x25, x22, uint64(p521Uint1(x29))) + var x32 uint64 + var x33 uint64 + x32, x33 = bits.Add64(x23, x20, uint64(p521Uint1(x31))) + var x34 uint64 + var x35 uint64 + x34, x35 = bits.Add64(x21, x18, uint64(p521Uint1(x33))) + var x36 uint64 + var x37 uint64 + x36, x37 = bits.Add64(x19, x16, uint64(p521Uint1(x35))) + var x38 uint64 + var x39 uint64 + x38, x39 = bits.Add64(x17, x14, uint64(p521Uint1(x37))) + var x40 uint64 + var x41 uint64 + x40, x41 = bits.Add64(x15, x12, uint64(p521Uint1(x39))) + var x42 uint64 + var x43 uint64 + x42, x43 = bits.Add64(x13, x10, uint64(p521Uint1(x41))) + x44 := (uint64(p521Uint1(x43)) + x11) + var x45 uint64 + var x46 uint64 + x46, x45 = bits.Mul64(x26, 0x1ff) + var x47 uint64 + var x48 uint64 + x48, x47 = bits.Mul64(x26, 0xffffffffffffffff) + var x49 uint64 + var x50 uint64 + x50, x49 = bits.Mul64(x26, 0xffffffffffffffff) + var x51 uint64 + var x52 uint64 + x52, x51 = bits.Mul64(x26, 0xffffffffffffffff) + var x53 uint64 + var x54 uint64 + x54, x53 = bits.Mul64(x26, 0xffffffffffffffff) + var x55 uint64 + var x56 uint64 + x56, x55 = bits.Mul64(x26, 0xffffffffffffffff) + var x57 uint64 + var x58 uint64 + x58, x57 = bits.Mul64(x26, 0xffffffffffffffff) + var x59 uint64 + var x60 uint64 + x60, x59 = bits.Mul64(x26, 0xffffffffffffffff) + var x61 uint64 + var x62 uint64 + x62, x61 = bits.Mul64(x26, 0xffffffffffffffff) + var x63 uint64 + var x64 uint64 + x63, x64 = bits.Add64(x62, x59, uint64(0x0)) + var x65 uint64 + var x66 uint64 + x65, x66 = bits.Add64(x60, x57, uint64(p521Uint1(x64))) + var x67 uint64 + var x68 uint64 + x67, x68 = bits.Add64(x58, x55, uint64(p521Uint1(x66))) + var x69 uint64 + var x70 uint64 + x69, x70 = bits.Add64(x56, x53, uint64(p521Uint1(x68))) + var x71 uint64 + var x72 uint64 + x71, x72 = bits.Add64(x54, x51, uint64(p521Uint1(x70))) + var x73 uint64 + var x74 uint64 + x73, x74 = bits.Add64(x52, x49, uint64(p521Uint1(x72))) + var x75 uint64 + var x76 uint64 + x75, x76 = bits.Add64(x50, x47, uint64(p521Uint1(x74))) + var x77 uint64 + var x78 uint64 + x77, x78 = bits.Add64(x48, x45, uint64(p521Uint1(x76))) + x79 := (uint64(p521Uint1(x78)) + x46) + var x81 uint64 + _, x81 = bits.Add64(x26, x61, uint64(0x0)) + var x82 uint64 + var x83 uint64 + x82, x83 = bits.Add64(x28, x63, uint64(p521Uint1(x81))) + var x84 uint64 + var x85 uint64 + x84, x85 = bits.Add64(x30, x65, uint64(p521Uint1(x83))) + var x86 uint64 + var x87 uint64 + x86, x87 = bits.Add64(x32, x67, uint64(p521Uint1(x85))) + var x88 uint64 + var x89 uint64 + x88, x89 = bits.Add64(x34, x69, uint64(p521Uint1(x87))) + var x90 uint64 + var x91 uint64 + x90, x91 = bits.Add64(x36, x71, uint64(p521Uint1(x89))) + var x92 uint64 + var x93 uint64 + x92, x93 = bits.Add64(x38, x73, uint64(p521Uint1(x91))) + var x94 uint64 + var x95 uint64 + x94, x95 = bits.Add64(x40, x75, uint64(p521Uint1(x93))) + var x96 uint64 + var x97 uint64 + x96, x97 = bits.Add64(x42, x77, uint64(p521Uint1(x95))) + var x98 uint64 + var x99 uint64 + x98, x99 = bits.Add64(x44, x79, uint64(p521Uint1(x97))) + var x100 uint64 + var x101 uint64 + x101, x100 = bits.Mul64(x1, arg2[8]) + var x102 uint64 + var x103 uint64 + x103, x102 = bits.Mul64(x1, arg2[7]) + var x104 uint64 + var x105 uint64 + x105, x104 = bits.Mul64(x1, arg2[6]) + var x106 uint64 + var x107 uint64 + x107, x106 = bits.Mul64(x1, arg2[5]) + var x108 uint64 + var x109 uint64 + x109, x108 = bits.Mul64(x1, arg2[4]) + var x110 uint64 + var x111 uint64 + x111, x110 = bits.Mul64(x1, arg2[3]) + var x112 uint64 + var x113 uint64 + x113, x112 = bits.Mul64(x1, arg2[2]) + var x114 uint64 + var x115 uint64 + x115, x114 = bits.Mul64(x1, arg2[1]) + var x116 uint64 + var x117 uint64 + x117, x116 = bits.Mul64(x1, arg2[0]) + var x118 uint64 + var x119 uint64 + x118, x119 = bits.Add64(x117, x114, uint64(0x0)) + var x120 uint64 + var x121 uint64 + x120, x121 = bits.Add64(x115, x112, uint64(p521Uint1(x119))) + var x122 uint64 + var x123 uint64 + x122, x123 = bits.Add64(x113, x110, uint64(p521Uint1(x121))) + var x124 uint64 + var x125 uint64 + x124, x125 = bits.Add64(x111, x108, uint64(p521Uint1(x123))) + var x126 uint64 + var x127 uint64 + x126, x127 = bits.Add64(x109, x106, uint64(p521Uint1(x125))) + var x128 uint64 + var x129 uint64 + x128, x129 = bits.Add64(x107, x104, uint64(p521Uint1(x127))) + var x130 uint64 + var x131 uint64 + x130, x131 = bits.Add64(x105, x102, uint64(p521Uint1(x129))) + var x132 uint64 + var x133 uint64 + x132, x133 = bits.Add64(x103, x100, uint64(p521Uint1(x131))) + x134 := (uint64(p521Uint1(x133)) + x101) + var x135 uint64 + var x136 uint64 + x135, x136 = bits.Add64(x82, x116, uint64(0x0)) + var x137 uint64 + var x138 uint64 + x137, x138 = bits.Add64(x84, x118, uint64(p521Uint1(x136))) + var x139 uint64 + var x140 uint64 + x139, x140 = bits.Add64(x86, x120, uint64(p521Uint1(x138))) + var x141 uint64 + var x142 uint64 + x141, x142 = bits.Add64(x88, x122, uint64(p521Uint1(x140))) + var x143 uint64 + var x144 uint64 + x143, x144 = bits.Add64(x90, x124, uint64(p521Uint1(x142))) + var x145 uint64 + var x146 uint64 + x145, x146 = bits.Add64(x92, x126, uint64(p521Uint1(x144))) + var x147 uint64 + var x148 uint64 + x147, x148 = bits.Add64(x94, x128, uint64(p521Uint1(x146))) + var x149 uint64 + var x150 uint64 + x149, x150 = bits.Add64(x96, x130, uint64(p521Uint1(x148))) + var x151 uint64 + var x152 uint64 + x151, x152 = bits.Add64(x98, x132, uint64(p521Uint1(x150))) + var x153 uint64 + var x154 uint64 + x153, x154 = bits.Add64(uint64(p521Uint1(x99)), x134, uint64(p521Uint1(x152))) + var x155 uint64 + var x156 uint64 + x156, x155 = bits.Mul64(x135, 0x1ff) + var x157 uint64 + var x158 uint64 + x158, x157 = bits.Mul64(x135, 0xffffffffffffffff) + var x159 uint64 + var x160 uint64 + x160, x159 = bits.Mul64(x135, 0xffffffffffffffff) + var x161 uint64 + var x162 uint64 + x162, x161 = bits.Mul64(x135, 0xffffffffffffffff) + var x163 uint64 + var x164 uint64 + x164, x163 = bits.Mul64(x135, 0xffffffffffffffff) + var x165 uint64 + var x166 uint64 + x166, x165 = bits.Mul64(x135, 0xffffffffffffffff) + var x167 uint64 + var x168 uint64 + x168, x167 = bits.Mul64(x135, 0xffffffffffffffff) + var x169 uint64 + var x170 uint64 + x170, x169 = bits.Mul64(x135, 0xffffffffffffffff) + var x171 uint64 + var x172 uint64 + x172, x171 = bits.Mul64(x135, 0xffffffffffffffff) + var x173 uint64 + var x174 uint64 + x173, x174 = bits.Add64(x172, x169, uint64(0x0)) + var x175 uint64 + var x176 uint64 + x175, x176 = bits.Add64(x170, x167, uint64(p521Uint1(x174))) + var x177 uint64 + var x178 uint64 + x177, x178 = bits.Add64(x168, x165, uint64(p521Uint1(x176))) + var x179 uint64 + var x180 uint64 + x179, x180 = bits.Add64(x166, x163, uint64(p521Uint1(x178))) + var x181 uint64 + var x182 uint64 + x181, x182 = bits.Add64(x164, x161, uint64(p521Uint1(x180))) + var x183 uint64 + var x184 uint64 + x183, x184 = bits.Add64(x162, x159, uint64(p521Uint1(x182))) + var x185 uint64 + var x186 uint64 + x185, x186 = bits.Add64(x160, x157, uint64(p521Uint1(x184))) + var x187 uint64 + var x188 uint64 + x187, x188 = bits.Add64(x158, x155, uint64(p521Uint1(x186))) + x189 := (uint64(p521Uint1(x188)) + x156) + var x191 uint64 + _, x191 = bits.Add64(x135, x171, uint64(0x0)) + var x192 uint64 + var x193 uint64 + x192, x193 = bits.Add64(x137, x173, uint64(p521Uint1(x191))) + var x194 uint64 + var x195 uint64 + x194, x195 = bits.Add64(x139, x175, uint64(p521Uint1(x193))) + var x196 uint64 + var x197 uint64 + x196, x197 = bits.Add64(x141, x177, uint64(p521Uint1(x195))) + var x198 uint64 + var x199 uint64 + x198, x199 = bits.Add64(x143, x179, uint64(p521Uint1(x197))) + var x200 uint64 + var x201 uint64 + x200, x201 = bits.Add64(x145, x181, uint64(p521Uint1(x199))) + var x202 uint64 + var x203 uint64 + x202, x203 = bits.Add64(x147, x183, uint64(p521Uint1(x201))) + var x204 uint64 + var x205 uint64 + x204, x205 = bits.Add64(x149, x185, uint64(p521Uint1(x203))) + var x206 uint64 + var x207 uint64 + x206, x207 = bits.Add64(x151, x187, uint64(p521Uint1(x205))) + var x208 uint64 + var x209 uint64 + x208, x209 = bits.Add64(x153, x189, uint64(p521Uint1(x207))) + x210 := (uint64(p521Uint1(x209)) + uint64(p521Uint1(x154))) + var x211 uint64 + var x212 uint64 + x212, x211 = bits.Mul64(x2, arg2[8]) + var x213 uint64 + var x214 uint64 + x214, x213 = bits.Mul64(x2, arg2[7]) + var x215 uint64 + var x216 uint64 + x216, x215 = bits.Mul64(x2, arg2[6]) + var x217 uint64 + var x218 uint64 + x218, x217 = bits.Mul64(x2, arg2[5]) + var x219 uint64 + var x220 uint64 + x220, x219 = bits.Mul64(x2, arg2[4]) + var x221 uint64 + var x222 uint64 + x222, x221 = bits.Mul64(x2, arg2[3]) + var x223 uint64 + var x224 uint64 + x224, x223 = bits.Mul64(x2, arg2[2]) + var x225 uint64 + var x226 uint64 + x226, x225 = bits.Mul64(x2, arg2[1]) + var x227 uint64 + var x228 uint64 + x228, x227 = bits.Mul64(x2, arg2[0]) + var x229 uint64 + var x230 uint64 + x229, x230 = bits.Add64(x228, x225, uint64(0x0)) + var x231 uint64 + var x232 uint64 + x231, x232 = bits.Add64(x226, x223, uint64(p521Uint1(x230))) + var x233 uint64 + var x234 uint64 + x233, x234 = bits.Add64(x224, x221, uint64(p521Uint1(x232))) + var x235 uint64 + var x236 uint64 + x235, x236 = bits.Add64(x222, x219, uint64(p521Uint1(x234))) + var x237 uint64 + var x238 uint64 + x237, x238 = bits.Add64(x220, x217, uint64(p521Uint1(x236))) + var x239 uint64 + var x240 uint64 + x239, x240 = bits.Add64(x218, x215, uint64(p521Uint1(x238))) + var x241 uint64 + var x242 uint64 + x241, x242 = bits.Add64(x216, x213, uint64(p521Uint1(x240))) + var x243 uint64 + var x244 uint64 + x243, x244 = bits.Add64(x214, x211, uint64(p521Uint1(x242))) + x245 := (uint64(p521Uint1(x244)) + x212) + var x246 uint64 + var x247 uint64 + x246, x247 = bits.Add64(x192, x227, uint64(0x0)) + var x248 uint64 + var x249 uint64 + x248, x249 = bits.Add64(x194, x229, uint64(p521Uint1(x247))) + var x250 uint64 + var x251 uint64 + x250, x251 = bits.Add64(x196, x231, uint64(p521Uint1(x249))) + var x252 uint64 + var x253 uint64 + x252, x253 = bits.Add64(x198, x233, uint64(p521Uint1(x251))) + var x254 uint64 + var x255 uint64 + x254, x255 = bits.Add64(x200, x235, uint64(p521Uint1(x253))) + var x256 uint64 + var x257 uint64 + x256, x257 = bits.Add64(x202, x237, uint64(p521Uint1(x255))) + var x258 uint64 + var x259 uint64 + x258, x259 = bits.Add64(x204, x239, uint64(p521Uint1(x257))) + var x260 uint64 + var x261 uint64 + x260, x261 = bits.Add64(x206, x241, uint64(p521Uint1(x259))) + var x262 uint64 + var x263 uint64 + x262, x263 = bits.Add64(x208, x243, uint64(p521Uint1(x261))) + var x264 uint64 + var x265 uint64 + x264, x265 = bits.Add64(x210, x245, uint64(p521Uint1(x263))) + var x266 uint64 + var x267 uint64 + x267, x266 = bits.Mul64(x246, 0x1ff) + var x268 uint64 + var x269 uint64 + x269, x268 = bits.Mul64(x246, 0xffffffffffffffff) + var x270 uint64 + var x271 uint64 + x271, x270 = bits.Mul64(x246, 0xffffffffffffffff) + var x272 uint64 + var x273 uint64 + x273, x272 = bits.Mul64(x246, 0xffffffffffffffff) + var x274 uint64 + var x275 uint64 + x275, x274 = bits.Mul64(x246, 0xffffffffffffffff) + var x276 uint64 + var x277 uint64 + x277, x276 = bits.Mul64(x246, 0xffffffffffffffff) + var x278 uint64 + var x279 uint64 + x279, x278 = bits.Mul64(x246, 0xffffffffffffffff) + var x280 uint64 + var x281 uint64 + x281, x280 = bits.Mul64(x246, 0xffffffffffffffff) + var x282 uint64 + var x283 uint64 + x283, x282 = bits.Mul64(x246, 0xffffffffffffffff) + var x284 uint64 + var x285 uint64 + x284, x285 = bits.Add64(x283, x280, uint64(0x0)) + var x286 uint64 + var x287 uint64 + x286, x287 = bits.Add64(x281, x278, uint64(p521Uint1(x285))) + var x288 uint64 + var x289 uint64 + x288, x289 = bits.Add64(x279, x276, uint64(p521Uint1(x287))) + var x290 uint64 + var x291 uint64 + x290, x291 = bits.Add64(x277, x274, uint64(p521Uint1(x289))) + var x292 uint64 + var x293 uint64 + x292, x293 = bits.Add64(x275, x272, uint64(p521Uint1(x291))) + var x294 uint64 + var x295 uint64 + x294, x295 = bits.Add64(x273, x270, uint64(p521Uint1(x293))) + var x296 uint64 + var x297 uint64 + x296, x297 = bits.Add64(x271, x268, uint64(p521Uint1(x295))) + var x298 uint64 + var x299 uint64 + x298, x299 = bits.Add64(x269, x266, uint64(p521Uint1(x297))) + x300 := (uint64(p521Uint1(x299)) + x267) + var x302 uint64 + _, x302 = bits.Add64(x246, x282, uint64(0x0)) + var x303 uint64 + var x304 uint64 + x303, x304 = bits.Add64(x248, x284, uint64(p521Uint1(x302))) + var x305 uint64 + var x306 uint64 + x305, x306 = bits.Add64(x250, x286, uint64(p521Uint1(x304))) + var x307 uint64 + var x308 uint64 + x307, x308 = bits.Add64(x252, x288, uint64(p521Uint1(x306))) + var x309 uint64 + var x310 uint64 + x309, x310 = bits.Add64(x254, x290, uint64(p521Uint1(x308))) + var x311 uint64 + var x312 uint64 + x311, x312 = bits.Add64(x256, x292, uint64(p521Uint1(x310))) + var x313 uint64 + var x314 uint64 + x313, x314 = bits.Add64(x258, x294, uint64(p521Uint1(x312))) + var x315 uint64 + var x316 uint64 + x315, x316 = bits.Add64(x260, x296, uint64(p521Uint1(x314))) + var x317 uint64 + var x318 uint64 + x317, x318 = bits.Add64(x262, x298, uint64(p521Uint1(x316))) + var x319 uint64 + var x320 uint64 + x319, x320 = bits.Add64(x264, x300, uint64(p521Uint1(x318))) + x321 := (uint64(p521Uint1(x320)) + uint64(p521Uint1(x265))) + var x322 uint64 + var x323 uint64 + x323, x322 = bits.Mul64(x3, arg2[8]) + var x324 uint64 + var x325 uint64 + x325, x324 = bits.Mul64(x3, arg2[7]) + var x326 uint64 + var x327 uint64 + x327, x326 = bits.Mul64(x3, arg2[6]) + var x328 uint64 + var x329 uint64 + x329, x328 = bits.Mul64(x3, arg2[5]) + var x330 uint64 + var x331 uint64 + x331, x330 = bits.Mul64(x3, arg2[4]) + var x332 uint64 + var x333 uint64 + x333, x332 = bits.Mul64(x3, arg2[3]) + var x334 uint64 + var x335 uint64 + x335, x334 = bits.Mul64(x3, arg2[2]) + var x336 uint64 + var x337 uint64 + x337, x336 = bits.Mul64(x3, arg2[1]) + var x338 uint64 + var x339 uint64 + x339, x338 = bits.Mul64(x3, arg2[0]) + var x340 uint64 + var x341 uint64 + x340, x341 = bits.Add64(x339, x336, uint64(0x0)) + var x342 uint64 + var x343 uint64 + x342, x343 = bits.Add64(x337, x334, uint64(p521Uint1(x341))) + var x344 uint64 + var x345 uint64 + x344, x345 = bits.Add64(x335, x332, uint64(p521Uint1(x343))) + var x346 uint64 + var x347 uint64 + x346, x347 = bits.Add64(x333, x330, uint64(p521Uint1(x345))) + var x348 uint64 + var x349 uint64 + x348, x349 = bits.Add64(x331, x328, uint64(p521Uint1(x347))) + var x350 uint64 + var x351 uint64 + x350, x351 = bits.Add64(x329, x326, uint64(p521Uint1(x349))) + var x352 uint64 + var x353 uint64 + x352, x353 = bits.Add64(x327, x324, uint64(p521Uint1(x351))) + var x354 uint64 + var x355 uint64 + x354, x355 = bits.Add64(x325, x322, uint64(p521Uint1(x353))) + x356 := (uint64(p521Uint1(x355)) + x323) + var x357 uint64 + var x358 uint64 + x357, x358 = bits.Add64(x303, x338, uint64(0x0)) + var x359 uint64 + var x360 uint64 + x359, x360 = bits.Add64(x305, x340, uint64(p521Uint1(x358))) + var x361 uint64 + var x362 uint64 + x361, x362 = bits.Add64(x307, x342, uint64(p521Uint1(x360))) + var x363 uint64 + var x364 uint64 + x363, x364 = bits.Add64(x309, x344, uint64(p521Uint1(x362))) + var x365 uint64 + var x366 uint64 + x365, x366 = bits.Add64(x311, x346, uint64(p521Uint1(x364))) + var x367 uint64 + var x368 uint64 + x367, x368 = bits.Add64(x313, x348, uint64(p521Uint1(x366))) + var x369 uint64 + var x370 uint64 + x369, x370 = bits.Add64(x315, x350, uint64(p521Uint1(x368))) + var x371 uint64 + var x372 uint64 + x371, x372 = bits.Add64(x317, x352, uint64(p521Uint1(x370))) + var x373 uint64 + var x374 uint64 + x373, x374 = bits.Add64(x319, x354, uint64(p521Uint1(x372))) + var x375 uint64 + var x376 uint64 + x375, x376 = bits.Add64(x321, x356, uint64(p521Uint1(x374))) + var x377 uint64 + var x378 uint64 + x378, x377 = bits.Mul64(x357, 0x1ff) + var x379 uint64 + var x380 uint64 + x380, x379 = bits.Mul64(x357, 0xffffffffffffffff) + var x381 uint64 + var x382 uint64 + x382, x381 = bits.Mul64(x357, 0xffffffffffffffff) + var x383 uint64 + var x384 uint64 + x384, x383 = bits.Mul64(x357, 0xffffffffffffffff) + var x385 uint64 + var x386 uint64 + x386, x385 = bits.Mul64(x357, 0xffffffffffffffff) + var x387 uint64 + var x388 uint64 + x388, x387 = bits.Mul64(x357, 0xffffffffffffffff) + var x389 uint64 + var x390 uint64 + x390, x389 = bits.Mul64(x357, 0xffffffffffffffff) + var x391 uint64 + var x392 uint64 + x392, x391 = bits.Mul64(x357, 0xffffffffffffffff) + var x393 uint64 + var x394 uint64 + x394, x393 = bits.Mul64(x357, 0xffffffffffffffff) + var x395 uint64 + var x396 uint64 + x395, x396 = bits.Add64(x394, x391, uint64(0x0)) + var x397 uint64 + var x398 uint64 + x397, x398 = bits.Add64(x392, x389, uint64(p521Uint1(x396))) + var x399 uint64 + var x400 uint64 + x399, x400 = bits.Add64(x390, x387, uint64(p521Uint1(x398))) + var x401 uint64 + var x402 uint64 + x401, x402 = bits.Add64(x388, x385, uint64(p521Uint1(x400))) + var x403 uint64 + var x404 uint64 + x403, x404 = bits.Add64(x386, x383, uint64(p521Uint1(x402))) + var x405 uint64 + var x406 uint64 + x405, x406 = bits.Add64(x384, x381, uint64(p521Uint1(x404))) + var x407 uint64 + var x408 uint64 + x407, x408 = bits.Add64(x382, x379, uint64(p521Uint1(x406))) + var x409 uint64 + var x410 uint64 + x409, x410 = bits.Add64(x380, x377, uint64(p521Uint1(x408))) + x411 := (uint64(p521Uint1(x410)) + x378) + var x413 uint64 + _, x413 = bits.Add64(x357, x393, uint64(0x0)) + var x414 uint64 + var x415 uint64 + x414, x415 = bits.Add64(x359, x395, uint64(p521Uint1(x413))) + var x416 uint64 + var x417 uint64 + x416, x417 = bits.Add64(x361, x397, uint64(p521Uint1(x415))) + var x418 uint64 + var x419 uint64 + x418, x419 = bits.Add64(x363, x399, uint64(p521Uint1(x417))) + var x420 uint64 + var x421 uint64 + x420, x421 = bits.Add64(x365, x401, uint64(p521Uint1(x419))) + var x422 uint64 + var x423 uint64 + x422, x423 = bits.Add64(x367, x403, uint64(p521Uint1(x421))) + var x424 uint64 + var x425 uint64 + x424, x425 = bits.Add64(x369, x405, uint64(p521Uint1(x423))) + var x426 uint64 + var x427 uint64 + x426, x427 = bits.Add64(x371, x407, uint64(p521Uint1(x425))) + var x428 uint64 + var x429 uint64 + x428, x429 = bits.Add64(x373, x409, uint64(p521Uint1(x427))) + var x430 uint64 + var x431 uint64 + x430, x431 = bits.Add64(x375, x411, uint64(p521Uint1(x429))) + x432 := (uint64(p521Uint1(x431)) + uint64(p521Uint1(x376))) + var x433 uint64 + var x434 uint64 + x434, x433 = bits.Mul64(x4, arg2[8]) + var x435 uint64 + var x436 uint64 + x436, x435 = bits.Mul64(x4, arg2[7]) + var x437 uint64 + var x438 uint64 + x438, x437 = bits.Mul64(x4, arg2[6]) + var x439 uint64 + var x440 uint64 + x440, x439 = bits.Mul64(x4, arg2[5]) + var x441 uint64 + var x442 uint64 + x442, x441 = bits.Mul64(x4, arg2[4]) + var x443 uint64 + var x444 uint64 + x444, x443 = bits.Mul64(x4, arg2[3]) + var x445 uint64 + var x446 uint64 + x446, x445 = bits.Mul64(x4, arg2[2]) + var x447 uint64 + var x448 uint64 + x448, x447 = bits.Mul64(x4, arg2[1]) + var x449 uint64 + var x450 uint64 + x450, x449 = bits.Mul64(x4, arg2[0]) + var x451 uint64 + var x452 uint64 + x451, x452 = bits.Add64(x450, x447, uint64(0x0)) + var x453 uint64 + var x454 uint64 + x453, x454 = bits.Add64(x448, x445, uint64(p521Uint1(x452))) + var x455 uint64 + var x456 uint64 + x455, x456 = bits.Add64(x446, x443, uint64(p521Uint1(x454))) + var x457 uint64 + var x458 uint64 + x457, x458 = bits.Add64(x444, x441, uint64(p521Uint1(x456))) + var x459 uint64 + var x460 uint64 + x459, x460 = bits.Add64(x442, x439, uint64(p521Uint1(x458))) + var x461 uint64 + var x462 uint64 + x461, x462 = bits.Add64(x440, x437, uint64(p521Uint1(x460))) + var x463 uint64 + var x464 uint64 + x463, x464 = bits.Add64(x438, x435, uint64(p521Uint1(x462))) + var x465 uint64 + var x466 uint64 + x465, x466 = bits.Add64(x436, x433, uint64(p521Uint1(x464))) + x467 := (uint64(p521Uint1(x466)) + x434) + var x468 uint64 + var x469 uint64 + x468, x469 = bits.Add64(x414, x449, uint64(0x0)) + var x470 uint64 + var x471 uint64 + x470, x471 = bits.Add64(x416, x451, uint64(p521Uint1(x469))) + var x472 uint64 + var x473 uint64 + x472, x473 = bits.Add64(x418, x453, uint64(p521Uint1(x471))) + var x474 uint64 + var x475 uint64 + x474, x475 = bits.Add64(x420, x455, uint64(p521Uint1(x473))) + var x476 uint64 + var x477 uint64 + x476, x477 = bits.Add64(x422, x457, uint64(p521Uint1(x475))) + var x478 uint64 + var x479 uint64 + x478, x479 = bits.Add64(x424, x459, uint64(p521Uint1(x477))) + var x480 uint64 + var x481 uint64 + x480, x481 = bits.Add64(x426, x461, uint64(p521Uint1(x479))) + var x482 uint64 + var x483 uint64 + x482, x483 = bits.Add64(x428, x463, uint64(p521Uint1(x481))) + var x484 uint64 + var x485 uint64 + x484, x485 = bits.Add64(x430, x465, uint64(p521Uint1(x483))) + var x486 uint64 + var x487 uint64 + x486, x487 = bits.Add64(x432, x467, uint64(p521Uint1(x485))) + var x488 uint64 + var x489 uint64 + x489, x488 = bits.Mul64(x468, 0x1ff) + var x490 uint64 + var x491 uint64 + x491, x490 = bits.Mul64(x468, 0xffffffffffffffff) + var x492 uint64 + var x493 uint64 + x493, x492 = bits.Mul64(x468, 0xffffffffffffffff) + var x494 uint64 + var x495 uint64 + x495, x494 = bits.Mul64(x468, 0xffffffffffffffff) + var x496 uint64 + var x497 uint64 + x497, x496 = bits.Mul64(x468, 0xffffffffffffffff) + var x498 uint64 + var x499 uint64 + x499, x498 = bits.Mul64(x468, 0xffffffffffffffff) + var x500 uint64 + var x501 uint64 + x501, x500 = bits.Mul64(x468, 0xffffffffffffffff) + var x502 uint64 + var x503 uint64 + x503, x502 = bits.Mul64(x468, 0xffffffffffffffff) + var x504 uint64 + var x505 uint64 + x505, x504 = bits.Mul64(x468, 0xffffffffffffffff) + var x506 uint64 + var x507 uint64 + x506, x507 = bits.Add64(x505, x502, uint64(0x0)) + var x508 uint64 + var x509 uint64 + x508, x509 = bits.Add64(x503, x500, uint64(p521Uint1(x507))) + var x510 uint64 + var x511 uint64 + x510, x511 = bits.Add64(x501, x498, uint64(p521Uint1(x509))) + var x512 uint64 + var x513 uint64 + x512, x513 = bits.Add64(x499, x496, uint64(p521Uint1(x511))) + var x514 uint64 + var x515 uint64 + x514, x515 = bits.Add64(x497, x494, uint64(p521Uint1(x513))) + var x516 uint64 + var x517 uint64 + x516, x517 = bits.Add64(x495, x492, uint64(p521Uint1(x515))) + var x518 uint64 + var x519 uint64 + x518, x519 = bits.Add64(x493, x490, uint64(p521Uint1(x517))) + var x520 uint64 + var x521 uint64 + x520, x521 = bits.Add64(x491, x488, uint64(p521Uint1(x519))) + x522 := (uint64(p521Uint1(x521)) + x489) + var x524 uint64 + _, x524 = bits.Add64(x468, x504, uint64(0x0)) + var x525 uint64 + var x526 uint64 + x525, x526 = bits.Add64(x470, x506, uint64(p521Uint1(x524))) + var x527 uint64 + var x528 uint64 + x527, x528 = bits.Add64(x472, x508, uint64(p521Uint1(x526))) + var x529 uint64 + var x530 uint64 + x529, x530 = bits.Add64(x474, x510, uint64(p521Uint1(x528))) + var x531 uint64 + var x532 uint64 + x531, x532 = bits.Add64(x476, x512, uint64(p521Uint1(x530))) + var x533 uint64 + var x534 uint64 + x533, x534 = bits.Add64(x478, x514, uint64(p521Uint1(x532))) + var x535 uint64 + var x536 uint64 + x535, x536 = bits.Add64(x480, x516, uint64(p521Uint1(x534))) + var x537 uint64 + var x538 uint64 + x537, x538 = bits.Add64(x482, x518, uint64(p521Uint1(x536))) + var x539 uint64 + var x540 uint64 + x539, x540 = bits.Add64(x484, x520, uint64(p521Uint1(x538))) + var x541 uint64 + var x542 uint64 + x541, x542 = bits.Add64(x486, x522, uint64(p521Uint1(x540))) + x543 := (uint64(p521Uint1(x542)) + uint64(p521Uint1(x487))) + var x544 uint64 + var x545 uint64 + x545, x544 = bits.Mul64(x5, arg2[8]) + var x546 uint64 + var x547 uint64 + x547, x546 = bits.Mul64(x5, arg2[7]) + var x548 uint64 + var x549 uint64 + x549, x548 = bits.Mul64(x5, arg2[6]) + var x550 uint64 + var x551 uint64 + x551, x550 = bits.Mul64(x5, arg2[5]) + var x552 uint64 + var x553 uint64 + x553, x552 = bits.Mul64(x5, arg2[4]) + var x554 uint64 + var x555 uint64 + x555, x554 = bits.Mul64(x5, arg2[3]) + var x556 uint64 + var x557 uint64 + x557, x556 = bits.Mul64(x5, arg2[2]) + var x558 uint64 + var x559 uint64 + x559, x558 = bits.Mul64(x5, arg2[1]) + var x560 uint64 + var x561 uint64 + x561, x560 = bits.Mul64(x5, arg2[0]) + var x562 uint64 + var x563 uint64 + x562, x563 = bits.Add64(x561, x558, uint64(0x0)) + var x564 uint64 + var x565 uint64 + x564, x565 = bits.Add64(x559, x556, uint64(p521Uint1(x563))) + var x566 uint64 + var x567 uint64 + x566, x567 = bits.Add64(x557, x554, uint64(p521Uint1(x565))) + var x568 uint64 + var x569 uint64 + x568, x569 = bits.Add64(x555, x552, uint64(p521Uint1(x567))) + var x570 uint64 + var x571 uint64 + x570, x571 = bits.Add64(x553, x550, uint64(p521Uint1(x569))) + var x572 uint64 + var x573 uint64 + x572, x573 = bits.Add64(x551, x548, uint64(p521Uint1(x571))) + var x574 uint64 + var x575 uint64 + x574, x575 = bits.Add64(x549, x546, uint64(p521Uint1(x573))) + var x576 uint64 + var x577 uint64 + x576, x577 = bits.Add64(x547, x544, uint64(p521Uint1(x575))) + x578 := (uint64(p521Uint1(x577)) + x545) + var x579 uint64 + var x580 uint64 + x579, x580 = bits.Add64(x525, x560, uint64(0x0)) + var x581 uint64 + var x582 uint64 + x581, x582 = bits.Add64(x527, x562, uint64(p521Uint1(x580))) + var x583 uint64 + var x584 uint64 + x583, x584 = bits.Add64(x529, x564, uint64(p521Uint1(x582))) + var x585 uint64 + var x586 uint64 + x585, x586 = bits.Add64(x531, x566, uint64(p521Uint1(x584))) + var x587 uint64 + var x588 uint64 + x587, x588 = bits.Add64(x533, x568, uint64(p521Uint1(x586))) + var x589 uint64 + var x590 uint64 + x589, x590 = bits.Add64(x535, x570, uint64(p521Uint1(x588))) + var x591 uint64 + var x592 uint64 + x591, x592 = bits.Add64(x537, x572, uint64(p521Uint1(x590))) + var x593 uint64 + var x594 uint64 + x593, x594 = bits.Add64(x539, x574, uint64(p521Uint1(x592))) + var x595 uint64 + var x596 uint64 + x595, x596 = bits.Add64(x541, x576, uint64(p521Uint1(x594))) + var x597 uint64 + var x598 uint64 + x597, x598 = bits.Add64(x543, x578, uint64(p521Uint1(x596))) + var x599 uint64 + var x600 uint64 + x600, x599 = bits.Mul64(x579, 0x1ff) + var x601 uint64 + var x602 uint64 + x602, x601 = bits.Mul64(x579, 0xffffffffffffffff) + var x603 uint64 + var x604 uint64 + x604, x603 = bits.Mul64(x579, 0xffffffffffffffff) + var x605 uint64 + var x606 uint64 + x606, x605 = bits.Mul64(x579, 0xffffffffffffffff) + var x607 uint64 + var x608 uint64 + x608, x607 = bits.Mul64(x579, 0xffffffffffffffff) + var x609 uint64 + var x610 uint64 + x610, x609 = bits.Mul64(x579, 0xffffffffffffffff) + var x611 uint64 + var x612 uint64 + x612, x611 = bits.Mul64(x579, 0xffffffffffffffff) + var x613 uint64 + var x614 uint64 + x614, x613 = bits.Mul64(x579, 0xffffffffffffffff) + var x615 uint64 + var x616 uint64 + x616, x615 = bits.Mul64(x579, 0xffffffffffffffff) + var x617 uint64 + var x618 uint64 + x617, x618 = bits.Add64(x616, x613, uint64(0x0)) + var x619 uint64 + var x620 uint64 + x619, x620 = bits.Add64(x614, x611, uint64(p521Uint1(x618))) + var x621 uint64 + var x622 uint64 + x621, x622 = bits.Add64(x612, x609, uint64(p521Uint1(x620))) + var x623 uint64 + var x624 uint64 + x623, x624 = bits.Add64(x610, x607, uint64(p521Uint1(x622))) + var x625 uint64 + var x626 uint64 + x625, x626 = bits.Add64(x608, x605, uint64(p521Uint1(x624))) + var x627 uint64 + var x628 uint64 + x627, x628 = bits.Add64(x606, x603, uint64(p521Uint1(x626))) + var x629 uint64 + var x630 uint64 + x629, x630 = bits.Add64(x604, x601, uint64(p521Uint1(x628))) + var x631 uint64 + var x632 uint64 + x631, x632 = bits.Add64(x602, x599, uint64(p521Uint1(x630))) + x633 := (uint64(p521Uint1(x632)) + x600) + var x635 uint64 + _, x635 = bits.Add64(x579, x615, uint64(0x0)) + var x636 uint64 + var x637 uint64 + x636, x637 = bits.Add64(x581, x617, uint64(p521Uint1(x635))) + var x638 uint64 + var x639 uint64 + x638, x639 = bits.Add64(x583, x619, uint64(p521Uint1(x637))) + var x640 uint64 + var x641 uint64 + x640, x641 = bits.Add64(x585, x621, uint64(p521Uint1(x639))) + var x642 uint64 + var x643 uint64 + x642, x643 = bits.Add64(x587, x623, uint64(p521Uint1(x641))) + var x644 uint64 + var x645 uint64 + x644, x645 = bits.Add64(x589, x625, uint64(p521Uint1(x643))) + var x646 uint64 + var x647 uint64 + x646, x647 = bits.Add64(x591, x627, uint64(p521Uint1(x645))) + var x648 uint64 + var x649 uint64 + x648, x649 = bits.Add64(x593, x629, uint64(p521Uint1(x647))) + var x650 uint64 + var x651 uint64 + x650, x651 = bits.Add64(x595, x631, uint64(p521Uint1(x649))) + var x652 uint64 + var x653 uint64 + x652, x653 = bits.Add64(x597, x633, uint64(p521Uint1(x651))) + x654 := (uint64(p521Uint1(x653)) + uint64(p521Uint1(x598))) + var x655 uint64 + var x656 uint64 + x656, x655 = bits.Mul64(x6, arg2[8]) + var x657 uint64 + var x658 uint64 + x658, x657 = bits.Mul64(x6, arg2[7]) + var x659 uint64 + var x660 uint64 + x660, x659 = bits.Mul64(x6, arg2[6]) + var x661 uint64 + var x662 uint64 + x662, x661 = bits.Mul64(x6, arg2[5]) + var x663 uint64 + var x664 uint64 + x664, x663 = bits.Mul64(x6, arg2[4]) + var x665 uint64 + var x666 uint64 + x666, x665 = bits.Mul64(x6, arg2[3]) + var x667 uint64 + var x668 uint64 + x668, x667 = bits.Mul64(x6, arg2[2]) + var x669 uint64 + var x670 uint64 + x670, x669 = bits.Mul64(x6, arg2[1]) + var x671 uint64 + var x672 uint64 + x672, x671 = bits.Mul64(x6, arg2[0]) + var x673 uint64 + var x674 uint64 + x673, x674 = bits.Add64(x672, x669, uint64(0x0)) + var x675 uint64 + var x676 uint64 + x675, x676 = bits.Add64(x670, x667, uint64(p521Uint1(x674))) + var x677 uint64 + var x678 uint64 + x677, x678 = bits.Add64(x668, x665, uint64(p521Uint1(x676))) + var x679 uint64 + var x680 uint64 + x679, x680 = bits.Add64(x666, x663, uint64(p521Uint1(x678))) + var x681 uint64 + var x682 uint64 + x681, x682 = bits.Add64(x664, x661, uint64(p521Uint1(x680))) + var x683 uint64 + var x684 uint64 + x683, x684 = bits.Add64(x662, x659, uint64(p521Uint1(x682))) + var x685 uint64 + var x686 uint64 + x685, x686 = bits.Add64(x660, x657, uint64(p521Uint1(x684))) + var x687 uint64 + var x688 uint64 + x687, x688 = bits.Add64(x658, x655, uint64(p521Uint1(x686))) + x689 := (uint64(p521Uint1(x688)) + x656) + var x690 uint64 + var x691 uint64 + x690, x691 = bits.Add64(x636, x671, uint64(0x0)) + var x692 uint64 + var x693 uint64 + x692, x693 = bits.Add64(x638, x673, uint64(p521Uint1(x691))) + var x694 uint64 + var x695 uint64 + x694, x695 = bits.Add64(x640, x675, uint64(p521Uint1(x693))) + var x696 uint64 + var x697 uint64 + x696, x697 = bits.Add64(x642, x677, uint64(p521Uint1(x695))) + var x698 uint64 + var x699 uint64 + x698, x699 = bits.Add64(x644, x679, uint64(p521Uint1(x697))) + var x700 uint64 + var x701 uint64 + x700, x701 = bits.Add64(x646, x681, uint64(p521Uint1(x699))) + var x702 uint64 + var x703 uint64 + x702, x703 = bits.Add64(x648, x683, uint64(p521Uint1(x701))) + var x704 uint64 + var x705 uint64 + x704, x705 = bits.Add64(x650, x685, uint64(p521Uint1(x703))) + var x706 uint64 + var x707 uint64 + x706, x707 = bits.Add64(x652, x687, uint64(p521Uint1(x705))) + var x708 uint64 + var x709 uint64 + x708, x709 = bits.Add64(x654, x689, uint64(p521Uint1(x707))) + var x710 uint64 + var x711 uint64 + x711, x710 = bits.Mul64(x690, 0x1ff) + var x712 uint64 + var x713 uint64 + x713, x712 = bits.Mul64(x690, 0xffffffffffffffff) + var x714 uint64 + var x715 uint64 + x715, x714 = bits.Mul64(x690, 0xffffffffffffffff) + var x716 uint64 + var x717 uint64 + x717, x716 = bits.Mul64(x690, 0xffffffffffffffff) + var x718 uint64 + var x719 uint64 + x719, x718 = bits.Mul64(x690, 0xffffffffffffffff) + var x720 uint64 + var x721 uint64 + x721, x720 = bits.Mul64(x690, 0xffffffffffffffff) + var x722 uint64 + var x723 uint64 + x723, x722 = bits.Mul64(x690, 0xffffffffffffffff) + var x724 uint64 + var x725 uint64 + x725, x724 = bits.Mul64(x690, 0xffffffffffffffff) + var x726 uint64 + var x727 uint64 + x727, x726 = bits.Mul64(x690, 0xffffffffffffffff) + var x728 uint64 + var x729 uint64 + x728, x729 = bits.Add64(x727, x724, uint64(0x0)) + var x730 uint64 + var x731 uint64 + x730, x731 = bits.Add64(x725, x722, uint64(p521Uint1(x729))) + var x732 uint64 + var x733 uint64 + x732, x733 = bits.Add64(x723, x720, uint64(p521Uint1(x731))) + var x734 uint64 + var x735 uint64 + x734, x735 = bits.Add64(x721, x718, uint64(p521Uint1(x733))) + var x736 uint64 + var x737 uint64 + x736, x737 = bits.Add64(x719, x716, uint64(p521Uint1(x735))) + var x738 uint64 + var x739 uint64 + x738, x739 = bits.Add64(x717, x714, uint64(p521Uint1(x737))) + var x740 uint64 + var x741 uint64 + x740, x741 = bits.Add64(x715, x712, uint64(p521Uint1(x739))) + var x742 uint64 + var x743 uint64 + x742, x743 = bits.Add64(x713, x710, uint64(p521Uint1(x741))) + x744 := (uint64(p521Uint1(x743)) + x711) + var x746 uint64 + _, x746 = bits.Add64(x690, x726, uint64(0x0)) + var x747 uint64 + var x748 uint64 + x747, x748 = bits.Add64(x692, x728, uint64(p521Uint1(x746))) + var x749 uint64 + var x750 uint64 + x749, x750 = bits.Add64(x694, x730, uint64(p521Uint1(x748))) + var x751 uint64 + var x752 uint64 + x751, x752 = bits.Add64(x696, x732, uint64(p521Uint1(x750))) + var x753 uint64 + var x754 uint64 + x753, x754 = bits.Add64(x698, x734, uint64(p521Uint1(x752))) + var x755 uint64 + var x756 uint64 + x755, x756 = bits.Add64(x700, x736, uint64(p521Uint1(x754))) + var x757 uint64 + var x758 uint64 + x757, x758 = bits.Add64(x702, x738, uint64(p521Uint1(x756))) + var x759 uint64 + var x760 uint64 + x759, x760 = bits.Add64(x704, x740, uint64(p521Uint1(x758))) + var x761 uint64 + var x762 uint64 + x761, x762 = bits.Add64(x706, x742, uint64(p521Uint1(x760))) + var x763 uint64 + var x764 uint64 + x763, x764 = bits.Add64(x708, x744, uint64(p521Uint1(x762))) + x765 := (uint64(p521Uint1(x764)) + uint64(p521Uint1(x709))) + var x766 uint64 + var x767 uint64 + x767, x766 = bits.Mul64(x7, arg2[8]) + var x768 uint64 + var x769 uint64 + x769, x768 = bits.Mul64(x7, arg2[7]) + var x770 uint64 + var x771 uint64 + x771, x770 = bits.Mul64(x7, arg2[6]) + var x772 uint64 + var x773 uint64 + x773, x772 = bits.Mul64(x7, arg2[5]) + var x774 uint64 + var x775 uint64 + x775, x774 = bits.Mul64(x7, arg2[4]) + var x776 uint64 + var x777 uint64 + x777, x776 = bits.Mul64(x7, arg2[3]) + var x778 uint64 + var x779 uint64 + x779, x778 = bits.Mul64(x7, arg2[2]) + var x780 uint64 + var x781 uint64 + x781, x780 = bits.Mul64(x7, arg2[1]) + var x782 uint64 + var x783 uint64 + x783, x782 = bits.Mul64(x7, arg2[0]) + var x784 uint64 + var x785 uint64 + x784, x785 = bits.Add64(x783, x780, uint64(0x0)) + var x786 uint64 + var x787 uint64 + x786, x787 = bits.Add64(x781, x778, uint64(p521Uint1(x785))) + var x788 uint64 + var x789 uint64 + x788, x789 = bits.Add64(x779, x776, uint64(p521Uint1(x787))) + var x790 uint64 + var x791 uint64 + x790, x791 = bits.Add64(x777, x774, uint64(p521Uint1(x789))) + var x792 uint64 + var x793 uint64 + x792, x793 = bits.Add64(x775, x772, uint64(p521Uint1(x791))) + var x794 uint64 + var x795 uint64 + x794, x795 = bits.Add64(x773, x770, uint64(p521Uint1(x793))) + var x796 uint64 + var x797 uint64 + x796, x797 = bits.Add64(x771, x768, uint64(p521Uint1(x795))) + var x798 uint64 + var x799 uint64 + x798, x799 = bits.Add64(x769, x766, uint64(p521Uint1(x797))) + x800 := (uint64(p521Uint1(x799)) + x767) + var x801 uint64 + var x802 uint64 + x801, x802 = bits.Add64(x747, x782, uint64(0x0)) + var x803 uint64 + var x804 uint64 + x803, x804 = bits.Add64(x749, x784, uint64(p521Uint1(x802))) + var x805 uint64 + var x806 uint64 + x805, x806 = bits.Add64(x751, x786, uint64(p521Uint1(x804))) + var x807 uint64 + var x808 uint64 + x807, x808 = bits.Add64(x753, x788, uint64(p521Uint1(x806))) + var x809 uint64 + var x810 uint64 + x809, x810 = bits.Add64(x755, x790, uint64(p521Uint1(x808))) + var x811 uint64 + var x812 uint64 + x811, x812 = bits.Add64(x757, x792, uint64(p521Uint1(x810))) + var x813 uint64 + var x814 uint64 + x813, x814 = bits.Add64(x759, x794, uint64(p521Uint1(x812))) + var x815 uint64 + var x816 uint64 + x815, x816 = bits.Add64(x761, x796, uint64(p521Uint1(x814))) + var x817 uint64 + var x818 uint64 + x817, x818 = bits.Add64(x763, x798, uint64(p521Uint1(x816))) + var x819 uint64 + var x820 uint64 + x819, x820 = bits.Add64(x765, x800, uint64(p521Uint1(x818))) + var x821 uint64 + var x822 uint64 + x822, x821 = bits.Mul64(x801, 0x1ff) + var x823 uint64 + var x824 uint64 + x824, x823 = bits.Mul64(x801, 0xffffffffffffffff) + var x825 uint64 + var x826 uint64 + x826, x825 = bits.Mul64(x801, 0xffffffffffffffff) + var x827 uint64 + var x828 uint64 + x828, x827 = bits.Mul64(x801, 0xffffffffffffffff) + var x829 uint64 + var x830 uint64 + x830, x829 = bits.Mul64(x801, 0xffffffffffffffff) + var x831 uint64 + var x832 uint64 + x832, x831 = bits.Mul64(x801, 0xffffffffffffffff) + var x833 uint64 + var x834 uint64 + x834, x833 = bits.Mul64(x801, 0xffffffffffffffff) + var x835 uint64 + var x836 uint64 + x836, x835 = bits.Mul64(x801, 0xffffffffffffffff) + var x837 uint64 + var x838 uint64 + x838, x837 = bits.Mul64(x801, 0xffffffffffffffff) + var x839 uint64 + var x840 uint64 + x839, x840 = bits.Add64(x838, x835, uint64(0x0)) + var x841 uint64 + var x842 uint64 + x841, x842 = bits.Add64(x836, x833, uint64(p521Uint1(x840))) + var x843 uint64 + var x844 uint64 + x843, x844 = bits.Add64(x834, x831, uint64(p521Uint1(x842))) + var x845 uint64 + var x846 uint64 + x845, x846 = bits.Add64(x832, x829, uint64(p521Uint1(x844))) + var x847 uint64 + var x848 uint64 + x847, x848 = bits.Add64(x830, x827, uint64(p521Uint1(x846))) + var x849 uint64 + var x850 uint64 + x849, x850 = bits.Add64(x828, x825, uint64(p521Uint1(x848))) + var x851 uint64 + var x852 uint64 + x851, x852 = bits.Add64(x826, x823, uint64(p521Uint1(x850))) + var x853 uint64 + var x854 uint64 + x853, x854 = bits.Add64(x824, x821, uint64(p521Uint1(x852))) + x855 := (uint64(p521Uint1(x854)) + x822) + var x857 uint64 + _, x857 = bits.Add64(x801, x837, uint64(0x0)) + var x858 uint64 + var x859 uint64 + x858, x859 = bits.Add64(x803, x839, uint64(p521Uint1(x857))) + var x860 uint64 + var x861 uint64 + x860, x861 = bits.Add64(x805, x841, uint64(p521Uint1(x859))) + var x862 uint64 + var x863 uint64 + x862, x863 = bits.Add64(x807, x843, uint64(p521Uint1(x861))) + var x864 uint64 + var x865 uint64 + x864, x865 = bits.Add64(x809, x845, uint64(p521Uint1(x863))) + var x866 uint64 + var x867 uint64 + x866, x867 = bits.Add64(x811, x847, uint64(p521Uint1(x865))) + var x868 uint64 + var x869 uint64 + x868, x869 = bits.Add64(x813, x849, uint64(p521Uint1(x867))) + var x870 uint64 + var x871 uint64 + x870, x871 = bits.Add64(x815, x851, uint64(p521Uint1(x869))) + var x872 uint64 + var x873 uint64 + x872, x873 = bits.Add64(x817, x853, uint64(p521Uint1(x871))) + var x874 uint64 + var x875 uint64 + x874, x875 = bits.Add64(x819, x855, uint64(p521Uint1(x873))) + x876 := (uint64(p521Uint1(x875)) + uint64(p521Uint1(x820))) + var x877 uint64 + var x878 uint64 + x878, x877 = bits.Mul64(x8, arg2[8]) + var x879 uint64 + var x880 uint64 + x880, x879 = bits.Mul64(x8, arg2[7]) + var x881 uint64 + var x882 uint64 + x882, x881 = bits.Mul64(x8, arg2[6]) + var x883 uint64 + var x884 uint64 + x884, x883 = bits.Mul64(x8, arg2[5]) + var x885 uint64 + var x886 uint64 + x886, x885 = bits.Mul64(x8, arg2[4]) + var x887 uint64 + var x888 uint64 + x888, x887 = bits.Mul64(x8, arg2[3]) + var x889 uint64 + var x890 uint64 + x890, x889 = bits.Mul64(x8, arg2[2]) + var x891 uint64 + var x892 uint64 + x892, x891 = bits.Mul64(x8, arg2[1]) + var x893 uint64 + var x894 uint64 + x894, x893 = bits.Mul64(x8, arg2[0]) + var x895 uint64 + var x896 uint64 + x895, x896 = bits.Add64(x894, x891, uint64(0x0)) + var x897 uint64 + var x898 uint64 + x897, x898 = bits.Add64(x892, x889, uint64(p521Uint1(x896))) + var x899 uint64 + var x900 uint64 + x899, x900 = bits.Add64(x890, x887, uint64(p521Uint1(x898))) + var x901 uint64 + var x902 uint64 + x901, x902 = bits.Add64(x888, x885, uint64(p521Uint1(x900))) + var x903 uint64 + var x904 uint64 + x903, x904 = bits.Add64(x886, x883, uint64(p521Uint1(x902))) + var x905 uint64 + var x906 uint64 + x905, x906 = bits.Add64(x884, x881, uint64(p521Uint1(x904))) + var x907 uint64 + var x908 uint64 + x907, x908 = bits.Add64(x882, x879, uint64(p521Uint1(x906))) + var x909 uint64 + var x910 uint64 + x909, x910 = bits.Add64(x880, x877, uint64(p521Uint1(x908))) + x911 := (uint64(p521Uint1(x910)) + x878) + var x912 uint64 + var x913 uint64 + x912, x913 = bits.Add64(x858, x893, uint64(0x0)) + var x914 uint64 + var x915 uint64 + x914, x915 = bits.Add64(x860, x895, uint64(p521Uint1(x913))) + var x916 uint64 + var x917 uint64 + x916, x917 = bits.Add64(x862, x897, uint64(p521Uint1(x915))) + var x918 uint64 + var x919 uint64 + x918, x919 = bits.Add64(x864, x899, uint64(p521Uint1(x917))) + var x920 uint64 + var x921 uint64 + x920, x921 = bits.Add64(x866, x901, uint64(p521Uint1(x919))) + var x922 uint64 + var x923 uint64 + x922, x923 = bits.Add64(x868, x903, uint64(p521Uint1(x921))) + var x924 uint64 + var x925 uint64 + x924, x925 = bits.Add64(x870, x905, uint64(p521Uint1(x923))) + var x926 uint64 + var x927 uint64 + x926, x927 = bits.Add64(x872, x907, uint64(p521Uint1(x925))) + var x928 uint64 + var x929 uint64 + x928, x929 = bits.Add64(x874, x909, uint64(p521Uint1(x927))) + var x930 uint64 + var x931 uint64 + x930, x931 = bits.Add64(x876, x911, uint64(p521Uint1(x929))) + var x932 uint64 + var x933 uint64 + x933, x932 = bits.Mul64(x912, 0x1ff) + var x934 uint64 + var x935 uint64 + x935, x934 = bits.Mul64(x912, 0xffffffffffffffff) + var x936 uint64 + var x937 uint64 + x937, x936 = bits.Mul64(x912, 0xffffffffffffffff) + var x938 uint64 + var x939 uint64 + x939, x938 = bits.Mul64(x912, 0xffffffffffffffff) + var x940 uint64 + var x941 uint64 + x941, x940 = bits.Mul64(x912, 0xffffffffffffffff) + var x942 uint64 + var x943 uint64 + x943, x942 = bits.Mul64(x912, 0xffffffffffffffff) + var x944 uint64 + var x945 uint64 + x945, x944 = bits.Mul64(x912, 0xffffffffffffffff) + var x946 uint64 + var x947 uint64 + x947, x946 = bits.Mul64(x912, 0xffffffffffffffff) + var x948 uint64 + var x949 uint64 + x949, x948 = bits.Mul64(x912, 0xffffffffffffffff) + var x950 uint64 + var x951 uint64 + x950, x951 = bits.Add64(x949, x946, uint64(0x0)) + var x952 uint64 + var x953 uint64 + x952, x953 = bits.Add64(x947, x944, uint64(p521Uint1(x951))) + var x954 uint64 + var x955 uint64 + x954, x955 = bits.Add64(x945, x942, uint64(p521Uint1(x953))) + var x956 uint64 + var x957 uint64 + x956, x957 = bits.Add64(x943, x940, uint64(p521Uint1(x955))) + var x958 uint64 + var x959 uint64 + x958, x959 = bits.Add64(x941, x938, uint64(p521Uint1(x957))) + var x960 uint64 + var x961 uint64 + x960, x961 = bits.Add64(x939, x936, uint64(p521Uint1(x959))) + var x962 uint64 + var x963 uint64 + x962, x963 = bits.Add64(x937, x934, uint64(p521Uint1(x961))) + var x964 uint64 + var x965 uint64 + x964, x965 = bits.Add64(x935, x932, uint64(p521Uint1(x963))) + x966 := (uint64(p521Uint1(x965)) + x933) + var x968 uint64 + _, x968 = bits.Add64(x912, x948, uint64(0x0)) + var x969 uint64 + var x970 uint64 + x969, x970 = bits.Add64(x914, x950, uint64(p521Uint1(x968))) + var x971 uint64 + var x972 uint64 + x971, x972 = bits.Add64(x916, x952, uint64(p521Uint1(x970))) + var x973 uint64 + var x974 uint64 + x973, x974 = bits.Add64(x918, x954, uint64(p521Uint1(x972))) + var x975 uint64 + var x976 uint64 + x975, x976 = bits.Add64(x920, x956, uint64(p521Uint1(x974))) + var x977 uint64 + var x978 uint64 + x977, x978 = bits.Add64(x922, x958, uint64(p521Uint1(x976))) + var x979 uint64 + var x980 uint64 + x979, x980 = bits.Add64(x924, x960, uint64(p521Uint1(x978))) + var x981 uint64 + var x982 uint64 + x981, x982 = bits.Add64(x926, x962, uint64(p521Uint1(x980))) + var x983 uint64 + var x984 uint64 + x983, x984 = bits.Add64(x928, x964, uint64(p521Uint1(x982))) + var x985 uint64 + var x986 uint64 + x985, x986 = bits.Add64(x930, x966, uint64(p521Uint1(x984))) + x987 := (uint64(p521Uint1(x986)) + uint64(p521Uint1(x931))) + var x988 uint64 + var x989 uint64 + x988, x989 = bits.Sub64(x969, 0xffffffffffffffff, uint64(0x0)) + var x990 uint64 + var x991 uint64 + x990, x991 = bits.Sub64(x971, 0xffffffffffffffff, uint64(p521Uint1(x989))) + var x992 uint64 + var x993 uint64 + x992, x993 = bits.Sub64(x973, 0xffffffffffffffff, uint64(p521Uint1(x991))) + var x994 uint64 + var x995 uint64 + x994, x995 = bits.Sub64(x975, 0xffffffffffffffff, uint64(p521Uint1(x993))) + var x996 uint64 + var x997 uint64 + x996, x997 = bits.Sub64(x977, 0xffffffffffffffff, uint64(p521Uint1(x995))) + var x998 uint64 + var x999 uint64 + x998, x999 = bits.Sub64(x979, 0xffffffffffffffff, uint64(p521Uint1(x997))) + var x1000 uint64 + var x1001 uint64 + x1000, x1001 = bits.Sub64(x981, 0xffffffffffffffff, uint64(p521Uint1(x999))) + var x1002 uint64 + var x1003 uint64 + x1002, x1003 = bits.Sub64(x983, 0xffffffffffffffff, uint64(p521Uint1(x1001))) + var x1004 uint64 + var x1005 uint64 + x1004, x1005 = bits.Sub64(x985, 0x1ff, uint64(p521Uint1(x1003))) + var x1007 uint64 + _, x1007 = bits.Sub64(x987, uint64(0x0), uint64(p521Uint1(x1005))) + var x1008 uint64 + p521CmovznzU64(&x1008, p521Uint1(x1007), x988, x969) + var x1009 uint64 + p521CmovznzU64(&x1009, p521Uint1(x1007), x990, x971) + var x1010 uint64 + p521CmovznzU64(&x1010, p521Uint1(x1007), x992, x973) + var x1011 uint64 + p521CmovznzU64(&x1011, p521Uint1(x1007), x994, x975) + var x1012 uint64 + p521CmovznzU64(&x1012, p521Uint1(x1007), x996, x977) + var x1013 uint64 + p521CmovznzU64(&x1013, p521Uint1(x1007), x998, x979) + var x1014 uint64 + p521CmovznzU64(&x1014, p521Uint1(x1007), x1000, x981) + var x1015 uint64 + p521CmovznzU64(&x1015, p521Uint1(x1007), x1002, x983) + var x1016 uint64 + p521CmovznzU64(&x1016, p521Uint1(x1007), x1004, x985) + out1[0] = x1008 + out1[1] = x1009 + out1[2] = x1010 + out1[3] = x1011 + out1[4] = x1012 + out1[5] = x1013 + out1[6] = x1014 + out1[7] = x1015 + out1[8] = x1016 } -// p521AddcarryxU57 is an addition with carry. +// p521Square squares a field element in the Montgomery domain. // +// Preconditions: +// 0 ≤ eval arg1 < m // Postconditions: -// out1 = (arg1 + arg2 + arg3) mod 2^57 -// out2 = ⌊(arg1 + arg2 + arg3) / 2^57⌋ +// eval (from_montgomery out1) mod m = (eval (from_montgomery arg1) * eval (from_montgomery arg1)) mod m +// 0 ≤ eval out1 < m // -// Input Bounds: -// arg1: [0x0 ~> 0x1] -// arg2: [0x0 ~> 0x1ffffffffffffff] -// arg3: [0x0 ~> 0x1ffffffffffffff] -// Output Bounds: -// out1: [0x0 ~> 0x1ffffffffffffff] -// out2: [0x0 ~> 0x1] -func p521AddcarryxU57(out1 *uint64, out2 *p521Uint1, arg1 p521Uint1, arg2 uint64, arg3 uint64) { - x1 := ((uint64(arg1) + arg2) + arg3) - x2 := (x1 & 0x1ffffffffffffff) - x3 := p521Uint1((x1 >> 57)) - *out1 = x2 - *out2 = x3 +func p521Square(out1 *p521MontgomeryDomainFieldElement, arg1 *p521MontgomeryDomainFieldElement) { + x1 := arg1[1] + x2 := arg1[2] + x3 := arg1[3] + x4 := arg1[4] + x5 := arg1[5] + x6 := arg1[6] + x7 := arg1[7] + x8 := arg1[8] + x9 := arg1[0] + var x10 uint64 + var x11 uint64 + x11, x10 = bits.Mul64(x9, arg1[8]) + var x12 uint64 + var x13 uint64 + x13, x12 = bits.Mul64(x9, arg1[7]) + var x14 uint64 + var x15 uint64 + x15, x14 = bits.Mul64(x9, arg1[6]) + var x16 uint64 + var x17 uint64 + x17, x16 = bits.Mul64(x9, arg1[5]) + var x18 uint64 + var x19 uint64 + x19, x18 = bits.Mul64(x9, arg1[4]) + var x20 uint64 + var x21 uint64 + x21, x20 = bits.Mul64(x9, arg1[3]) + var x22 uint64 + var x23 uint64 + x23, x22 = bits.Mul64(x9, arg1[2]) + var x24 uint64 + var x25 uint64 + x25, x24 = bits.Mul64(x9, arg1[1]) + var x26 uint64 + var x27 uint64 + x27, x26 = bits.Mul64(x9, arg1[0]) + var x28 uint64 + var x29 uint64 + x28, x29 = bits.Add64(x27, x24, uint64(0x0)) + var x30 uint64 + var x31 uint64 + x30, x31 = bits.Add64(x25, x22, uint64(p521Uint1(x29))) + var x32 uint64 + var x33 uint64 + x32, x33 = bits.Add64(x23, x20, uint64(p521Uint1(x31))) + var x34 uint64 + var x35 uint64 + x34, x35 = bits.Add64(x21, x18, uint64(p521Uint1(x33))) + var x36 uint64 + var x37 uint64 + x36, x37 = bits.Add64(x19, x16, uint64(p521Uint1(x35))) + var x38 uint64 + var x39 uint64 + x38, x39 = bits.Add64(x17, x14, uint64(p521Uint1(x37))) + var x40 uint64 + var x41 uint64 + x40, x41 = bits.Add64(x15, x12, uint64(p521Uint1(x39))) + var x42 uint64 + var x43 uint64 + x42, x43 = bits.Add64(x13, x10, uint64(p521Uint1(x41))) + x44 := (uint64(p521Uint1(x43)) + x11) + var x45 uint64 + var x46 uint64 + x46, x45 = bits.Mul64(x26, 0x1ff) + var x47 uint64 + var x48 uint64 + x48, x47 = bits.Mul64(x26, 0xffffffffffffffff) + var x49 uint64 + var x50 uint64 + x50, x49 = bits.Mul64(x26, 0xffffffffffffffff) + var x51 uint64 + var x52 uint64 + x52, x51 = bits.Mul64(x26, 0xffffffffffffffff) + var x53 uint64 + var x54 uint64 + x54, x53 = bits.Mul64(x26, 0xffffffffffffffff) + var x55 uint64 + var x56 uint64 + x56, x55 = bits.Mul64(x26, 0xffffffffffffffff) + var x57 uint64 + var x58 uint64 + x58, x57 = bits.Mul64(x26, 0xffffffffffffffff) + var x59 uint64 + var x60 uint64 + x60, x59 = bits.Mul64(x26, 0xffffffffffffffff) + var x61 uint64 + var x62 uint64 + x62, x61 = bits.Mul64(x26, 0xffffffffffffffff) + var x63 uint64 + var x64 uint64 + x63, x64 = bits.Add64(x62, x59, uint64(0x0)) + var x65 uint64 + var x66 uint64 + x65, x66 = bits.Add64(x60, x57, uint64(p521Uint1(x64))) + var x67 uint64 + var x68 uint64 + x67, x68 = bits.Add64(x58, x55, uint64(p521Uint1(x66))) + var x69 uint64 + var x70 uint64 + x69, x70 = bits.Add64(x56, x53, uint64(p521Uint1(x68))) + var x71 uint64 + var x72 uint64 + x71, x72 = bits.Add64(x54, x51, uint64(p521Uint1(x70))) + var x73 uint64 + var x74 uint64 + x73, x74 = bits.Add64(x52, x49, uint64(p521Uint1(x72))) + var x75 uint64 + var x76 uint64 + x75, x76 = bits.Add64(x50, x47, uint64(p521Uint1(x74))) + var x77 uint64 + var x78 uint64 + x77, x78 = bits.Add64(x48, x45, uint64(p521Uint1(x76))) + x79 := (uint64(p521Uint1(x78)) + x46) + var x81 uint64 + _, x81 = bits.Add64(x26, x61, uint64(0x0)) + var x82 uint64 + var x83 uint64 + x82, x83 = bits.Add64(x28, x63, uint64(p521Uint1(x81))) + var x84 uint64 + var x85 uint64 + x84, x85 = bits.Add64(x30, x65, uint64(p521Uint1(x83))) + var x86 uint64 + var x87 uint64 + x86, x87 = bits.Add64(x32, x67, uint64(p521Uint1(x85))) + var x88 uint64 + var x89 uint64 + x88, x89 = bits.Add64(x34, x69, uint64(p521Uint1(x87))) + var x90 uint64 + var x91 uint64 + x90, x91 = bits.Add64(x36, x71, uint64(p521Uint1(x89))) + var x92 uint64 + var x93 uint64 + x92, x93 = bits.Add64(x38, x73, uint64(p521Uint1(x91))) + var x94 uint64 + var x95 uint64 + x94, x95 = bits.Add64(x40, x75, uint64(p521Uint1(x93))) + var x96 uint64 + var x97 uint64 + x96, x97 = bits.Add64(x42, x77, uint64(p521Uint1(x95))) + var x98 uint64 + var x99 uint64 + x98, x99 = bits.Add64(x44, x79, uint64(p521Uint1(x97))) + var x100 uint64 + var x101 uint64 + x101, x100 = bits.Mul64(x1, arg1[8]) + var x102 uint64 + var x103 uint64 + x103, x102 = bits.Mul64(x1, arg1[7]) + var x104 uint64 + var x105 uint64 + x105, x104 = bits.Mul64(x1, arg1[6]) + var x106 uint64 + var x107 uint64 + x107, x106 = bits.Mul64(x1, arg1[5]) + var x108 uint64 + var x109 uint64 + x109, x108 = bits.Mul64(x1, arg1[4]) + var x110 uint64 + var x111 uint64 + x111, x110 = bits.Mul64(x1, arg1[3]) + var x112 uint64 + var x113 uint64 + x113, x112 = bits.Mul64(x1, arg1[2]) + var x114 uint64 + var x115 uint64 + x115, x114 = bits.Mul64(x1, arg1[1]) + var x116 uint64 + var x117 uint64 + x117, x116 = bits.Mul64(x1, arg1[0]) + var x118 uint64 + var x119 uint64 + x118, x119 = bits.Add64(x117, x114, uint64(0x0)) + var x120 uint64 + var x121 uint64 + x120, x121 = bits.Add64(x115, x112, uint64(p521Uint1(x119))) + var x122 uint64 + var x123 uint64 + x122, x123 = bits.Add64(x113, x110, uint64(p521Uint1(x121))) + var x124 uint64 + var x125 uint64 + x124, x125 = bits.Add64(x111, x108, uint64(p521Uint1(x123))) + var x126 uint64 + var x127 uint64 + x126, x127 = bits.Add64(x109, x106, uint64(p521Uint1(x125))) + var x128 uint64 + var x129 uint64 + x128, x129 = bits.Add64(x107, x104, uint64(p521Uint1(x127))) + var x130 uint64 + var x131 uint64 + x130, x131 = bits.Add64(x105, x102, uint64(p521Uint1(x129))) + var x132 uint64 + var x133 uint64 + x132, x133 = bits.Add64(x103, x100, uint64(p521Uint1(x131))) + x134 := (uint64(p521Uint1(x133)) + x101) + var x135 uint64 + var x136 uint64 + x135, x136 = bits.Add64(x82, x116, uint64(0x0)) + var x137 uint64 + var x138 uint64 + x137, x138 = bits.Add64(x84, x118, uint64(p521Uint1(x136))) + var x139 uint64 + var x140 uint64 + x139, x140 = bits.Add64(x86, x120, uint64(p521Uint1(x138))) + var x141 uint64 + var x142 uint64 + x141, x142 = bits.Add64(x88, x122, uint64(p521Uint1(x140))) + var x143 uint64 + var x144 uint64 + x143, x144 = bits.Add64(x90, x124, uint64(p521Uint1(x142))) + var x145 uint64 + var x146 uint64 + x145, x146 = bits.Add64(x92, x126, uint64(p521Uint1(x144))) + var x147 uint64 + var x148 uint64 + x147, x148 = bits.Add64(x94, x128, uint64(p521Uint1(x146))) + var x149 uint64 + var x150 uint64 + x149, x150 = bits.Add64(x96, x130, uint64(p521Uint1(x148))) + var x151 uint64 + var x152 uint64 + x151, x152 = bits.Add64(x98, x132, uint64(p521Uint1(x150))) + var x153 uint64 + var x154 uint64 + x153, x154 = bits.Add64(uint64(p521Uint1(x99)), x134, uint64(p521Uint1(x152))) + var x155 uint64 + var x156 uint64 + x156, x155 = bits.Mul64(x135, 0x1ff) + var x157 uint64 + var x158 uint64 + x158, x157 = bits.Mul64(x135, 0xffffffffffffffff) + var x159 uint64 + var x160 uint64 + x160, x159 = bits.Mul64(x135, 0xffffffffffffffff) + var x161 uint64 + var x162 uint64 + x162, x161 = bits.Mul64(x135, 0xffffffffffffffff) + var x163 uint64 + var x164 uint64 + x164, x163 = bits.Mul64(x135, 0xffffffffffffffff) + var x165 uint64 + var x166 uint64 + x166, x165 = bits.Mul64(x135, 0xffffffffffffffff) + var x167 uint64 + var x168 uint64 + x168, x167 = bits.Mul64(x135, 0xffffffffffffffff) + var x169 uint64 + var x170 uint64 + x170, x169 = bits.Mul64(x135, 0xffffffffffffffff) + var x171 uint64 + var x172 uint64 + x172, x171 = bits.Mul64(x135, 0xffffffffffffffff) + var x173 uint64 + var x174 uint64 + x173, x174 = bits.Add64(x172, x169, uint64(0x0)) + var x175 uint64 + var x176 uint64 + x175, x176 = bits.Add64(x170, x167, uint64(p521Uint1(x174))) + var x177 uint64 + var x178 uint64 + x177, x178 = bits.Add64(x168, x165, uint64(p521Uint1(x176))) + var x179 uint64 + var x180 uint64 + x179, x180 = bits.Add64(x166, x163, uint64(p521Uint1(x178))) + var x181 uint64 + var x182 uint64 + x181, x182 = bits.Add64(x164, x161, uint64(p521Uint1(x180))) + var x183 uint64 + var x184 uint64 + x183, x184 = bits.Add64(x162, x159, uint64(p521Uint1(x182))) + var x185 uint64 + var x186 uint64 + x185, x186 = bits.Add64(x160, x157, uint64(p521Uint1(x184))) + var x187 uint64 + var x188 uint64 + x187, x188 = bits.Add64(x158, x155, uint64(p521Uint1(x186))) + x189 := (uint64(p521Uint1(x188)) + x156) + var x191 uint64 + _, x191 = bits.Add64(x135, x171, uint64(0x0)) + var x192 uint64 + var x193 uint64 + x192, x193 = bits.Add64(x137, x173, uint64(p521Uint1(x191))) + var x194 uint64 + var x195 uint64 + x194, x195 = bits.Add64(x139, x175, uint64(p521Uint1(x193))) + var x196 uint64 + var x197 uint64 + x196, x197 = bits.Add64(x141, x177, uint64(p521Uint1(x195))) + var x198 uint64 + var x199 uint64 + x198, x199 = bits.Add64(x143, x179, uint64(p521Uint1(x197))) + var x200 uint64 + var x201 uint64 + x200, x201 = bits.Add64(x145, x181, uint64(p521Uint1(x199))) + var x202 uint64 + var x203 uint64 + x202, x203 = bits.Add64(x147, x183, uint64(p521Uint1(x201))) + var x204 uint64 + var x205 uint64 + x204, x205 = bits.Add64(x149, x185, uint64(p521Uint1(x203))) + var x206 uint64 + var x207 uint64 + x206, x207 = bits.Add64(x151, x187, uint64(p521Uint1(x205))) + var x208 uint64 + var x209 uint64 + x208, x209 = bits.Add64(x153, x189, uint64(p521Uint1(x207))) + x210 := (uint64(p521Uint1(x209)) + uint64(p521Uint1(x154))) + var x211 uint64 + var x212 uint64 + x212, x211 = bits.Mul64(x2, arg1[8]) + var x213 uint64 + var x214 uint64 + x214, x213 = bits.Mul64(x2, arg1[7]) + var x215 uint64 + var x216 uint64 + x216, x215 = bits.Mul64(x2, arg1[6]) + var x217 uint64 + var x218 uint64 + x218, x217 = bits.Mul64(x2, arg1[5]) + var x219 uint64 + var x220 uint64 + x220, x219 = bits.Mul64(x2, arg1[4]) + var x221 uint64 + var x222 uint64 + x222, x221 = bits.Mul64(x2, arg1[3]) + var x223 uint64 + var x224 uint64 + x224, x223 = bits.Mul64(x2, arg1[2]) + var x225 uint64 + var x226 uint64 + x226, x225 = bits.Mul64(x2, arg1[1]) + var x227 uint64 + var x228 uint64 + x228, x227 = bits.Mul64(x2, arg1[0]) + var x229 uint64 + var x230 uint64 + x229, x230 = bits.Add64(x228, x225, uint64(0x0)) + var x231 uint64 + var x232 uint64 + x231, x232 = bits.Add64(x226, x223, uint64(p521Uint1(x230))) + var x233 uint64 + var x234 uint64 + x233, x234 = bits.Add64(x224, x221, uint64(p521Uint1(x232))) + var x235 uint64 + var x236 uint64 + x235, x236 = bits.Add64(x222, x219, uint64(p521Uint1(x234))) + var x237 uint64 + var x238 uint64 + x237, x238 = bits.Add64(x220, x217, uint64(p521Uint1(x236))) + var x239 uint64 + var x240 uint64 + x239, x240 = bits.Add64(x218, x215, uint64(p521Uint1(x238))) + var x241 uint64 + var x242 uint64 + x241, x242 = bits.Add64(x216, x213, uint64(p521Uint1(x240))) + var x243 uint64 + var x244 uint64 + x243, x244 = bits.Add64(x214, x211, uint64(p521Uint1(x242))) + x245 := (uint64(p521Uint1(x244)) + x212) + var x246 uint64 + var x247 uint64 + x246, x247 = bits.Add64(x192, x227, uint64(0x0)) + var x248 uint64 + var x249 uint64 + x248, x249 = bits.Add64(x194, x229, uint64(p521Uint1(x247))) + var x250 uint64 + var x251 uint64 + x250, x251 = bits.Add64(x196, x231, uint64(p521Uint1(x249))) + var x252 uint64 + var x253 uint64 + x252, x253 = bits.Add64(x198, x233, uint64(p521Uint1(x251))) + var x254 uint64 + var x255 uint64 + x254, x255 = bits.Add64(x200, x235, uint64(p521Uint1(x253))) + var x256 uint64 + var x257 uint64 + x256, x257 = bits.Add64(x202, x237, uint64(p521Uint1(x255))) + var x258 uint64 + var x259 uint64 + x258, x259 = bits.Add64(x204, x239, uint64(p521Uint1(x257))) + var x260 uint64 + var x261 uint64 + x260, x261 = bits.Add64(x206, x241, uint64(p521Uint1(x259))) + var x262 uint64 + var x263 uint64 + x262, x263 = bits.Add64(x208, x243, uint64(p521Uint1(x261))) + var x264 uint64 + var x265 uint64 + x264, x265 = bits.Add64(x210, x245, uint64(p521Uint1(x263))) + var x266 uint64 + var x267 uint64 + x267, x266 = bits.Mul64(x246, 0x1ff) + var x268 uint64 + var x269 uint64 + x269, x268 = bits.Mul64(x246, 0xffffffffffffffff) + var x270 uint64 + var x271 uint64 + x271, x270 = bits.Mul64(x246, 0xffffffffffffffff) + var x272 uint64 + var x273 uint64 + x273, x272 = bits.Mul64(x246, 0xffffffffffffffff) + var x274 uint64 + var x275 uint64 + x275, x274 = bits.Mul64(x246, 0xffffffffffffffff) + var x276 uint64 + var x277 uint64 + x277, x276 = bits.Mul64(x246, 0xffffffffffffffff) + var x278 uint64 + var x279 uint64 + x279, x278 = bits.Mul64(x246, 0xffffffffffffffff) + var x280 uint64 + var x281 uint64 + x281, x280 = bits.Mul64(x246, 0xffffffffffffffff) + var x282 uint64 + var x283 uint64 + x283, x282 = bits.Mul64(x246, 0xffffffffffffffff) + var x284 uint64 + var x285 uint64 + x284, x285 = bits.Add64(x283, x280, uint64(0x0)) + var x286 uint64 + var x287 uint64 + x286, x287 = bits.Add64(x281, x278, uint64(p521Uint1(x285))) + var x288 uint64 + var x289 uint64 + x288, x289 = bits.Add64(x279, x276, uint64(p521Uint1(x287))) + var x290 uint64 + var x291 uint64 + x290, x291 = bits.Add64(x277, x274, uint64(p521Uint1(x289))) + var x292 uint64 + var x293 uint64 + x292, x293 = bits.Add64(x275, x272, uint64(p521Uint1(x291))) + var x294 uint64 + var x295 uint64 + x294, x295 = bits.Add64(x273, x270, uint64(p521Uint1(x293))) + var x296 uint64 + var x297 uint64 + x296, x297 = bits.Add64(x271, x268, uint64(p521Uint1(x295))) + var x298 uint64 + var x299 uint64 + x298, x299 = bits.Add64(x269, x266, uint64(p521Uint1(x297))) + x300 := (uint64(p521Uint1(x299)) + x267) + var x302 uint64 + _, x302 = bits.Add64(x246, x282, uint64(0x0)) + var x303 uint64 + var x304 uint64 + x303, x304 = bits.Add64(x248, x284, uint64(p521Uint1(x302))) + var x305 uint64 + var x306 uint64 + x305, x306 = bits.Add64(x250, x286, uint64(p521Uint1(x304))) + var x307 uint64 + var x308 uint64 + x307, x308 = bits.Add64(x252, x288, uint64(p521Uint1(x306))) + var x309 uint64 + var x310 uint64 + x309, x310 = bits.Add64(x254, x290, uint64(p521Uint1(x308))) + var x311 uint64 + var x312 uint64 + x311, x312 = bits.Add64(x256, x292, uint64(p521Uint1(x310))) + var x313 uint64 + var x314 uint64 + x313, x314 = bits.Add64(x258, x294, uint64(p521Uint1(x312))) + var x315 uint64 + var x316 uint64 + x315, x316 = bits.Add64(x260, x296, uint64(p521Uint1(x314))) + var x317 uint64 + var x318 uint64 + x317, x318 = bits.Add64(x262, x298, uint64(p521Uint1(x316))) + var x319 uint64 + var x320 uint64 + x319, x320 = bits.Add64(x264, x300, uint64(p521Uint1(x318))) + x321 := (uint64(p521Uint1(x320)) + uint64(p521Uint1(x265))) + var x322 uint64 + var x323 uint64 + x323, x322 = bits.Mul64(x3, arg1[8]) + var x324 uint64 + var x325 uint64 + x325, x324 = bits.Mul64(x3, arg1[7]) + var x326 uint64 + var x327 uint64 + x327, x326 = bits.Mul64(x3, arg1[6]) + var x328 uint64 + var x329 uint64 + x329, x328 = bits.Mul64(x3, arg1[5]) + var x330 uint64 + var x331 uint64 + x331, x330 = bits.Mul64(x3, arg1[4]) + var x332 uint64 + var x333 uint64 + x333, x332 = bits.Mul64(x3, arg1[3]) + var x334 uint64 + var x335 uint64 + x335, x334 = bits.Mul64(x3, arg1[2]) + var x336 uint64 + var x337 uint64 + x337, x336 = bits.Mul64(x3, arg1[1]) + var x338 uint64 + var x339 uint64 + x339, x338 = bits.Mul64(x3, arg1[0]) + var x340 uint64 + var x341 uint64 + x340, x341 = bits.Add64(x339, x336, uint64(0x0)) + var x342 uint64 + var x343 uint64 + x342, x343 = bits.Add64(x337, x334, uint64(p521Uint1(x341))) + var x344 uint64 + var x345 uint64 + x344, x345 = bits.Add64(x335, x332, uint64(p521Uint1(x343))) + var x346 uint64 + var x347 uint64 + x346, x347 = bits.Add64(x333, x330, uint64(p521Uint1(x345))) + var x348 uint64 + var x349 uint64 + x348, x349 = bits.Add64(x331, x328, uint64(p521Uint1(x347))) + var x350 uint64 + var x351 uint64 + x350, x351 = bits.Add64(x329, x326, uint64(p521Uint1(x349))) + var x352 uint64 + var x353 uint64 + x352, x353 = bits.Add64(x327, x324, uint64(p521Uint1(x351))) + var x354 uint64 + var x355 uint64 + x354, x355 = bits.Add64(x325, x322, uint64(p521Uint1(x353))) + x356 := (uint64(p521Uint1(x355)) + x323) + var x357 uint64 + var x358 uint64 + x357, x358 = bits.Add64(x303, x338, uint64(0x0)) + var x359 uint64 + var x360 uint64 + x359, x360 = bits.Add64(x305, x340, uint64(p521Uint1(x358))) + var x361 uint64 + var x362 uint64 + x361, x362 = bits.Add64(x307, x342, uint64(p521Uint1(x360))) + var x363 uint64 + var x364 uint64 + x363, x364 = bits.Add64(x309, x344, uint64(p521Uint1(x362))) + var x365 uint64 + var x366 uint64 + x365, x366 = bits.Add64(x311, x346, uint64(p521Uint1(x364))) + var x367 uint64 + var x368 uint64 + x367, x368 = bits.Add64(x313, x348, uint64(p521Uint1(x366))) + var x369 uint64 + var x370 uint64 + x369, x370 = bits.Add64(x315, x350, uint64(p521Uint1(x368))) + var x371 uint64 + var x372 uint64 + x371, x372 = bits.Add64(x317, x352, uint64(p521Uint1(x370))) + var x373 uint64 + var x374 uint64 + x373, x374 = bits.Add64(x319, x354, uint64(p521Uint1(x372))) + var x375 uint64 + var x376 uint64 + x375, x376 = bits.Add64(x321, x356, uint64(p521Uint1(x374))) + var x377 uint64 + var x378 uint64 + x378, x377 = bits.Mul64(x357, 0x1ff) + var x379 uint64 + var x380 uint64 + x380, x379 = bits.Mul64(x357, 0xffffffffffffffff) + var x381 uint64 + var x382 uint64 + x382, x381 = bits.Mul64(x357, 0xffffffffffffffff) + var x383 uint64 + var x384 uint64 + x384, x383 = bits.Mul64(x357, 0xffffffffffffffff) + var x385 uint64 + var x386 uint64 + x386, x385 = bits.Mul64(x357, 0xffffffffffffffff) + var x387 uint64 + var x388 uint64 + x388, x387 = bits.Mul64(x357, 0xffffffffffffffff) + var x389 uint64 + var x390 uint64 + x390, x389 = bits.Mul64(x357, 0xffffffffffffffff) + var x391 uint64 + var x392 uint64 + x392, x391 = bits.Mul64(x357, 0xffffffffffffffff) + var x393 uint64 + var x394 uint64 + x394, x393 = bits.Mul64(x357, 0xffffffffffffffff) + var x395 uint64 + var x396 uint64 + x395, x396 = bits.Add64(x394, x391, uint64(0x0)) + var x397 uint64 + var x398 uint64 + x397, x398 = bits.Add64(x392, x389, uint64(p521Uint1(x396))) + var x399 uint64 + var x400 uint64 + x399, x400 = bits.Add64(x390, x387, uint64(p521Uint1(x398))) + var x401 uint64 + var x402 uint64 + x401, x402 = bits.Add64(x388, x385, uint64(p521Uint1(x400))) + var x403 uint64 + var x404 uint64 + x403, x404 = bits.Add64(x386, x383, uint64(p521Uint1(x402))) + var x405 uint64 + var x406 uint64 + x405, x406 = bits.Add64(x384, x381, uint64(p521Uint1(x404))) + var x407 uint64 + var x408 uint64 + x407, x408 = bits.Add64(x382, x379, uint64(p521Uint1(x406))) + var x409 uint64 + var x410 uint64 + x409, x410 = bits.Add64(x380, x377, uint64(p521Uint1(x408))) + x411 := (uint64(p521Uint1(x410)) + x378) + var x413 uint64 + _, x413 = bits.Add64(x357, x393, uint64(0x0)) + var x414 uint64 + var x415 uint64 + x414, x415 = bits.Add64(x359, x395, uint64(p521Uint1(x413))) + var x416 uint64 + var x417 uint64 + x416, x417 = bits.Add64(x361, x397, uint64(p521Uint1(x415))) + var x418 uint64 + var x419 uint64 + x418, x419 = bits.Add64(x363, x399, uint64(p521Uint1(x417))) + var x420 uint64 + var x421 uint64 + x420, x421 = bits.Add64(x365, x401, uint64(p521Uint1(x419))) + var x422 uint64 + var x423 uint64 + x422, x423 = bits.Add64(x367, x403, uint64(p521Uint1(x421))) + var x424 uint64 + var x425 uint64 + x424, x425 = bits.Add64(x369, x405, uint64(p521Uint1(x423))) + var x426 uint64 + var x427 uint64 + x426, x427 = bits.Add64(x371, x407, uint64(p521Uint1(x425))) + var x428 uint64 + var x429 uint64 + x428, x429 = bits.Add64(x373, x409, uint64(p521Uint1(x427))) + var x430 uint64 + var x431 uint64 + x430, x431 = bits.Add64(x375, x411, uint64(p521Uint1(x429))) + x432 := (uint64(p521Uint1(x431)) + uint64(p521Uint1(x376))) + var x433 uint64 + var x434 uint64 + x434, x433 = bits.Mul64(x4, arg1[8]) + var x435 uint64 + var x436 uint64 + x436, x435 = bits.Mul64(x4, arg1[7]) + var x437 uint64 + var x438 uint64 + x438, x437 = bits.Mul64(x4, arg1[6]) + var x439 uint64 + var x440 uint64 + x440, x439 = bits.Mul64(x4, arg1[5]) + var x441 uint64 + var x442 uint64 + x442, x441 = bits.Mul64(x4, arg1[4]) + var x443 uint64 + var x444 uint64 + x444, x443 = bits.Mul64(x4, arg1[3]) + var x445 uint64 + var x446 uint64 + x446, x445 = bits.Mul64(x4, arg1[2]) + var x447 uint64 + var x448 uint64 + x448, x447 = bits.Mul64(x4, arg1[1]) + var x449 uint64 + var x450 uint64 + x450, x449 = bits.Mul64(x4, arg1[0]) + var x451 uint64 + var x452 uint64 + x451, x452 = bits.Add64(x450, x447, uint64(0x0)) + var x453 uint64 + var x454 uint64 + x453, x454 = bits.Add64(x448, x445, uint64(p521Uint1(x452))) + var x455 uint64 + var x456 uint64 + x455, x456 = bits.Add64(x446, x443, uint64(p521Uint1(x454))) + var x457 uint64 + var x458 uint64 + x457, x458 = bits.Add64(x444, x441, uint64(p521Uint1(x456))) + var x459 uint64 + var x460 uint64 + x459, x460 = bits.Add64(x442, x439, uint64(p521Uint1(x458))) + var x461 uint64 + var x462 uint64 + x461, x462 = bits.Add64(x440, x437, uint64(p521Uint1(x460))) + var x463 uint64 + var x464 uint64 + x463, x464 = bits.Add64(x438, x435, uint64(p521Uint1(x462))) + var x465 uint64 + var x466 uint64 + x465, x466 = bits.Add64(x436, x433, uint64(p521Uint1(x464))) + x467 := (uint64(p521Uint1(x466)) + x434) + var x468 uint64 + var x469 uint64 + x468, x469 = bits.Add64(x414, x449, uint64(0x0)) + var x470 uint64 + var x471 uint64 + x470, x471 = bits.Add64(x416, x451, uint64(p521Uint1(x469))) + var x472 uint64 + var x473 uint64 + x472, x473 = bits.Add64(x418, x453, uint64(p521Uint1(x471))) + var x474 uint64 + var x475 uint64 + x474, x475 = bits.Add64(x420, x455, uint64(p521Uint1(x473))) + var x476 uint64 + var x477 uint64 + x476, x477 = bits.Add64(x422, x457, uint64(p521Uint1(x475))) + var x478 uint64 + var x479 uint64 + x478, x479 = bits.Add64(x424, x459, uint64(p521Uint1(x477))) + var x480 uint64 + var x481 uint64 + x480, x481 = bits.Add64(x426, x461, uint64(p521Uint1(x479))) + var x482 uint64 + var x483 uint64 + x482, x483 = bits.Add64(x428, x463, uint64(p521Uint1(x481))) + var x484 uint64 + var x485 uint64 + x484, x485 = bits.Add64(x430, x465, uint64(p521Uint1(x483))) + var x486 uint64 + var x487 uint64 + x486, x487 = bits.Add64(x432, x467, uint64(p521Uint1(x485))) + var x488 uint64 + var x489 uint64 + x489, x488 = bits.Mul64(x468, 0x1ff) + var x490 uint64 + var x491 uint64 + x491, x490 = bits.Mul64(x468, 0xffffffffffffffff) + var x492 uint64 + var x493 uint64 + x493, x492 = bits.Mul64(x468, 0xffffffffffffffff) + var x494 uint64 + var x495 uint64 + x495, x494 = bits.Mul64(x468, 0xffffffffffffffff) + var x496 uint64 + var x497 uint64 + x497, x496 = bits.Mul64(x468, 0xffffffffffffffff) + var x498 uint64 + var x499 uint64 + x499, x498 = bits.Mul64(x468, 0xffffffffffffffff) + var x500 uint64 + var x501 uint64 + x501, x500 = bits.Mul64(x468, 0xffffffffffffffff) + var x502 uint64 + var x503 uint64 + x503, x502 = bits.Mul64(x468, 0xffffffffffffffff) + var x504 uint64 + var x505 uint64 + x505, x504 = bits.Mul64(x468, 0xffffffffffffffff) + var x506 uint64 + var x507 uint64 + x506, x507 = bits.Add64(x505, x502, uint64(0x0)) + var x508 uint64 + var x509 uint64 + x508, x509 = bits.Add64(x503, x500, uint64(p521Uint1(x507))) + var x510 uint64 + var x511 uint64 + x510, x511 = bits.Add64(x501, x498, uint64(p521Uint1(x509))) + var x512 uint64 + var x513 uint64 + x512, x513 = bits.Add64(x499, x496, uint64(p521Uint1(x511))) + var x514 uint64 + var x515 uint64 + x514, x515 = bits.Add64(x497, x494, uint64(p521Uint1(x513))) + var x516 uint64 + var x517 uint64 + x516, x517 = bits.Add64(x495, x492, uint64(p521Uint1(x515))) + var x518 uint64 + var x519 uint64 + x518, x519 = bits.Add64(x493, x490, uint64(p521Uint1(x517))) + var x520 uint64 + var x521 uint64 + x520, x521 = bits.Add64(x491, x488, uint64(p521Uint1(x519))) + x522 := (uint64(p521Uint1(x521)) + x489) + var x524 uint64 + _, x524 = bits.Add64(x468, x504, uint64(0x0)) + var x525 uint64 + var x526 uint64 + x525, x526 = bits.Add64(x470, x506, uint64(p521Uint1(x524))) + var x527 uint64 + var x528 uint64 + x527, x528 = bits.Add64(x472, x508, uint64(p521Uint1(x526))) + var x529 uint64 + var x530 uint64 + x529, x530 = bits.Add64(x474, x510, uint64(p521Uint1(x528))) + var x531 uint64 + var x532 uint64 + x531, x532 = bits.Add64(x476, x512, uint64(p521Uint1(x530))) + var x533 uint64 + var x534 uint64 + x533, x534 = bits.Add64(x478, x514, uint64(p521Uint1(x532))) + var x535 uint64 + var x536 uint64 + x535, x536 = bits.Add64(x480, x516, uint64(p521Uint1(x534))) + var x537 uint64 + var x538 uint64 + x537, x538 = bits.Add64(x482, x518, uint64(p521Uint1(x536))) + var x539 uint64 + var x540 uint64 + x539, x540 = bits.Add64(x484, x520, uint64(p521Uint1(x538))) + var x541 uint64 + var x542 uint64 + x541, x542 = bits.Add64(x486, x522, uint64(p521Uint1(x540))) + x543 := (uint64(p521Uint1(x542)) + uint64(p521Uint1(x487))) + var x544 uint64 + var x545 uint64 + x545, x544 = bits.Mul64(x5, arg1[8]) + var x546 uint64 + var x547 uint64 + x547, x546 = bits.Mul64(x5, arg1[7]) + var x548 uint64 + var x549 uint64 + x549, x548 = bits.Mul64(x5, arg1[6]) + var x550 uint64 + var x551 uint64 + x551, x550 = bits.Mul64(x5, arg1[5]) + var x552 uint64 + var x553 uint64 + x553, x552 = bits.Mul64(x5, arg1[4]) + var x554 uint64 + var x555 uint64 + x555, x554 = bits.Mul64(x5, arg1[3]) + var x556 uint64 + var x557 uint64 + x557, x556 = bits.Mul64(x5, arg1[2]) + var x558 uint64 + var x559 uint64 + x559, x558 = bits.Mul64(x5, arg1[1]) + var x560 uint64 + var x561 uint64 + x561, x560 = bits.Mul64(x5, arg1[0]) + var x562 uint64 + var x563 uint64 + x562, x563 = bits.Add64(x561, x558, uint64(0x0)) + var x564 uint64 + var x565 uint64 + x564, x565 = bits.Add64(x559, x556, uint64(p521Uint1(x563))) + var x566 uint64 + var x567 uint64 + x566, x567 = bits.Add64(x557, x554, uint64(p521Uint1(x565))) + var x568 uint64 + var x569 uint64 + x568, x569 = bits.Add64(x555, x552, uint64(p521Uint1(x567))) + var x570 uint64 + var x571 uint64 + x570, x571 = bits.Add64(x553, x550, uint64(p521Uint1(x569))) + var x572 uint64 + var x573 uint64 + x572, x573 = bits.Add64(x551, x548, uint64(p521Uint1(x571))) + var x574 uint64 + var x575 uint64 + x574, x575 = bits.Add64(x549, x546, uint64(p521Uint1(x573))) + var x576 uint64 + var x577 uint64 + x576, x577 = bits.Add64(x547, x544, uint64(p521Uint1(x575))) + x578 := (uint64(p521Uint1(x577)) + x545) + var x579 uint64 + var x580 uint64 + x579, x580 = bits.Add64(x525, x560, uint64(0x0)) + var x581 uint64 + var x582 uint64 + x581, x582 = bits.Add64(x527, x562, uint64(p521Uint1(x580))) + var x583 uint64 + var x584 uint64 + x583, x584 = bits.Add64(x529, x564, uint64(p521Uint1(x582))) + var x585 uint64 + var x586 uint64 + x585, x586 = bits.Add64(x531, x566, uint64(p521Uint1(x584))) + var x587 uint64 + var x588 uint64 + x587, x588 = bits.Add64(x533, x568, uint64(p521Uint1(x586))) + var x589 uint64 + var x590 uint64 + x589, x590 = bits.Add64(x535, x570, uint64(p521Uint1(x588))) + var x591 uint64 + var x592 uint64 + x591, x592 = bits.Add64(x537, x572, uint64(p521Uint1(x590))) + var x593 uint64 + var x594 uint64 + x593, x594 = bits.Add64(x539, x574, uint64(p521Uint1(x592))) + var x595 uint64 + var x596 uint64 + x595, x596 = bits.Add64(x541, x576, uint64(p521Uint1(x594))) + var x597 uint64 + var x598 uint64 + x597, x598 = bits.Add64(x543, x578, uint64(p521Uint1(x596))) + var x599 uint64 + var x600 uint64 + x600, x599 = bits.Mul64(x579, 0x1ff) + var x601 uint64 + var x602 uint64 + x602, x601 = bits.Mul64(x579, 0xffffffffffffffff) + var x603 uint64 + var x604 uint64 + x604, x603 = bits.Mul64(x579, 0xffffffffffffffff) + var x605 uint64 + var x606 uint64 + x606, x605 = bits.Mul64(x579, 0xffffffffffffffff) + var x607 uint64 + var x608 uint64 + x608, x607 = bits.Mul64(x579, 0xffffffffffffffff) + var x609 uint64 + var x610 uint64 + x610, x609 = bits.Mul64(x579, 0xffffffffffffffff) + var x611 uint64 + var x612 uint64 + x612, x611 = bits.Mul64(x579, 0xffffffffffffffff) + var x613 uint64 + var x614 uint64 + x614, x613 = bits.Mul64(x579, 0xffffffffffffffff) + var x615 uint64 + var x616 uint64 + x616, x615 = bits.Mul64(x579, 0xffffffffffffffff) + var x617 uint64 + var x618 uint64 + x617, x618 = bits.Add64(x616, x613, uint64(0x0)) + var x619 uint64 + var x620 uint64 + x619, x620 = bits.Add64(x614, x611, uint64(p521Uint1(x618))) + var x621 uint64 + var x622 uint64 + x621, x622 = bits.Add64(x612, x609, uint64(p521Uint1(x620))) + var x623 uint64 + var x624 uint64 + x623, x624 = bits.Add64(x610, x607, uint64(p521Uint1(x622))) + var x625 uint64 + var x626 uint64 + x625, x626 = bits.Add64(x608, x605, uint64(p521Uint1(x624))) + var x627 uint64 + var x628 uint64 + x627, x628 = bits.Add64(x606, x603, uint64(p521Uint1(x626))) + var x629 uint64 + var x630 uint64 + x629, x630 = bits.Add64(x604, x601, uint64(p521Uint1(x628))) + var x631 uint64 + var x632 uint64 + x631, x632 = bits.Add64(x602, x599, uint64(p521Uint1(x630))) + x633 := (uint64(p521Uint1(x632)) + x600) + var x635 uint64 + _, x635 = bits.Add64(x579, x615, uint64(0x0)) + var x636 uint64 + var x637 uint64 + x636, x637 = bits.Add64(x581, x617, uint64(p521Uint1(x635))) + var x638 uint64 + var x639 uint64 + x638, x639 = bits.Add64(x583, x619, uint64(p521Uint1(x637))) + var x640 uint64 + var x641 uint64 + x640, x641 = bits.Add64(x585, x621, uint64(p521Uint1(x639))) + var x642 uint64 + var x643 uint64 + x642, x643 = bits.Add64(x587, x623, uint64(p521Uint1(x641))) + var x644 uint64 + var x645 uint64 + x644, x645 = bits.Add64(x589, x625, uint64(p521Uint1(x643))) + var x646 uint64 + var x647 uint64 + x646, x647 = bits.Add64(x591, x627, uint64(p521Uint1(x645))) + var x648 uint64 + var x649 uint64 + x648, x649 = bits.Add64(x593, x629, uint64(p521Uint1(x647))) + var x650 uint64 + var x651 uint64 + x650, x651 = bits.Add64(x595, x631, uint64(p521Uint1(x649))) + var x652 uint64 + var x653 uint64 + x652, x653 = bits.Add64(x597, x633, uint64(p521Uint1(x651))) + x654 := (uint64(p521Uint1(x653)) + uint64(p521Uint1(x598))) + var x655 uint64 + var x656 uint64 + x656, x655 = bits.Mul64(x6, arg1[8]) + var x657 uint64 + var x658 uint64 + x658, x657 = bits.Mul64(x6, arg1[7]) + var x659 uint64 + var x660 uint64 + x660, x659 = bits.Mul64(x6, arg1[6]) + var x661 uint64 + var x662 uint64 + x662, x661 = bits.Mul64(x6, arg1[5]) + var x663 uint64 + var x664 uint64 + x664, x663 = bits.Mul64(x6, arg1[4]) + var x665 uint64 + var x666 uint64 + x666, x665 = bits.Mul64(x6, arg1[3]) + var x667 uint64 + var x668 uint64 + x668, x667 = bits.Mul64(x6, arg1[2]) + var x669 uint64 + var x670 uint64 + x670, x669 = bits.Mul64(x6, arg1[1]) + var x671 uint64 + var x672 uint64 + x672, x671 = bits.Mul64(x6, arg1[0]) + var x673 uint64 + var x674 uint64 + x673, x674 = bits.Add64(x672, x669, uint64(0x0)) + var x675 uint64 + var x676 uint64 + x675, x676 = bits.Add64(x670, x667, uint64(p521Uint1(x674))) + var x677 uint64 + var x678 uint64 + x677, x678 = bits.Add64(x668, x665, uint64(p521Uint1(x676))) + var x679 uint64 + var x680 uint64 + x679, x680 = bits.Add64(x666, x663, uint64(p521Uint1(x678))) + var x681 uint64 + var x682 uint64 + x681, x682 = bits.Add64(x664, x661, uint64(p521Uint1(x680))) + var x683 uint64 + var x684 uint64 + x683, x684 = bits.Add64(x662, x659, uint64(p521Uint1(x682))) + var x685 uint64 + var x686 uint64 + x685, x686 = bits.Add64(x660, x657, uint64(p521Uint1(x684))) + var x687 uint64 + var x688 uint64 + x687, x688 = bits.Add64(x658, x655, uint64(p521Uint1(x686))) + x689 := (uint64(p521Uint1(x688)) + x656) + var x690 uint64 + var x691 uint64 + x690, x691 = bits.Add64(x636, x671, uint64(0x0)) + var x692 uint64 + var x693 uint64 + x692, x693 = bits.Add64(x638, x673, uint64(p521Uint1(x691))) + var x694 uint64 + var x695 uint64 + x694, x695 = bits.Add64(x640, x675, uint64(p521Uint1(x693))) + var x696 uint64 + var x697 uint64 + x696, x697 = bits.Add64(x642, x677, uint64(p521Uint1(x695))) + var x698 uint64 + var x699 uint64 + x698, x699 = bits.Add64(x644, x679, uint64(p521Uint1(x697))) + var x700 uint64 + var x701 uint64 + x700, x701 = bits.Add64(x646, x681, uint64(p521Uint1(x699))) + var x702 uint64 + var x703 uint64 + x702, x703 = bits.Add64(x648, x683, uint64(p521Uint1(x701))) + var x704 uint64 + var x705 uint64 + x704, x705 = bits.Add64(x650, x685, uint64(p521Uint1(x703))) + var x706 uint64 + var x707 uint64 + x706, x707 = bits.Add64(x652, x687, uint64(p521Uint1(x705))) + var x708 uint64 + var x709 uint64 + x708, x709 = bits.Add64(x654, x689, uint64(p521Uint1(x707))) + var x710 uint64 + var x711 uint64 + x711, x710 = bits.Mul64(x690, 0x1ff) + var x712 uint64 + var x713 uint64 + x713, x712 = bits.Mul64(x690, 0xffffffffffffffff) + var x714 uint64 + var x715 uint64 + x715, x714 = bits.Mul64(x690, 0xffffffffffffffff) + var x716 uint64 + var x717 uint64 + x717, x716 = bits.Mul64(x690, 0xffffffffffffffff) + var x718 uint64 + var x719 uint64 + x719, x718 = bits.Mul64(x690, 0xffffffffffffffff) + var x720 uint64 + var x721 uint64 + x721, x720 = bits.Mul64(x690, 0xffffffffffffffff) + var x722 uint64 + var x723 uint64 + x723, x722 = bits.Mul64(x690, 0xffffffffffffffff) + var x724 uint64 + var x725 uint64 + x725, x724 = bits.Mul64(x690, 0xffffffffffffffff) + var x726 uint64 + var x727 uint64 + x727, x726 = bits.Mul64(x690, 0xffffffffffffffff) + var x728 uint64 + var x729 uint64 + x728, x729 = bits.Add64(x727, x724, uint64(0x0)) + var x730 uint64 + var x731 uint64 + x730, x731 = bits.Add64(x725, x722, uint64(p521Uint1(x729))) + var x732 uint64 + var x733 uint64 + x732, x733 = bits.Add64(x723, x720, uint64(p521Uint1(x731))) + var x734 uint64 + var x735 uint64 + x734, x735 = bits.Add64(x721, x718, uint64(p521Uint1(x733))) + var x736 uint64 + var x737 uint64 + x736, x737 = bits.Add64(x719, x716, uint64(p521Uint1(x735))) + var x738 uint64 + var x739 uint64 + x738, x739 = bits.Add64(x717, x714, uint64(p521Uint1(x737))) + var x740 uint64 + var x741 uint64 + x740, x741 = bits.Add64(x715, x712, uint64(p521Uint1(x739))) + var x742 uint64 + var x743 uint64 + x742, x743 = bits.Add64(x713, x710, uint64(p521Uint1(x741))) + x744 := (uint64(p521Uint1(x743)) + x711) + var x746 uint64 + _, x746 = bits.Add64(x690, x726, uint64(0x0)) + var x747 uint64 + var x748 uint64 + x747, x748 = bits.Add64(x692, x728, uint64(p521Uint1(x746))) + var x749 uint64 + var x750 uint64 + x749, x750 = bits.Add64(x694, x730, uint64(p521Uint1(x748))) + var x751 uint64 + var x752 uint64 + x751, x752 = bits.Add64(x696, x732, uint64(p521Uint1(x750))) + var x753 uint64 + var x754 uint64 + x753, x754 = bits.Add64(x698, x734, uint64(p521Uint1(x752))) + var x755 uint64 + var x756 uint64 + x755, x756 = bits.Add64(x700, x736, uint64(p521Uint1(x754))) + var x757 uint64 + var x758 uint64 + x757, x758 = bits.Add64(x702, x738, uint64(p521Uint1(x756))) + var x759 uint64 + var x760 uint64 + x759, x760 = bits.Add64(x704, x740, uint64(p521Uint1(x758))) + var x761 uint64 + var x762 uint64 + x761, x762 = bits.Add64(x706, x742, uint64(p521Uint1(x760))) + var x763 uint64 + var x764 uint64 + x763, x764 = bits.Add64(x708, x744, uint64(p521Uint1(x762))) + x765 := (uint64(p521Uint1(x764)) + uint64(p521Uint1(x709))) + var x766 uint64 + var x767 uint64 + x767, x766 = bits.Mul64(x7, arg1[8]) + var x768 uint64 + var x769 uint64 + x769, x768 = bits.Mul64(x7, arg1[7]) + var x770 uint64 + var x771 uint64 + x771, x770 = bits.Mul64(x7, arg1[6]) + var x772 uint64 + var x773 uint64 + x773, x772 = bits.Mul64(x7, arg1[5]) + var x774 uint64 + var x775 uint64 + x775, x774 = bits.Mul64(x7, arg1[4]) + var x776 uint64 + var x777 uint64 + x777, x776 = bits.Mul64(x7, arg1[3]) + var x778 uint64 + var x779 uint64 + x779, x778 = bits.Mul64(x7, arg1[2]) + var x780 uint64 + var x781 uint64 + x781, x780 = bits.Mul64(x7, arg1[1]) + var x782 uint64 + var x783 uint64 + x783, x782 = bits.Mul64(x7, arg1[0]) + var x784 uint64 + var x785 uint64 + x784, x785 = bits.Add64(x783, x780, uint64(0x0)) + var x786 uint64 + var x787 uint64 + x786, x787 = bits.Add64(x781, x778, uint64(p521Uint1(x785))) + var x788 uint64 + var x789 uint64 + x788, x789 = bits.Add64(x779, x776, uint64(p521Uint1(x787))) + var x790 uint64 + var x791 uint64 + x790, x791 = bits.Add64(x777, x774, uint64(p521Uint1(x789))) + var x792 uint64 + var x793 uint64 + x792, x793 = bits.Add64(x775, x772, uint64(p521Uint1(x791))) + var x794 uint64 + var x795 uint64 + x794, x795 = bits.Add64(x773, x770, uint64(p521Uint1(x793))) + var x796 uint64 + var x797 uint64 + x796, x797 = bits.Add64(x771, x768, uint64(p521Uint1(x795))) + var x798 uint64 + var x799 uint64 + x798, x799 = bits.Add64(x769, x766, uint64(p521Uint1(x797))) + x800 := (uint64(p521Uint1(x799)) + x767) + var x801 uint64 + var x802 uint64 + x801, x802 = bits.Add64(x747, x782, uint64(0x0)) + var x803 uint64 + var x804 uint64 + x803, x804 = bits.Add64(x749, x784, uint64(p521Uint1(x802))) + var x805 uint64 + var x806 uint64 + x805, x806 = bits.Add64(x751, x786, uint64(p521Uint1(x804))) + var x807 uint64 + var x808 uint64 + x807, x808 = bits.Add64(x753, x788, uint64(p521Uint1(x806))) + var x809 uint64 + var x810 uint64 + x809, x810 = bits.Add64(x755, x790, uint64(p521Uint1(x808))) + var x811 uint64 + var x812 uint64 + x811, x812 = bits.Add64(x757, x792, uint64(p521Uint1(x810))) + var x813 uint64 + var x814 uint64 + x813, x814 = bits.Add64(x759, x794, uint64(p521Uint1(x812))) + var x815 uint64 + var x816 uint64 + x815, x816 = bits.Add64(x761, x796, uint64(p521Uint1(x814))) + var x817 uint64 + var x818 uint64 + x817, x818 = bits.Add64(x763, x798, uint64(p521Uint1(x816))) + var x819 uint64 + var x820 uint64 + x819, x820 = bits.Add64(x765, x800, uint64(p521Uint1(x818))) + var x821 uint64 + var x822 uint64 + x822, x821 = bits.Mul64(x801, 0x1ff) + var x823 uint64 + var x824 uint64 + x824, x823 = bits.Mul64(x801, 0xffffffffffffffff) + var x825 uint64 + var x826 uint64 + x826, x825 = bits.Mul64(x801, 0xffffffffffffffff) + var x827 uint64 + var x828 uint64 + x828, x827 = bits.Mul64(x801, 0xffffffffffffffff) + var x829 uint64 + var x830 uint64 + x830, x829 = bits.Mul64(x801, 0xffffffffffffffff) + var x831 uint64 + var x832 uint64 + x832, x831 = bits.Mul64(x801, 0xffffffffffffffff) + var x833 uint64 + var x834 uint64 + x834, x833 = bits.Mul64(x801, 0xffffffffffffffff) + var x835 uint64 + var x836 uint64 + x836, x835 = bits.Mul64(x801, 0xffffffffffffffff) + var x837 uint64 + var x838 uint64 + x838, x837 = bits.Mul64(x801, 0xffffffffffffffff) + var x839 uint64 + var x840 uint64 + x839, x840 = bits.Add64(x838, x835, uint64(0x0)) + var x841 uint64 + var x842 uint64 + x841, x842 = bits.Add64(x836, x833, uint64(p521Uint1(x840))) + var x843 uint64 + var x844 uint64 + x843, x844 = bits.Add64(x834, x831, uint64(p521Uint1(x842))) + var x845 uint64 + var x846 uint64 + x845, x846 = bits.Add64(x832, x829, uint64(p521Uint1(x844))) + var x847 uint64 + var x848 uint64 + x847, x848 = bits.Add64(x830, x827, uint64(p521Uint1(x846))) + var x849 uint64 + var x850 uint64 + x849, x850 = bits.Add64(x828, x825, uint64(p521Uint1(x848))) + var x851 uint64 + var x852 uint64 + x851, x852 = bits.Add64(x826, x823, uint64(p521Uint1(x850))) + var x853 uint64 + var x854 uint64 + x853, x854 = bits.Add64(x824, x821, uint64(p521Uint1(x852))) + x855 := (uint64(p521Uint1(x854)) + x822) + var x857 uint64 + _, x857 = bits.Add64(x801, x837, uint64(0x0)) + var x858 uint64 + var x859 uint64 + x858, x859 = bits.Add64(x803, x839, uint64(p521Uint1(x857))) + var x860 uint64 + var x861 uint64 + x860, x861 = bits.Add64(x805, x841, uint64(p521Uint1(x859))) + var x862 uint64 + var x863 uint64 + x862, x863 = bits.Add64(x807, x843, uint64(p521Uint1(x861))) + var x864 uint64 + var x865 uint64 + x864, x865 = bits.Add64(x809, x845, uint64(p521Uint1(x863))) + var x866 uint64 + var x867 uint64 + x866, x867 = bits.Add64(x811, x847, uint64(p521Uint1(x865))) + var x868 uint64 + var x869 uint64 + x868, x869 = bits.Add64(x813, x849, uint64(p521Uint1(x867))) + var x870 uint64 + var x871 uint64 + x870, x871 = bits.Add64(x815, x851, uint64(p521Uint1(x869))) + var x872 uint64 + var x873 uint64 + x872, x873 = bits.Add64(x817, x853, uint64(p521Uint1(x871))) + var x874 uint64 + var x875 uint64 + x874, x875 = bits.Add64(x819, x855, uint64(p521Uint1(x873))) + x876 := (uint64(p521Uint1(x875)) + uint64(p521Uint1(x820))) + var x877 uint64 + var x878 uint64 + x878, x877 = bits.Mul64(x8, arg1[8]) + var x879 uint64 + var x880 uint64 + x880, x879 = bits.Mul64(x8, arg1[7]) + var x881 uint64 + var x882 uint64 + x882, x881 = bits.Mul64(x8, arg1[6]) + var x883 uint64 + var x884 uint64 + x884, x883 = bits.Mul64(x8, arg1[5]) + var x885 uint64 + var x886 uint64 + x886, x885 = bits.Mul64(x8, arg1[4]) + var x887 uint64 + var x888 uint64 + x888, x887 = bits.Mul64(x8, arg1[3]) + var x889 uint64 + var x890 uint64 + x890, x889 = bits.Mul64(x8, arg1[2]) + var x891 uint64 + var x892 uint64 + x892, x891 = bits.Mul64(x8, arg1[1]) + var x893 uint64 + var x894 uint64 + x894, x893 = bits.Mul64(x8, arg1[0]) + var x895 uint64 + var x896 uint64 + x895, x896 = bits.Add64(x894, x891, uint64(0x0)) + var x897 uint64 + var x898 uint64 + x897, x898 = bits.Add64(x892, x889, uint64(p521Uint1(x896))) + var x899 uint64 + var x900 uint64 + x899, x900 = bits.Add64(x890, x887, uint64(p521Uint1(x898))) + var x901 uint64 + var x902 uint64 + x901, x902 = bits.Add64(x888, x885, uint64(p521Uint1(x900))) + var x903 uint64 + var x904 uint64 + x903, x904 = bits.Add64(x886, x883, uint64(p521Uint1(x902))) + var x905 uint64 + var x906 uint64 + x905, x906 = bits.Add64(x884, x881, uint64(p521Uint1(x904))) + var x907 uint64 + var x908 uint64 + x907, x908 = bits.Add64(x882, x879, uint64(p521Uint1(x906))) + var x909 uint64 + var x910 uint64 + x909, x910 = bits.Add64(x880, x877, uint64(p521Uint1(x908))) + x911 := (uint64(p521Uint1(x910)) + x878) + var x912 uint64 + var x913 uint64 + x912, x913 = bits.Add64(x858, x893, uint64(0x0)) + var x914 uint64 + var x915 uint64 + x914, x915 = bits.Add64(x860, x895, uint64(p521Uint1(x913))) + var x916 uint64 + var x917 uint64 + x916, x917 = bits.Add64(x862, x897, uint64(p521Uint1(x915))) + var x918 uint64 + var x919 uint64 + x918, x919 = bits.Add64(x864, x899, uint64(p521Uint1(x917))) + var x920 uint64 + var x921 uint64 + x920, x921 = bits.Add64(x866, x901, uint64(p521Uint1(x919))) + var x922 uint64 + var x923 uint64 + x922, x923 = bits.Add64(x868, x903, uint64(p521Uint1(x921))) + var x924 uint64 + var x925 uint64 + x924, x925 = bits.Add64(x870, x905, uint64(p521Uint1(x923))) + var x926 uint64 + var x927 uint64 + x926, x927 = bits.Add64(x872, x907, uint64(p521Uint1(x925))) + var x928 uint64 + var x929 uint64 + x928, x929 = bits.Add64(x874, x909, uint64(p521Uint1(x927))) + var x930 uint64 + var x931 uint64 + x930, x931 = bits.Add64(x876, x911, uint64(p521Uint1(x929))) + var x932 uint64 + var x933 uint64 + x933, x932 = bits.Mul64(x912, 0x1ff) + var x934 uint64 + var x935 uint64 + x935, x934 = bits.Mul64(x912, 0xffffffffffffffff) + var x936 uint64 + var x937 uint64 + x937, x936 = bits.Mul64(x912, 0xffffffffffffffff) + var x938 uint64 + var x939 uint64 + x939, x938 = bits.Mul64(x912, 0xffffffffffffffff) + var x940 uint64 + var x941 uint64 + x941, x940 = bits.Mul64(x912, 0xffffffffffffffff) + var x942 uint64 + var x943 uint64 + x943, x942 = bits.Mul64(x912, 0xffffffffffffffff) + var x944 uint64 + var x945 uint64 + x945, x944 = bits.Mul64(x912, 0xffffffffffffffff) + var x946 uint64 + var x947 uint64 + x947, x946 = bits.Mul64(x912, 0xffffffffffffffff) + var x948 uint64 + var x949 uint64 + x949, x948 = bits.Mul64(x912, 0xffffffffffffffff) + var x950 uint64 + var x951 uint64 + x950, x951 = bits.Add64(x949, x946, uint64(0x0)) + var x952 uint64 + var x953 uint64 + x952, x953 = bits.Add64(x947, x944, uint64(p521Uint1(x951))) + var x954 uint64 + var x955 uint64 + x954, x955 = bits.Add64(x945, x942, uint64(p521Uint1(x953))) + var x956 uint64 + var x957 uint64 + x956, x957 = bits.Add64(x943, x940, uint64(p521Uint1(x955))) + var x958 uint64 + var x959 uint64 + x958, x959 = bits.Add64(x941, x938, uint64(p521Uint1(x957))) + var x960 uint64 + var x961 uint64 + x960, x961 = bits.Add64(x939, x936, uint64(p521Uint1(x959))) + var x962 uint64 + var x963 uint64 + x962, x963 = bits.Add64(x937, x934, uint64(p521Uint1(x961))) + var x964 uint64 + var x965 uint64 + x964, x965 = bits.Add64(x935, x932, uint64(p521Uint1(x963))) + x966 := (uint64(p521Uint1(x965)) + x933) + var x968 uint64 + _, x968 = bits.Add64(x912, x948, uint64(0x0)) + var x969 uint64 + var x970 uint64 + x969, x970 = bits.Add64(x914, x950, uint64(p521Uint1(x968))) + var x971 uint64 + var x972 uint64 + x971, x972 = bits.Add64(x916, x952, uint64(p521Uint1(x970))) + var x973 uint64 + var x974 uint64 + x973, x974 = bits.Add64(x918, x954, uint64(p521Uint1(x972))) + var x975 uint64 + var x976 uint64 + x975, x976 = bits.Add64(x920, x956, uint64(p521Uint1(x974))) + var x977 uint64 + var x978 uint64 + x977, x978 = bits.Add64(x922, x958, uint64(p521Uint1(x976))) + var x979 uint64 + var x980 uint64 + x979, x980 = bits.Add64(x924, x960, uint64(p521Uint1(x978))) + var x981 uint64 + var x982 uint64 + x981, x982 = bits.Add64(x926, x962, uint64(p521Uint1(x980))) + var x983 uint64 + var x984 uint64 + x983, x984 = bits.Add64(x928, x964, uint64(p521Uint1(x982))) + var x985 uint64 + var x986 uint64 + x985, x986 = bits.Add64(x930, x966, uint64(p521Uint1(x984))) + x987 := (uint64(p521Uint1(x986)) + uint64(p521Uint1(x931))) + var x988 uint64 + var x989 uint64 + x988, x989 = bits.Sub64(x969, 0xffffffffffffffff, uint64(0x0)) + var x990 uint64 + var x991 uint64 + x990, x991 = bits.Sub64(x971, 0xffffffffffffffff, uint64(p521Uint1(x989))) + var x992 uint64 + var x993 uint64 + x992, x993 = bits.Sub64(x973, 0xffffffffffffffff, uint64(p521Uint1(x991))) + var x994 uint64 + var x995 uint64 + x994, x995 = bits.Sub64(x975, 0xffffffffffffffff, uint64(p521Uint1(x993))) + var x996 uint64 + var x997 uint64 + x996, x997 = bits.Sub64(x977, 0xffffffffffffffff, uint64(p521Uint1(x995))) + var x998 uint64 + var x999 uint64 + x998, x999 = bits.Sub64(x979, 0xffffffffffffffff, uint64(p521Uint1(x997))) + var x1000 uint64 + var x1001 uint64 + x1000, x1001 = bits.Sub64(x981, 0xffffffffffffffff, uint64(p521Uint1(x999))) + var x1002 uint64 + var x1003 uint64 + x1002, x1003 = bits.Sub64(x983, 0xffffffffffffffff, uint64(p521Uint1(x1001))) + var x1004 uint64 + var x1005 uint64 + x1004, x1005 = bits.Sub64(x985, 0x1ff, uint64(p521Uint1(x1003))) + var x1007 uint64 + _, x1007 = bits.Sub64(x987, uint64(0x0), uint64(p521Uint1(x1005))) + var x1008 uint64 + p521CmovznzU64(&x1008, p521Uint1(x1007), x988, x969) + var x1009 uint64 + p521CmovznzU64(&x1009, p521Uint1(x1007), x990, x971) + var x1010 uint64 + p521CmovznzU64(&x1010, p521Uint1(x1007), x992, x973) + var x1011 uint64 + p521CmovznzU64(&x1011, p521Uint1(x1007), x994, x975) + var x1012 uint64 + p521CmovznzU64(&x1012, p521Uint1(x1007), x996, x977) + var x1013 uint64 + p521CmovznzU64(&x1013, p521Uint1(x1007), x998, x979) + var x1014 uint64 + p521CmovznzU64(&x1014, p521Uint1(x1007), x1000, x981) + var x1015 uint64 + p521CmovznzU64(&x1015, p521Uint1(x1007), x1002, x983) + var x1016 uint64 + p521CmovznzU64(&x1016, p521Uint1(x1007), x1004, x985) + out1[0] = x1008 + out1[1] = x1009 + out1[2] = x1010 + out1[3] = x1011 + out1[4] = x1012 + out1[5] = x1013 + out1[6] = x1014 + out1[7] = x1015 + out1[8] = x1016 } -// p521SubborrowxU57 is a subtraction with borrow. +// p521Add adds two field elements in the Montgomery domain. // +// Preconditions: +// 0 ≤ eval arg1 < m +// 0 ≤ eval arg2 < m // Postconditions: -// out1 = (-arg1 + arg2 + -arg3) mod 2^57 -// out2 = -⌊(-arg1 + arg2 + -arg3) / 2^57⌋ +// eval (from_montgomery out1) mod m = (eval (from_montgomery arg1) + eval (from_montgomery arg2)) mod m +// 0 ≤ eval out1 < m // -// Input Bounds: -// arg1: [0x0 ~> 0x1] -// arg2: [0x0 ~> 0x1ffffffffffffff] -// arg3: [0x0 ~> 0x1ffffffffffffff] -// Output Bounds: -// out1: [0x0 ~> 0x1ffffffffffffff] -// out2: [0x0 ~> 0x1] -func p521SubborrowxU57(out1 *uint64, out2 *p521Uint1, arg1 p521Uint1, arg2 uint64, arg3 uint64) { - x1 := ((int64(arg2) - int64(arg1)) - int64(arg3)) - x2 := p521Int1((x1 >> 57)) - x3 := (uint64(x1) & 0x1ffffffffffffff) - *out1 = x3 - *out2 = (0x0 - p521Uint1(x2)) +func p521Add(out1 *p521MontgomeryDomainFieldElement, arg1 *p521MontgomeryDomainFieldElement, arg2 *p521MontgomeryDomainFieldElement) { + var x1 uint64 + var x2 uint64 + x1, x2 = bits.Add64(arg1[0], arg2[0], uint64(0x0)) + var x3 uint64 + var x4 uint64 + x3, x4 = bits.Add64(arg1[1], arg2[1], uint64(p521Uint1(x2))) + var x5 uint64 + var x6 uint64 + x5, x6 = bits.Add64(arg1[2], arg2[2], uint64(p521Uint1(x4))) + var x7 uint64 + var x8 uint64 + x7, x8 = bits.Add64(arg1[3], arg2[3], uint64(p521Uint1(x6))) + var x9 uint64 + var x10 uint64 + x9, x10 = bits.Add64(arg1[4], arg2[4], uint64(p521Uint1(x8))) + var x11 uint64 + var x12 uint64 + x11, x12 = bits.Add64(arg1[5], arg2[5], uint64(p521Uint1(x10))) + var x13 uint64 + var x14 uint64 + x13, x14 = bits.Add64(arg1[6], arg2[6], uint64(p521Uint1(x12))) + var x15 uint64 + var x16 uint64 + x15, x16 = bits.Add64(arg1[7], arg2[7], uint64(p521Uint1(x14))) + var x17 uint64 + var x18 uint64 + x17, x18 = bits.Add64(arg1[8], arg2[8], uint64(p521Uint1(x16))) + var x19 uint64 + var x20 uint64 + x19, x20 = bits.Sub64(x1, 0xffffffffffffffff, uint64(0x0)) + var x21 uint64 + var x22 uint64 + x21, x22 = bits.Sub64(x3, 0xffffffffffffffff, uint64(p521Uint1(x20))) + var x23 uint64 + var x24 uint64 + x23, x24 = bits.Sub64(x5, 0xffffffffffffffff, uint64(p521Uint1(x22))) + var x25 uint64 + var x26 uint64 + x25, x26 = bits.Sub64(x7, 0xffffffffffffffff, uint64(p521Uint1(x24))) + var x27 uint64 + var x28 uint64 + x27, x28 = bits.Sub64(x9, 0xffffffffffffffff, uint64(p521Uint1(x26))) + var x29 uint64 + var x30 uint64 + x29, x30 = bits.Sub64(x11, 0xffffffffffffffff, uint64(p521Uint1(x28))) + var x31 uint64 + var x32 uint64 + x31, x32 = bits.Sub64(x13, 0xffffffffffffffff, uint64(p521Uint1(x30))) + var x33 uint64 + var x34 uint64 + x33, x34 = bits.Sub64(x15, 0xffffffffffffffff, uint64(p521Uint1(x32))) + var x35 uint64 + var x36 uint64 + x35, x36 = bits.Sub64(x17, 0x1ff, uint64(p521Uint1(x34))) + var x38 uint64 + _, x38 = bits.Sub64(uint64(p521Uint1(x18)), uint64(0x0), uint64(p521Uint1(x36))) + var x39 uint64 + p521CmovznzU64(&x39, p521Uint1(x38), x19, x1) + var x40 uint64 + p521CmovznzU64(&x40, p521Uint1(x38), x21, x3) + var x41 uint64 + p521CmovznzU64(&x41, p521Uint1(x38), x23, x5) + var x42 uint64 + p521CmovznzU64(&x42, p521Uint1(x38), x25, x7) + var x43 uint64 + p521CmovznzU64(&x43, p521Uint1(x38), x27, x9) + var x44 uint64 + p521CmovznzU64(&x44, p521Uint1(x38), x29, x11) + var x45 uint64 + p521CmovznzU64(&x45, p521Uint1(x38), x31, x13) + var x46 uint64 + p521CmovznzU64(&x46, p521Uint1(x38), x33, x15) + var x47 uint64 + p521CmovznzU64(&x47, p521Uint1(x38), x35, x17) + out1[0] = x39 + out1[1] = x40 + out1[2] = x41 + out1[3] = x42 + out1[4] = x43 + out1[5] = x44 + out1[6] = x45 + out1[7] = x46 + out1[8] = x47 } -// p521CmovznzU64 is a single-word conditional move. +// p521Sub subtracts two field elements in the Montgomery domain. // +// Preconditions: +// 0 ≤ eval arg1 < m +// 0 ≤ eval arg2 < m // Postconditions: -// out1 = (if arg1 = 0 then arg2 else arg3) +// eval (from_montgomery out1) mod m = (eval (from_montgomery arg1) - eval (from_montgomery arg2)) mod m +// 0 ≤ eval out1 < m // -// Input Bounds: -// arg1: [0x0 ~> 0x1] -// arg2: [0x0 ~> 0xffffffffffffffff] -// arg3: [0x0 ~> 0xffffffffffffffff] -// Output Bounds: -// out1: [0x0 ~> 0xffffffffffffffff] -func p521CmovznzU64(out1 *uint64, arg1 p521Uint1, arg2 uint64, arg3 uint64) { - x1 := (uint64(arg1) * 0xffffffffffffffff) - x2 := ((x1 & arg3) | ((^x1) & arg2)) - *out1 = x2 +func p521Sub(out1 *p521MontgomeryDomainFieldElement, arg1 *p521MontgomeryDomainFieldElement, arg2 *p521MontgomeryDomainFieldElement) { + var x1 uint64 + var x2 uint64 + x1, x2 = bits.Sub64(arg1[0], arg2[0], uint64(0x0)) + var x3 uint64 + var x4 uint64 + x3, x4 = bits.Sub64(arg1[1], arg2[1], uint64(p521Uint1(x2))) + var x5 uint64 + var x6 uint64 + x5, x6 = bits.Sub64(arg1[2], arg2[2], uint64(p521Uint1(x4))) + var x7 uint64 + var x8 uint64 + x7, x8 = bits.Sub64(arg1[3], arg2[3], uint64(p521Uint1(x6))) + var x9 uint64 + var x10 uint64 + x9, x10 = bits.Sub64(arg1[4], arg2[4], uint64(p521Uint1(x8))) + var x11 uint64 + var x12 uint64 + x11, x12 = bits.Sub64(arg1[5], arg2[5], uint64(p521Uint1(x10))) + var x13 uint64 + var x14 uint64 + x13, x14 = bits.Sub64(arg1[6], arg2[6], uint64(p521Uint1(x12))) + var x15 uint64 + var x16 uint64 + x15, x16 = bits.Sub64(arg1[7], arg2[7], uint64(p521Uint1(x14))) + var x17 uint64 + var x18 uint64 + x17, x18 = bits.Sub64(arg1[8], arg2[8], uint64(p521Uint1(x16))) + var x19 uint64 + p521CmovznzU64(&x19, p521Uint1(x18), uint64(0x0), 0xffffffffffffffff) + var x20 uint64 + var x21 uint64 + x20, x21 = bits.Add64(x1, x19, uint64(0x0)) + var x22 uint64 + var x23 uint64 + x22, x23 = bits.Add64(x3, x19, uint64(p521Uint1(x21))) + var x24 uint64 + var x25 uint64 + x24, x25 = bits.Add64(x5, x19, uint64(p521Uint1(x23))) + var x26 uint64 + var x27 uint64 + x26, x27 = bits.Add64(x7, x19, uint64(p521Uint1(x25))) + var x28 uint64 + var x29 uint64 + x28, x29 = bits.Add64(x9, x19, uint64(p521Uint1(x27))) + var x30 uint64 + var x31 uint64 + x30, x31 = bits.Add64(x11, x19, uint64(p521Uint1(x29))) + var x32 uint64 + var x33 uint64 + x32, x33 = bits.Add64(x13, x19, uint64(p521Uint1(x31))) + var x34 uint64 + var x35 uint64 + x34, x35 = bits.Add64(x15, x19, uint64(p521Uint1(x33))) + var x36 uint64 + x36, _ = bits.Add64(x17, (x19 & 0x1ff), uint64(p521Uint1(x35))) + out1[0] = x20 + out1[1] = x22 + out1[2] = x24 + out1[3] = x26 + out1[4] = x28 + out1[5] = x30 + out1[6] = x32 + out1[7] = x34 + out1[8] = x36 } -// p521CarryMul multiplies two field elements and reduces the result. +// p521SetOne returns the field element one in the Montgomery domain. // // Postconditions: -// eval out1 mod m = (eval arg1 * eval arg2) mod m +// eval (from_montgomery out1) mod m = 1 mod m +// 0 ≤ eval out1 < m // -// Input Bounds: -// arg1: [[0x0 ~> 0xc00000000000000], [0x0 ~> 0xc00000000000000], [0x0 ~> 0xc00000000000000], [0x0 ~> 0xc00000000000000], [0x0 ~> 0xc00000000000000], [0x0 ~> 0xc00000000000000], [0x0 ~> 0xc00000000000000], [0x0 ~> 0xc00000000000000], [0x0 ~> 0x600000000000000]] -// arg2: [[0x0 ~> 0xc00000000000000], [0x0 ~> 0xc00000000000000], [0x0 ~> 0xc00000000000000], [0x0 ~> 0xc00000000000000], [0x0 ~> 0xc00000000000000], [0x0 ~> 0xc00000000000000], [0x0 ~> 0xc00000000000000], [0x0 ~> 0xc00000000000000], [0x0 ~> 0x600000000000000]] -// Output Bounds: -// out1: [[0x0 ~> 0x400000000000000], [0x0 ~> 0x400000000000000], [0x0 ~> 0x400000000000000], [0x0 ~> 0x400000000000000], [0x0 ~> 0x400000000000000], [0x0 ~> 0x400000000000000], [0x0 ~> 0x400000000000000], [0x0 ~> 0x400000000000000], [0x0 ~> 0x200000000000000]] -func p521CarryMul(out1 *[9]uint64, arg1 *[9]uint64, arg2 *[9]uint64) { - var x1 uint64 +func p521SetOne(out1 *p521MontgomeryDomainFieldElement) { + out1[0] = 0x80000000000000 + out1[1] = uint64(0x0) + out1[2] = uint64(0x0) + out1[3] = uint64(0x0) + out1[4] = uint64(0x0) + out1[5] = uint64(0x0) + out1[6] = uint64(0x0) + out1[7] = uint64(0x0) + out1[8] = uint64(0x0) +} + +// p521FromMontgomery translates a field element out of the Montgomery domain. +// +// Preconditions: +// 0 ≤ eval arg1 < m +// Postconditions: +// eval out1 mod m = (eval arg1 * ((2^64)⁻¹ mod m)^9) mod m +// 0 ≤ eval out1 < m +// +func p521FromMontgomery(out1 *p521NonMontgomeryDomainFieldElement, arg1 *p521MontgomeryDomainFieldElement) { + x1 := arg1[0] var x2 uint64 - x2, x1 = bits.Mul64(arg1[8], (arg2[8] * 0x2)) var x3 uint64 + x3, x2 = bits.Mul64(x1, 0x1ff) var x4 uint64 - x4, x3 = bits.Mul64(arg1[8], (arg2[7] * 0x2)) var x5 uint64 + x5, x4 = bits.Mul64(x1, 0xffffffffffffffff) var x6 uint64 - x6, x5 = bits.Mul64(arg1[8], (arg2[6] * 0x2)) var x7 uint64 + x7, x6 = bits.Mul64(x1, 0xffffffffffffffff) var x8 uint64 - x8, x7 = bits.Mul64(arg1[8], (arg2[5] * 0x2)) var x9 uint64 + x9, x8 = bits.Mul64(x1, 0xffffffffffffffff) var x10 uint64 - x10, x9 = bits.Mul64(arg1[8], (arg2[4] * 0x2)) var x11 uint64 + x11, x10 = bits.Mul64(x1, 0xffffffffffffffff) var x12 uint64 - x12, x11 = bits.Mul64(arg1[8], (arg2[3] * 0x2)) var x13 uint64 + x13, x12 = bits.Mul64(x1, 0xffffffffffffffff) var x14 uint64 - x14, x13 = bits.Mul64(arg1[8], (arg2[2] * 0x2)) var x15 uint64 + x15, x14 = bits.Mul64(x1, 0xffffffffffffffff) var x16 uint64 - x16, x15 = bits.Mul64(arg1[8], (arg2[1] * 0x2)) var x17 uint64 + x17, x16 = bits.Mul64(x1, 0xffffffffffffffff) var x18 uint64 - x18, x17 = bits.Mul64(arg1[7], (arg2[8] * 0x2)) var x19 uint64 + x19, x18 = bits.Mul64(x1, 0xffffffffffffffff) var x20 uint64 - x20, x19 = bits.Mul64(arg1[7], (arg2[7] * 0x2)) var x21 uint64 + x20, x21 = bits.Add64(x19, x16, uint64(0x0)) var x22 uint64 - x22, x21 = bits.Mul64(arg1[7], (arg2[6] * 0x2)) var x23 uint64 + x22, x23 = bits.Add64(x17, x14, uint64(p521Uint1(x21))) var x24 uint64 - x24, x23 = bits.Mul64(arg1[7], (arg2[5] * 0x2)) var x25 uint64 + x24, x25 = bits.Add64(x15, x12, uint64(p521Uint1(x23))) var x26 uint64 - x26, x25 = bits.Mul64(arg1[7], (arg2[4] * 0x2)) var x27 uint64 + x26, x27 = bits.Add64(x13, x10, uint64(p521Uint1(x25))) var x28 uint64 - x28, x27 = bits.Mul64(arg1[7], (arg2[3] * 0x2)) var x29 uint64 + x28, x29 = bits.Add64(x11, x8, uint64(p521Uint1(x27))) var x30 uint64 - x30, x29 = bits.Mul64(arg1[7], (arg2[2] * 0x2)) var x31 uint64 + x30, x31 = bits.Add64(x9, x6, uint64(p521Uint1(x29))) var x32 uint64 - x32, x31 = bits.Mul64(arg1[6], (arg2[8] * 0x2)) var x33 uint64 + x32, x33 = bits.Add64(x7, x4, uint64(p521Uint1(x31))) var x34 uint64 - x34, x33 = bits.Mul64(arg1[6], (arg2[7] * 0x2)) var x35 uint64 - var x36 uint64 - x36, x35 = bits.Mul64(arg1[6], (arg2[6] * 0x2)) + x34, x35 = bits.Add64(x5, x2, uint64(p521Uint1(x33))) var x37 uint64 + _, x37 = bits.Add64(x1, x18, uint64(0x0)) var x38 uint64 - x38, x37 = bits.Mul64(arg1[6], (arg2[5] * 0x2)) var x39 uint64 + x38, x39 = bits.Add64(uint64(0x0), x20, uint64(p521Uint1(x37))) var x40 uint64 - x40, x39 = bits.Mul64(arg1[6], (arg2[4] * 0x2)) var x41 uint64 + x40, x41 = bits.Add64(uint64(0x0), x22, uint64(p521Uint1(x39))) var x42 uint64 - x42, x41 = bits.Mul64(arg1[6], (arg2[3] * 0x2)) var x43 uint64 + x42, x43 = bits.Add64(uint64(0x0), x24, uint64(p521Uint1(x41))) var x44 uint64 - x44, x43 = bits.Mul64(arg1[5], (arg2[8] * 0x2)) var x45 uint64 + x44, x45 = bits.Add64(uint64(0x0), x26, uint64(p521Uint1(x43))) var x46 uint64 - x46, x45 = bits.Mul64(arg1[5], (arg2[7] * 0x2)) var x47 uint64 + x46, x47 = bits.Add64(uint64(0x0), x28, uint64(p521Uint1(x45))) var x48 uint64 - x48, x47 = bits.Mul64(arg1[5], (arg2[6] * 0x2)) var x49 uint64 + x48, x49 = bits.Add64(uint64(0x0), x30, uint64(p521Uint1(x47))) var x50 uint64 - x50, x49 = bits.Mul64(arg1[5], (arg2[5] * 0x2)) var x51 uint64 + x50, x51 = bits.Add64(uint64(0x0), x32, uint64(p521Uint1(x49))) var x52 uint64 - x52, x51 = bits.Mul64(arg1[5], (arg2[4] * 0x2)) var x53 uint64 + x52, x53 = bits.Add64(uint64(0x0), x34, uint64(p521Uint1(x51))) var x54 uint64 - x54, x53 = bits.Mul64(arg1[4], (arg2[8] * 0x2)) var x55 uint64 + x54, x55 = bits.Add64(x38, arg1[1], uint64(0x0)) var x56 uint64 - x56, x55 = bits.Mul64(arg1[4], (arg2[7] * 0x2)) var x57 uint64 + x56, x57 = bits.Add64(x40, uint64(0x0), uint64(p521Uint1(x55))) var x58 uint64 - x58, x57 = bits.Mul64(arg1[4], (arg2[6] * 0x2)) var x59 uint64 + x58, x59 = bits.Add64(x42, uint64(0x0), uint64(p521Uint1(x57))) var x60 uint64 - x60, x59 = bits.Mul64(arg1[4], (arg2[5] * 0x2)) var x61 uint64 + x60, x61 = bits.Add64(x44, uint64(0x0), uint64(p521Uint1(x59))) var x62 uint64 - x62, x61 = bits.Mul64(arg1[3], (arg2[8] * 0x2)) var x63 uint64 + x62, x63 = bits.Add64(x46, uint64(0x0), uint64(p521Uint1(x61))) var x64 uint64 - x64, x63 = bits.Mul64(arg1[3], (arg2[7] * 0x2)) var x65 uint64 + x64, x65 = bits.Add64(x48, uint64(0x0), uint64(p521Uint1(x63))) var x66 uint64 - x66, x65 = bits.Mul64(arg1[3], (arg2[6] * 0x2)) var x67 uint64 + x66, x67 = bits.Add64(x50, uint64(0x0), uint64(p521Uint1(x65))) var x68 uint64 - x68, x67 = bits.Mul64(arg1[2], (arg2[8] * 0x2)) var x69 uint64 + x68, x69 = bits.Add64(x52, uint64(0x0), uint64(p521Uint1(x67))) var x70 uint64 - x70, x69 = bits.Mul64(arg1[2], (arg2[7] * 0x2)) var x71 uint64 + x71, x70 = bits.Mul64(x54, 0x1ff) var x72 uint64 - x72, x71 = bits.Mul64(arg1[1], (arg2[8] * 0x2)) var x73 uint64 + x73, x72 = bits.Mul64(x54, 0xffffffffffffffff) var x74 uint64 - x74, x73 = bits.Mul64(arg1[8], arg2[0]) var x75 uint64 + x75, x74 = bits.Mul64(x54, 0xffffffffffffffff) var x76 uint64 - x76, x75 = bits.Mul64(arg1[7], arg2[1]) var x77 uint64 + x77, x76 = bits.Mul64(x54, 0xffffffffffffffff) var x78 uint64 - x78, x77 = bits.Mul64(arg1[7], arg2[0]) var x79 uint64 + x79, x78 = bits.Mul64(x54, 0xffffffffffffffff) var x80 uint64 - x80, x79 = bits.Mul64(arg1[6], arg2[2]) var x81 uint64 + x81, x80 = bits.Mul64(x54, 0xffffffffffffffff) var x82 uint64 - x82, x81 = bits.Mul64(arg1[6], arg2[1]) var x83 uint64 + x83, x82 = bits.Mul64(x54, 0xffffffffffffffff) var x84 uint64 - x84, x83 = bits.Mul64(arg1[6], arg2[0]) var x85 uint64 + x85, x84 = bits.Mul64(x54, 0xffffffffffffffff) var x86 uint64 - x86, x85 = bits.Mul64(arg1[5], arg2[3]) var x87 uint64 + x87, x86 = bits.Mul64(x54, 0xffffffffffffffff) var x88 uint64 - x88, x87 = bits.Mul64(arg1[5], arg2[2]) var x89 uint64 + x88, x89 = bits.Add64(x87, x84, uint64(0x0)) var x90 uint64 - x90, x89 = bits.Mul64(arg1[5], arg2[1]) var x91 uint64 + x90, x91 = bits.Add64(x85, x82, uint64(p521Uint1(x89))) var x92 uint64 - x92, x91 = bits.Mul64(arg1[5], arg2[0]) var x93 uint64 + x92, x93 = bits.Add64(x83, x80, uint64(p521Uint1(x91))) var x94 uint64 - x94, x93 = bits.Mul64(arg1[4], arg2[4]) var x95 uint64 + x94, x95 = bits.Add64(x81, x78, uint64(p521Uint1(x93))) var x96 uint64 - x96, x95 = bits.Mul64(arg1[4], arg2[3]) var x97 uint64 + x96, x97 = bits.Add64(x79, x76, uint64(p521Uint1(x95))) var x98 uint64 - x98, x97 = bits.Mul64(arg1[4], arg2[2]) var x99 uint64 + x98, x99 = bits.Add64(x77, x74, uint64(p521Uint1(x97))) var x100 uint64 - x100, x99 = bits.Mul64(arg1[4], arg2[1]) var x101 uint64 + x100, x101 = bits.Add64(x75, x72, uint64(p521Uint1(x99))) var x102 uint64 - x102, x101 = bits.Mul64(arg1[4], arg2[0]) var x103 uint64 - var x104 uint64 - x104, x103 = bits.Mul64(arg1[3], arg2[5]) + x102, x103 = bits.Add64(x73, x70, uint64(p521Uint1(x101))) var x105 uint64 + _, x105 = bits.Add64(x54, x86, uint64(0x0)) var x106 uint64 - x106, x105 = bits.Mul64(arg1[3], arg2[4]) var x107 uint64 + x106, x107 = bits.Add64(x56, x88, uint64(p521Uint1(x105))) var x108 uint64 - x108, x107 = bits.Mul64(arg1[3], arg2[3]) var x109 uint64 + x108, x109 = bits.Add64(x58, x90, uint64(p521Uint1(x107))) var x110 uint64 - x110, x109 = bits.Mul64(arg1[3], arg2[2]) var x111 uint64 + x110, x111 = bits.Add64(x60, x92, uint64(p521Uint1(x109))) var x112 uint64 - x112, x111 = bits.Mul64(arg1[3], arg2[1]) var x113 uint64 + x112, x113 = bits.Add64(x62, x94, uint64(p521Uint1(x111))) var x114 uint64 - x114, x113 = bits.Mul64(arg1[3], arg2[0]) var x115 uint64 + x114, x115 = bits.Add64(x64, x96, uint64(p521Uint1(x113))) var x116 uint64 - x116, x115 = bits.Mul64(arg1[2], arg2[6]) var x117 uint64 + x116, x117 = bits.Add64(x66, x98, uint64(p521Uint1(x115))) var x118 uint64 - x118, x117 = bits.Mul64(arg1[2], arg2[5]) var x119 uint64 + x118, x119 = bits.Add64(x68, x100, uint64(p521Uint1(x117))) var x120 uint64 - x120, x119 = bits.Mul64(arg1[2], arg2[4]) var x121 uint64 + x120, x121 = bits.Add64((uint64(p521Uint1(x69)) + (uint64(p521Uint1(x53)) + (uint64(p521Uint1(x35)) + x3))), x102, uint64(p521Uint1(x119))) var x122 uint64 - x122, x121 = bits.Mul64(arg1[2], arg2[3]) var x123 uint64 + x122, x123 = bits.Add64(x106, arg1[2], uint64(0x0)) var x124 uint64 - x124, x123 = bits.Mul64(arg1[2], arg2[2]) var x125 uint64 + x124, x125 = bits.Add64(x108, uint64(0x0), uint64(p521Uint1(x123))) var x126 uint64 - x126, x125 = bits.Mul64(arg1[2], arg2[1]) var x127 uint64 + x126, x127 = bits.Add64(x110, uint64(0x0), uint64(p521Uint1(x125))) var x128 uint64 - x128, x127 = bits.Mul64(arg1[2], arg2[0]) var x129 uint64 + x128, x129 = bits.Add64(x112, uint64(0x0), uint64(p521Uint1(x127))) var x130 uint64 - x130, x129 = bits.Mul64(arg1[1], arg2[7]) var x131 uint64 + x130, x131 = bits.Add64(x114, uint64(0x0), uint64(p521Uint1(x129))) var x132 uint64 - x132, x131 = bits.Mul64(arg1[1], arg2[6]) var x133 uint64 + x132, x133 = bits.Add64(x116, uint64(0x0), uint64(p521Uint1(x131))) var x134 uint64 - x134, x133 = bits.Mul64(arg1[1], arg2[5]) var x135 uint64 + x134, x135 = bits.Add64(x118, uint64(0x0), uint64(p521Uint1(x133))) var x136 uint64 - x136, x135 = bits.Mul64(arg1[1], arg2[4]) var x137 uint64 + x136, x137 = bits.Add64(x120, uint64(0x0), uint64(p521Uint1(x135))) var x138 uint64 - x138, x137 = bits.Mul64(arg1[1], arg2[3]) var x139 uint64 + x139, x138 = bits.Mul64(x122, 0x1ff) var x140 uint64 - x140, x139 = bits.Mul64(arg1[1], arg2[2]) var x141 uint64 + x141, x140 = bits.Mul64(x122, 0xffffffffffffffff) var x142 uint64 - x142, x141 = bits.Mul64(arg1[1], arg2[1]) var x143 uint64 + x143, x142 = bits.Mul64(x122, 0xffffffffffffffff) var x144 uint64 - x144, x143 = bits.Mul64(arg1[1], arg2[0]) var x145 uint64 + x145, x144 = bits.Mul64(x122, 0xffffffffffffffff) var x146 uint64 - x146, x145 = bits.Mul64(arg1[0], arg2[8]) var x147 uint64 + x147, x146 = bits.Mul64(x122, 0xffffffffffffffff) var x148 uint64 - x148, x147 = bits.Mul64(arg1[0], arg2[7]) var x149 uint64 + x149, x148 = bits.Mul64(x122, 0xffffffffffffffff) var x150 uint64 - x150, x149 = bits.Mul64(arg1[0], arg2[6]) var x151 uint64 + x151, x150 = bits.Mul64(x122, 0xffffffffffffffff) var x152 uint64 - x152, x151 = bits.Mul64(arg1[0], arg2[5]) var x153 uint64 + x153, x152 = bits.Mul64(x122, 0xffffffffffffffff) var x154 uint64 - x154, x153 = bits.Mul64(arg1[0], arg2[4]) var x155 uint64 + x155, x154 = bits.Mul64(x122, 0xffffffffffffffff) var x156 uint64 - x156, x155 = bits.Mul64(arg1[0], arg2[3]) var x157 uint64 + x156, x157 = bits.Add64(x155, x152, uint64(0x0)) var x158 uint64 - x158, x157 = bits.Mul64(arg1[0], arg2[2]) var x159 uint64 + x158, x159 = bits.Add64(x153, x150, uint64(p521Uint1(x157))) var x160 uint64 - x160, x159 = bits.Mul64(arg1[0], arg2[1]) var x161 uint64 + x160, x161 = bits.Add64(x151, x148, uint64(p521Uint1(x159))) var x162 uint64 - x162, x161 = bits.Mul64(arg1[0], arg2[0]) var x163 uint64 - var x164 p521Uint1 - x163, x164 = p521AddcarryxU64(x29, x15, 0x0) + x162, x163 = bits.Add64(x149, x146, uint64(p521Uint1(x161))) + var x164 uint64 var x165 uint64 - x165, _ = p521AddcarryxU64(x30, x16, x164) + x164, x165 = bits.Add64(x147, x144, uint64(p521Uint1(x163))) + var x166 uint64 var x167 uint64 - var x168 p521Uint1 - x167, x168 = p521AddcarryxU64(x41, x163, 0x0) + x166, x167 = bits.Add64(x145, x142, uint64(p521Uint1(x165))) + var x168 uint64 var x169 uint64 - x169, _ = p521AddcarryxU64(x42, x165, x168) + x168, x169 = bits.Add64(x143, x140, uint64(p521Uint1(x167))) + var x170 uint64 var x171 uint64 - var x172 p521Uint1 - x171, x172 = p521AddcarryxU64(x51, x167, 0x0) + x170, x171 = bits.Add64(x141, x138, uint64(p521Uint1(x169))) var x173 uint64 - x173, _ = p521AddcarryxU64(x52, x169, x172) + _, x173 = bits.Add64(x122, x154, uint64(0x0)) + var x174 uint64 var x175 uint64 - var x176 p521Uint1 - x175, x176 = p521AddcarryxU64(x59, x171, 0x0) + x174, x175 = bits.Add64(x124, x156, uint64(p521Uint1(x173))) + var x176 uint64 var x177 uint64 - x177, _ = p521AddcarryxU64(x60, x173, x176) + x176, x177 = bits.Add64(x126, x158, uint64(p521Uint1(x175))) + var x178 uint64 var x179 uint64 - var x180 p521Uint1 - x179, x180 = p521AddcarryxU64(x65, x175, 0x0) + x178, x179 = bits.Add64(x128, x160, uint64(p521Uint1(x177))) + var x180 uint64 var x181 uint64 - x181, _ = p521AddcarryxU64(x66, x177, x180) + x180, x181 = bits.Add64(x130, x162, uint64(p521Uint1(x179))) + var x182 uint64 var x183 uint64 - var x184 p521Uint1 - x183, x184 = p521AddcarryxU64(x69, x179, 0x0) + x182, x183 = bits.Add64(x132, x164, uint64(p521Uint1(x181))) + var x184 uint64 var x185 uint64 - x185, _ = p521AddcarryxU64(x70, x181, x184) + x184, x185 = bits.Add64(x134, x166, uint64(p521Uint1(x183))) + var x186 uint64 var x187 uint64 - var x188 p521Uint1 - x187, x188 = p521AddcarryxU64(x71, x183, 0x0) + x186, x187 = bits.Add64(x136, x168, uint64(p521Uint1(x185))) + var x188 uint64 var x189 uint64 - x189, _ = p521AddcarryxU64(x72, x185, x188) + x188, x189 = bits.Add64((uint64(p521Uint1(x137)) + (uint64(p521Uint1(x121)) + (uint64(p521Uint1(x103)) + x71))), x170, uint64(p521Uint1(x187))) + var x190 uint64 var x191 uint64 - var x192 p521Uint1 - x191, x192 = p521AddcarryxU64(x161, x187, 0x0) + x190, x191 = bits.Add64(x174, arg1[3], uint64(0x0)) + var x192 uint64 var x193 uint64 - x193, _ = p521AddcarryxU64(x162, x189, x192) - x195 := ((x191 >> 58) | ((x193 << 6) & 0xffffffffffffffff)) - x196 := (x193 >> 58) - x197 := (x191 & 0x3ffffffffffffff) + x192, x193 = bits.Add64(x176, uint64(0x0), uint64(p521Uint1(x191))) + var x194 uint64 + var x195 uint64 + x194, x195 = bits.Add64(x178, uint64(0x0), uint64(p521Uint1(x193))) + var x196 uint64 + var x197 uint64 + x196, x197 = bits.Add64(x180, uint64(0x0), uint64(p521Uint1(x195))) var x198 uint64 - var x199 p521Uint1 - x198, x199 = p521AddcarryxU64(x75, x73, 0x0) + var x199 uint64 + x198, x199 = bits.Add64(x182, uint64(0x0), uint64(p521Uint1(x197))) var x200 uint64 - x200, _ = p521AddcarryxU64(x76, x74, x199) + var x201 uint64 + x200, x201 = bits.Add64(x184, uint64(0x0), uint64(p521Uint1(x199))) var x202 uint64 - var x203 p521Uint1 - x202, x203 = p521AddcarryxU64(x79, x198, 0x0) + var x203 uint64 + x202, x203 = bits.Add64(x186, uint64(0x0), uint64(p521Uint1(x201))) var x204 uint64 - x204, _ = p521AddcarryxU64(x80, x200, x203) + var x205 uint64 + x204, x205 = bits.Add64(x188, uint64(0x0), uint64(p521Uint1(x203))) var x206 uint64 - var x207 p521Uint1 - x206, x207 = p521AddcarryxU64(x85, x202, 0x0) + var x207 uint64 + x207, x206 = bits.Mul64(x190, 0x1ff) var x208 uint64 - x208, _ = p521AddcarryxU64(x86, x204, x207) + var x209 uint64 + x209, x208 = bits.Mul64(x190, 0xffffffffffffffff) var x210 uint64 - var x211 p521Uint1 - x210, x211 = p521AddcarryxU64(x93, x206, 0x0) + var x211 uint64 + x211, x210 = bits.Mul64(x190, 0xffffffffffffffff) var x212 uint64 - x212, _ = p521AddcarryxU64(x94, x208, x211) + var x213 uint64 + x213, x212 = bits.Mul64(x190, 0xffffffffffffffff) var x214 uint64 - var x215 p521Uint1 - x214, x215 = p521AddcarryxU64(x103, x210, 0x0) + var x215 uint64 + x215, x214 = bits.Mul64(x190, 0xffffffffffffffff) var x216 uint64 - x216, _ = p521AddcarryxU64(x104, x212, x215) + var x217 uint64 + x217, x216 = bits.Mul64(x190, 0xffffffffffffffff) var x218 uint64 - var x219 p521Uint1 - x218, x219 = p521AddcarryxU64(x115, x214, 0x0) + var x219 uint64 + x219, x218 = bits.Mul64(x190, 0xffffffffffffffff) var x220 uint64 - x220, _ = p521AddcarryxU64(x116, x216, x219) + var x221 uint64 + x221, x220 = bits.Mul64(x190, 0xffffffffffffffff) var x222 uint64 - var x223 p521Uint1 - x222, x223 = p521AddcarryxU64(x129, x218, 0x0) + var x223 uint64 + x223, x222 = bits.Mul64(x190, 0xffffffffffffffff) var x224 uint64 - x224, _ = p521AddcarryxU64(x130, x220, x223) + var x225 uint64 + x224, x225 = bits.Add64(x223, x220, uint64(0x0)) var x226 uint64 - var x227 p521Uint1 - x226, x227 = p521AddcarryxU64(x145, x222, 0x0) + var x227 uint64 + x226, x227 = bits.Add64(x221, x218, uint64(p521Uint1(x225))) var x228 uint64 - x228, _ = p521AddcarryxU64(x146, x224, x227) + var x229 uint64 + x228, x229 = bits.Add64(x219, x216, uint64(p521Uint1(x227))) var x230 uint64 - var x231 p521Uint1 - x230, x231 = p521AddcarryxU64(x77, x1, 0x0) + var x231 uint64 + x230, x231 = bits.Add64(x217, x214, uint64(p521Uint1(x229))) var x232 uint64 - x232, _ = p521AddcarryxU64(x78, x2, x231) + var x233 uint64 + x232, x233 = bits.Add64(x215, x212, uint64(p521Uint1(x231))) var x234 uint64 - var x235 p521Uint1 - x234, x235 = p521AddcarryxU64(x81, x230, 0x0) + var x235 uint64 + x234, x235 = bits.Add64(x213, x210, uint64(p521Uint1(x233))) var x236 uint64 - x236, _ = p521AddcarryxU64(x82, x232, x235) + var x237 uint64 + x236, x237 = bits.Add64(x211, x208, uint64(p521Uint1(x235))) var x238 uint64 - var x239 p521Uint1 - x238, x239 = p521AddcarryxU64(x87, x234, 0x0) - var x240 uint64 - x240, _ = p521AddcarryxU64(x88, x236, x239) + var x239 uint64 + x238, x239 = bits.Add64(x209, x206, uint64(p521Uint1(x237))) + var x241 uint64 + _, x241 = bits.Add64(x190, x222, uint64(0x0)) var x242 uint64 - var x243 p521Uint1 - x242, x243 = p521AddcarryxU64(x95, x238, 0x0) + var x243 uint64 + x242, x243 = bits.Add64(x192, x224, uint64(p521Uint1(x241))) var x244 uint64 - x244, _ = p521AddcarryxU64(x96, x240, x243) + var x245 uint64 + x244, x245 = bits.Add64(x194, x226, uint64(p521Uint1(x243))) var x246 uint64 - var x247 p521Uint1 - x246, x247 = p521AddcarryxU64(x105, x242, 0x0) + var x247 uint64 + x246, x247 = bits.Add64(x196, x228, uint64(p521Uint1(x245))) var x248 uint64 - x248, _ = p521AddcarryxU64(x106, x244, x247) + var x249 uint64 + x248, x249 = bits.Add64(x198, x230, uint64(p521Uint1(x247))) var x250 uint64 - var x251 p521Uint1 - x250, x251 = p521AddcarryxU64(x117, x246, 0x0) + var x251 uint64 + x250, x251 = bits.Add64(x200, x232, uint64(p521Uint1(x249))) var x252 uint64 - x252, _ = p521AddcarryxU64(x118, x248, x251) + var x253 uint64 + x252, x253 = bits.Add64(x202, x234, uint64(p521Uint1(x251))) var x254 uint64 - var x255 p521Uint1 - x254, x255 = p521AddcarryxU64(x131, x250, 0x0) + var x255 uint64 + x254, x255 = bits.Add64(x204, x236, uint64(p521Uint1(x253))) var x256 uint64 - x256, _ = p521AddcarryxU64(x132, x252, x255) + var x257 uint64 + x256, x257 = bits.Add64((uint64(p521Uint1(x205)) + (uint64(p521Uint1(x189)) + (uint64(p521Uint1(x171)) + x139))), x238, uint64(p521Uint1(x255))) var x258 uint64 - var x259 p521Uint1 - x258, x259 = p521AddcarryxU64(x147, x254, 0x0) + var x259 uint64 + x258, x259 = bits.Add64(x242, arg1[4], uint64(0x0)) var x260 uint64 - x260, _ = p521AddcarryxU64(x148, x256, x259) + var x261 uint64 + x260, x261 = bits.Add64(x244, uint64(0x0), uint64(p521Uint1(x259))) var x262 uint64 - var x263 p521Uint1 - x262, x263 = p521AddcarryxU64(x17, x3, 0x0) + var x263 uint64 + x262, x263 = bits.Add64(x246, uint64(0x0), uint64(p521Uint1(x261))) var x264 uint64 - x264, _ = p521AddcarryxU64(x18, x4, x263) + var x265 uint64 + x264, x265 = bits.Add64(x248, uint64(0x0), uint64(p521Uint1(x263))) var x266 uint64 - var x267 p521Uint1 - x266, x267 = p521AddcarryxU64(x83, x262, 0x0) + var x267 uint64 + x266, x267 = bits.Add64(x250, uint64(0x0), uint64(p521Uint1(x265))) var x268 uint64 - x268, _ = p521AddcarryxU64(x84, x264, x267) + var x269 uint64 + x268, x269 = bits.Add64(x252, uint64(0x0), uint64(p521Uint1(x267))) var x270 uint64 - var x271 p521Uint1 - x270, x271 = p521AddcarryxU64(x89, x266, 0x0) + var x271 uint64 + x270, x271 = bits.Add64(x254, uint64(0x0), uint64(p521Uint1(x269))) var x272 uint64 - x272, _ = p521AddcarryxU64(x90, x268, x271) + var x273 uint64 + x272, x273 = bits.Add64(x256, uint64(0x0), uint64(p521Uint1(x271))) var x274 uint64 - var x275 p521Uint1 - x274, x275 = p521AddcarryxU64(x97, x270, 0x0) + var x275 uint64 + x275, x274 = bits.Mul64(x258, 0x1ff) var x276 uint64 - x276, _ = p521AddcarryxU64(x98, x272, x275) + var x277 uint64 + x277, x276 = bits.Mul64(x258, 0xffffffffffffffff) var x278 uint64 - var x279 p521Uint1 - x278, x279 = p521AddcarryxU64(x107, x274, 0x0) + var x279 uint64 + x279, x278 = bits.Mul64(x258, 0xffffffffffffffff) var x280 uint64 - x280, _ = p521AddcarryxU64(x108, x276, x279) + var x281 uint64 + x281, x280 = bits.Mul64(x258, 0xffffffffffffffff) var x282 uint64 - var x283 p521Uint1 - x282, x283 = p521AddcarryxU64(x119, x278, 0x0) + var x283 uint64 + x283, x282 = bits.Mul64(x258, 0xffffffffffffffff) var x284 uint64 - x284, _ = p521AddcarryxU64(x120, x280, x283) + var x285 uint64 + x285, x284 = bits.Mul64(x258, 0xffffffffffffffff) var x286 uint64 - var x287 p521Uint1 - x286, x287 = p521AddcarryxU64(x133, x282, 0x0) + var x287 uint64 + x287, x286 = bits.Mul64(x258, 0xffffffffffffffff) var x288 uint64 - x288, _ = p521AddcarryxU64(x134, x284, x287) + var x289 uint64 + x289, x288 = bits.Mul64(x258, 0xffffffffffffffff) var x290 uint64 - var x291 p521Uint1 - x290, x291 = p521AddcarryxU64(x149, x286, 0x0) + var x291 uint64 + x291, x290 = bits.Mul64(x258, 0xffffffffffffffff) var x292 uint64 - x292, _ = p521AddcarryxU64(x150, x288, x291) + var x293 uint64 + x292, x293 = bits.Add64(x291, x288, uint64(0x0)) var x294 uint64 - var x295 p521Uint1 - x294, x295 = p521AddcarryxU64(x19, x5, 0x0) + var x295 uint64 + x294, x295 = bits.Add64(x289, x286, uint64(p521Uint1(x293))) var x296 uint64 - x296, _ = p521AddcarryxU64(x20, x6, x295) + var x297 uint64 + x296, x297 = bits.Add64(x287, x284, uint64(p521Uint1(x295))) var x298 uint64 - var x299 p521Uint1 - x298, x299 = p521AddcarryxU64(x31, x294, 0x0) + var x299 uint64 + x298, x299 = bits.Add64(x285, x282, uint64(p521Uint1(x297))) var x300 uint64 - x300, _ = p521AddcarryxU64(x32, x296, x299) + var x301 uint64 + x300, x301 = bits.Add64(x283, x280, uint64(p521Uint1(x299))) var x302 uint64 - var x303 p521Uint1 - x302, x303 = p521AddcarryxU64(x91, x298, 0x0) + var x303 uint64 + x302, x303 = bits.Add64(x281, x278, uint64(p521Uint1(x301))) var x304 uint64 - x304, _ = p521AddcarryxU64(x92, x300, x303) + var x305 uint64 + x304, x305 = bits.Add64(x279, x276, uint64(p521Uint1(x303))) var x306 uint64 - var x307 p521Uint1 - x306, x307 = p521AddcarryxU64(x99, x302, 0x0) - var x308 uint64 - x308, _ = p521AddcarryxU64(x100, x304, x307) + var x307 uint64 + x306, x307 = bits.Add64(x277, x274, uint64(p521Uint1(x305))) + var x309 uint64 + _, x309 = bits.Add64(x258, x290, uint64(0x0)) var x310 uint64 - var x311 p521Uint1 - x310, x311 = p521AddcarryxU64(x109, x306, 0x0) + var x311 uint64 + x310, x311 = bits.Add64(x260, x292, uint64(p521Uint1(x309))) var x312 uint64 - x312, _ = p521AddcarryxU64(x110, x308, x311) + var x313 uint64 + x312, x313 = bits.Add64(x262, x294, uint64(p521Uint1(x311))) var x314 uint64 - var x315 p521Uint1 - x314, x315 = p521AddcarryxU64(x121, x310, 0x0) + var x315 uint64 + x314, x315 = bits.Add64(x264, x296, uint64(p521Uint1(x313))) var x316 uint64 - x316, _ = p521AddcarryxU64(x122, x312, x315) + var x317 uint64 + x316, x317 = bits.Add64(x266, x298, uint64(p521Uint1(x315))) var x318 uint64 - var x319 p521Uint1 - x318, x319 = p521AddcarryxU64(x135, x314, 0x0) + var x319 uint64 + x318, x319 = bits.Add64(x268, x300, uint64(p521Uint1(x317))) var x320 uint64 - x320, _ = p521AddcarryxU64(x136, x316, x319) + var x321 uint64 + x320, x321 = bits.Add64(x270, x302, uint64(p521Uint1(x319))) var x322 uint64 - var x323 p521Uint1 - x322, x323 = p521AddcarryxU64(x151, x318, 0x0) + var x323 uint64 + x322, x323 = bits.Add64(x272, x304, uint64(p521Uint1(x321))) var x324 uint64 - x324, _ = p521AddcarryxU64(x152, x320, x323) + var x325 uint64 + x324, x325 = bits.Add64((uint64(p521Uint1(x273)) + (uint64(p521Uint1(x257)) + (uint64(p521Uint1(x239)) + x207))), x306, uint64(p521Uint1(x323))) var x326 uint64 - var x327 p521Uint1 - x326, x327 = p521AddcarryxU64(x21, x7, 0x0) + var x327 uint64 + x326, x327 = bits.Add64(x310, arg1[5], uint64(0x0)) var x328 uint64 - x328, _ = p521AddcarryxU64(x22, x8, x327) + var x329 uint64 + x328, x329 = bits.Add64(x312, uint64(0x0), uint64(p521Uint1(x327))) var x330 uint64 - var x331 p521Uint1 - x330, x331 = p521AddcarryxU64(x33, x326, 0x0) + var x331 uint64 + x330, x331 = bits.Add64(x314, uint64(0x0), uint64(p521Uint1(x329))) var x332 uint64 - x332, _ = p521AddcarryxU64(x34, x328, x331) + var x333 uint64 + x332, x333 = bits.Add64(x316, uint64(0x0), uint64(p521Uint1(x331))) var x334 uint64 - var x335 p521Uint1 - x334, x335 = p521AddcarryxU64(x43, x330, 0x0) + var x335 uint64 + x334, x335 = bits.Add64(x318, uint64(0x0), uint64(p521Uint1(x333))) var x336 uint64 - x336, _ = p521AddcarryxU64(x44, x332, x335) + var x337 uint64 + x336, x337 = bits.Add64(x320, uint64(0x0), uint64(p521Uint1(x335))) var x338 uint64 - var x339 p521Uint1 - x338, x339 = p521AddcarryxU64(x101, x334, 0x0) + var x339 uint64 + x338, x339 = bits.Add64(x322, uint64(0x0), uint64(p521Uint1(x337))) var x340 uint64 - x340, _ = p521AddcarryxU64(x102, x336, x339) + var x341 uint64 + x340, x341 = bits.Add64(x324, uint64(0x0), uint64(p521Uint1(x339))) var x342 uint64 - var x343 p521Uint1 - x342, x343 = p521AddcarryxU64(x111, x338, 0x0) + var x343 uint64 + x343, x342 = bits.Mul64(x326, 0x1ff) var x344 uint64 - x344, _ = p521AddcarryxU64(x112, x340, x343) + var x345 uint64 + x345, x344 = bits.Mul64(x326, 0xffffffffffffffff) var x346 uint64 - var x347 p521Uint1 - x346, x347 = p521AddcarryxU64(x123, x342, 0x0) + var x347 uint64 + x347, x346 = bits.Mul64(x326, 0xffffffffffffffff) var x348 uint64 - x348, _ = p521AddcarryxU64(x124, x344, x347) + var x349 uint64 + x349, x348 = bits.Mul64(x326, 0xffffffffffffffff) var x350 uint64 - var x351 p521Uint1 - x350, x351 = p521AddcarryxU64(x137, x346, 0x0) + var x351 uint64 + x351, x350 = bits.Mul64(x326, 0xffffffffffffffff) var x352 uint64 - x352, _ = p521AddcarryxU64(x138, x348, x351) + var x353 uint64 + x353, x352 = bits.Mul64(x326, 0xffffffffffffffff) var x354 uint64 - var x355 p521Uint1 - x354, x355 = p521AddcarryxU64(x153, x350, 0x0) + var x355 uint64 + x355, x354 = bits.Mul64(x326, 0xffffffffffffffff) var x356 uint64 - x356, _ = p521AddcarryxU64(x154, x352, x355) + var x357 uint64 + x357, x356 = bits.Mul64(x326, 0xffffffffffffffff) var x358 uint64 - var x359 p521Uint1 - x358, x359 = p521AddcarryxU64(x23, x9, 0x0) + var x359 uint64 + x359, x358 = bits.Mul64(x326, 0xffffffffffffffff) var x360 uint64 - x360, _ = p521AddcarryxU64(x24, x10, x359) + var x361 uint64 + x360, x361 = bits.Add64(x359, x356, uint64(0x0)) var x362 uint64 - var x363 p521Uint1 - x362, x363 = p521AddcarryxU64(x35, x358, 0x0) + var x363 uint64 + x362, x363 = bits.Add64(x357, x354, uint64(p521Uint1(x361))) var x364 uint64 - x364, _ = p521AddcarryxU64(x36, x360, x363) + var x365 uint64 + x364, x365 = bits.Add64(x355, x352, uint64(p521Uint1(x363))) var x366 uint64 - var x367 p521Uint1 - x366, x367 = p521AddcarryxU64(x45, x362, 0x0) + var x367 uint64 + x366, x367 = bits.Add64(x353, x350, uint64(p521Uint1(x365))) var x368 uint64 - x368, _ = p521AddcarryxU64(x46, x364, x367) + var x369 uint64 + x368, x369 = bits.Add64(x351, x348, uint64(p521Uint1(x367))) var x370 uint64 - var x371 p521Uint1 - x370, x371 = p521AddcarryxU64(x53, x366, 0x0) + var x371 uint64 + x370, x371 = bits.Add64(x349, x346, uint64(p521Uint1(x369))) var x372 uint64 - x372, _ = p521AddcarryxU64(x54, x368, x371) + var x373 uint64 + x372, x373 = bits.Add64(x347, x344, uint64(p521Uint1(x371))) var x374 uint64 - var x375 p521Uint1 - x374, x375 = p521AddcarryxU64(x113, x370, 0x0) - var x376 uint64 - x376, _ = p521AddcarryxU64(x114, x372, x375) + var x375 uint64 + x374, x375 = bits.Add64(x345, x342, uint64(p521Uint1(x373))) + var x377 uint64 + _, x377 = bits.Add64(x326, x358, uint64(0x0)) var x378 uint64 - var x379 p521Uint1 - x378, x379 = p521AddcarryxU64(x125, x374, 0x0) + var x379 uint64 + x378, x379 = bits.Add64(x328, x360, uint64(p521Uint1(x377))) var x380 uint64 - x380, _ = p521AddcarryxU64(x126, x376, x379) + var x381 uint64 + x380, x381 = bits.Add64(x330, x362, uint64(p521Uint1(x379))) var x382 uint64 - var x383 p521Uint1 - x382, x383 = p521AddcarryxU64(x139, x378, 0x0) + var x383 uint64 + x382, x383 = bits.Add64(x332, x364, uint64(p521Uint1(x381))) var x384 uint64 - x384, _ = p521AddcarryxU64(x140, x380, x383) + var x385 uint64 + x384, x385 = bits.Add64(x334, x366, uint64(p521Uint1(x383))) var x386 uint64 - var x387 p521Uint1 - x386, x387 = p521AddcarryxU64(x155, x382, 0x0) + var x387 uint64 + x386, x387 = bits.Add64(x336, x368, uint64(p521Uint1(x385))) var x388 uint64 - x388, _ = p521AddcarryxU64(x156, x384, x387) + var x389 uint64 + x388, x389 = bits.Add64(x338, x370, uint64(p521Uint1(x387))) var x390 uint64 - var x391 p521Uint1 - x390, x391 = p521AddcarryxU64(x25, x11, 0x0) + var x391 uint64 + x390, x391 = bits.Add64(x340, x372, uint64(p521Uint1(x389))) var x392 uint64 - x392, _ = p521AddcarryxU64(x26, x12, x391) + var x393 uint64 + x392, x393 = bits.Add64((uint64(p521Uint1(x341)) + (uint64(p521Uint1(x325)) + (uint64(p521Uint1(x307)) + x275))), x374, uint64(p521Uint1(x391))) var x394 uint64 - var x395 p521Uint1 - x394, x395 = p521AddcarryxU64(x37, x390, 0x0) + var x395 uint64 + x394, x395 = bits.Add64(x378, arg1[6], uint64(0x0)) var x396 uint64 - x396, _ = p521AddcarryxU64(x38, x392, x395) + var x397 uint64 + x396, x397 = bits.Add64(x380, uint64(0x0), uint64(p521Uint1(x395))) var x398 uint64 - var x399 p521Uint1 - x398, x399 = p521AddcarryxU64(x47, x394, 0x0) + var x399 uint64 + x398, x399 = bits.Add64(x382, uint64(0x0), uint64(p521Uint1(x397))) var x400 uint64 - x400, _ = p521AddcarryxU64(x48, x396, x399) + var x401 uint64 + x400, x401 = bits.Add64(x384, uint64(0x0), uint64(p521Uint1(x399))) var x402 uint64 - var x403 p521Uint1 - x402, x403 = p521AddcarryxU64(x55, x398, 0x0) + var x403 uint64 + x402, x403 = bits.Add64(x386, uint64(0x0), uint64(p521Uint1(x401))) var x404 uint64 - x404, _ = p521AddcarryxU64(x56, x400, x403) + var x405 uint64 + x404, x405 = bits.Add64(x388, uint64(0x0), uint64(p521Uint1(x403))) var x406 uint64 - var x407 p521Uint1 - x406, x407 = p521AddcarryxU64(x61, x402, 0x0) + var x407 uint64 + x406, x407 = bits.Add64(x390, uint64(0x0), uint64(p521Uint1(x405))) var x408 uint64 - x408, _ = p521AddcarryxU64(x62, x404, x407) + var x409 uint64 + x408, x409 = bits.Add64(x392, uint64(0x0), uint64(p521Uint1(x407))) var x410 uint64 - var x411 p521Uint1 - x410, x411 = p521AddcarryxU64(x127, x406, 0x0) + var x411 uint64 + x411, x410 = bits.Mul64(x394, 0x1ff) var x412 uint64 - x412, _ = p521AddcarryxU64(x128, x408, x411) + var x413 uint64 + x413, x412 = bits.Mul64(x394, 0xffffffffffffffff) var x414 uint64 - var x415 p521Uint1 - x414, x415 = p521AddcarryxU64(x141, x410, 0x0) + var x415 uint64 + x415, x414 = bits.Mul64(x394, 0xffffffffffffffff) var x416 uint64 - x416, _ = p521AddcarryxU64(x142, x412, x415) + var x417 uint64 + x417, x416 = bits.Mul64(x394, 0xffffffffffffffff) var x418 uint64 - var x419 p521Uint1 - x418, x419 = p521AddcarryxU64(x157, x414, 0x0) + var x419 uint64 + x419, x418 = bits.Mul64(x394, 0xffffffffffffffff) var x420 uint64 - x420, _ = p521AddcarryxU64(x158, x416, x419) + var x421 uint64 + x421, x420 = bits.Mul64(x394, 0xffffffffffffffff) var x422 uint64 - var x423 p521Uint1 - x422, x423 = p521AddcarryxU64(x27, x13, 0x0) + var x423 uint64 + x423, x422 = bits.Mul64(x394, 0xffffffffffffffff) var x424 uint64 - x424, _ = p521AddcarryxU64(x28, x14, x423) + var x425 uint64 + x425, x424 = bits.Mul64(x394, 0xffffffffffffffff) var x426 uint64 - var x427 p521Uint1 - x426, x427 = p521AddcarryxU64(x39, x422, 0x0) + var x427 uint64 + x427, x426 = bits.Mul64(x394, 0xffffffffffffffff) var x428 uint64 - x428, _ = p521AddcarryxU64(x40, x424, x427) + var x429 uint64 + x428, x429 = bits.Add64(x427, x424, uint64(0x0)) var x430 uint64 - var x431 p521Uint1 - x430, x431 = p521AddcarryxU64(x49, x426, 0x0) + var x431 uint64 + x430, x431 = bits.Add64(x425, x422, uint64(p521Uint1(x429))) var x432 uint64 - x432, _ = p521AddcarryxU64(x50, x428, x431) + var x433 uint64 + x432, x433 = bits.Add64(x423, x420, uint64(p521Uint1(x431))) var x434 uint64 - var x435 p521Uint1 - x434, x435 = p521AddcarryxU64(x57, x430, 0x0) + var x435 uint64 + x434, x435 = bits.Add64(x421, x418, uint64(p521Uint1(x433))) var x436 uint64 - x436, _ = p521AddcarryxU64(x58, x432, x435) + var x437 uint64 + x436, x437 = bits.Add64(x419, x416, uint64(p521Uint1(x435))) var x438 uint64 - var x439 p521Uint1 - x438, x439 = p521AddcarryxU64(x63, x434, 0x0) + var x439 uint64 + x438, x439 = bits.Add64(x417, x414, uint64(p521Uint1(x437))) var x440 uint64 - x440, _ = p521AddcarryxU64(x64, x436, x439) + var x441 uint64 + x440, x441 = bits.Add64(x415, x412, uint64(p521Uint1(x439))) var x442 uint64 - var x443 p521Uint1 - x442, x443 = p521AddcarryxU64(x67, x438, 0x0) - var x444 uint64 - x444, _ = p521AddcarryxU64(x68, x440, x443) + var x443 uint64 + x442, x443 = bits.Add64(x413, x410, uint64(p521Uint1(x441))) + var x445 uint64 + _, x445 = bits.Add64(x394, x426, uint64(0x0)) var x446 uint64 - var x447 p521Uint1 - x446, x447 = p521AddcarryxU64(x143, x442, 0x0) + var x447 uint64 + x446, x447 = bits.Add64(x396, x428, uint64(p521Uint1(x445))) var x448 uint64 - x448, _ = p521AddcarryxU64(x144, x444, x447) + var x449 uint64 + x448, x449 = bits.Add64(x398, x430, uint64(p521Uint1(x447))) var x450 uint64 - var x451 p521Uint1 - x450, x451 = p521AddcarryxU64(x159, x446, 0x0) + var x451 uint64 + x450, x451 = bits.Add64(x400, x432, uint64(p521Uint1(x449))) var x452 uint64 - x452, _ = p521AddcarryxU64(x160, x448, x451) + var x453 uint64 + x452, x453 = bits.Add64(x402, x434, uint64(p521Uint1(x451))) var x454 uint64 - var x455 p521Uint1 - x454, x455 = p521AddcarryxU64(x195, x450, 0x0) + var x455 uint64 + x454, x455 = bits.Add64(x404, x436, uint64(p521Uint1(x453))) var x456 uint64 - x456, _ = p521AddcarryxU64(x196, x452, x455) - x458 := ((x454 >> 58) | ((x456 << 6) & 0xffffffffffffffff)) - x459 := (x456 >> 58) - x460 := (x454 & 0x3ffffffffffffff) + var x457 uint64 + x456, x457 = bits.Add64(x406, x438, uint64(p521Uint1(x455))) + var x458 uint64 + var x459 uint64 + x458, x459 = bits.Add64(x408, x440, uint64(p521Uint1(x457))) + var x460 uint64 var x461 uint64 - var x462 p521Uint1 - x461, x462 = p521AddcarryxU64(x458, x418, 0x0) + x460, x461 = bits.Add64((uint64(p521Uint1(x409)) + (uint64(p521Uint1(x393)) + (uint64(p521Uint1(x375)) + x343))), x442, uint64(p521Uint1(x459))) + var x462 uint64 var x463 uint64 - x463, _ = p521AddcarryxU64(x459, x420, x462) - x465 := ((x461 >> 58) | ((x463 << 6) & 0xffffffffffffffff)) - x466 := (x463 >> 58) - x467 := (x461 & 0x3ffffffffffffff) + x462, x463 = bits.Add64(x446, arg1[7], uint64(0x0)) + var x464 uint64 + var x465 uint64 + x464, x465 = bits.Add64(x448, uint64(0x0), uint64(p521Uint1(x463))) + var x466 uint64 + var x467 uint64 + x466, x467 = bits.Add64(x450, uint64(0x0), uint64(p521Uint1(x465))) var x468 uint64 - var x469 p521Uint1 - x468, x469 = p521AddcarryxU64(x465, x386, 0x0) + var x469 uint64 + x468, x469 = bits.Add64(x452, uint64(0x0), uint64(p521Uint1(x467))) var x470 uint64 - x470, _ = p521AddcarryxU64(x466, x388, x469) - x472 := ((x468 >> 58) | ((x470 << 6) & 0xffffffffffffffff)) - x473 := (x470 >> 58) - x474 := (x468 & 0x3ffffffffffffff) + var x471 uint64 + x470, x471 = bits.Add64(x454, uint64(0x0), uint64(p521Uint1(x469))) + var x472 uint64 + var x473 uint64 + x472, x473 = bits.Add64(x456, uint64(0x0), uint64(p521Uint1(x471))) + var x474 uint64 var x475 uint64 - var x476 p521Uint1 - x475, x476 = p521AddcarryxU64(x472, x354, 0x0) + x474, x475 = bits.Add64(x458, uint64(0x0), uint64(p521Uint1(x473))) + var x476 uint64 var x477 uint64 - x477, _ = p521AddcarryxU64(x473, x356, x476) - x479 := ((x475 >> 58) | ((x477 << 6) & 0xffffffffffffffff)) - x480 := (x477 >> 58) - x481 := (x475 & 0x3ffffffffffffff) + x476, x477 = bits.Add64(x460, uint64(0x0), uint64(p521Uint1(x475))) + var x478 uint64 + var x479 uint64 + x479, x478 = bits.Mul64(x462, 0x1ff) + var x480 uint64 + var x481 uint64 + x481, x480 = bits.Mul64(x462, 0xffffffffffffffff) var x482 uint64 - var x483 p521Uint1 - x482, x483 = p521AddcarryxU64(x479, x322, 0x0) + var x483 uint64 + x483, x482 = bits.Mul64(x462, 0xffffffffffffffff) var x484 uint64 - x484, _ = p521AddcarryxU64(x480, x324, x483) - x486 := ((x482 >> 58) | ((x484 << 6) & 0xffffffffffffffff)) - x487 := (x484 >> 58) - x488 := (x482 & 0x3ffffffffffffff) + var x485 uint64 + x485, x484 = bits.Mul64(x462, 0xffffffffffffffff) + var x486 uint64 + var x487 uint64 + x487, x486 = bits.Mul64(x462, 0xffffffffffffffff) + var x488 uint64 var x489 uint64 - var x490 p521Uint1 - x489, x490 = p521AddcarryxU64(x486, x290, 0x0) + x489, x488 = bits.Mul64(x462, 0xffffffffffffffff) + var x490 uint64 var x491 uint64 - x491, _ = p521AddcarryxU64(x487, x292, x490) - x493 := ((x489 >> 58) | ((x491 << 6) & 0xffffffffffffffff)) - x494 := (x491 >> 58) - x495 := (x489 & 0x3ffffffffffffff) + x491, x490 = bits.Mul64(x462, 0xffffffffffffffff) + var x492 uint64 + var x493 uint64 + x493, x492 = bits.Mul64(x462, 0xffffffffffffffff) + var x494 uint64 + var x495 uint64 + x495, x494 = bits.Mul64(x462, 0xffffffffffffffff) var x496 uint64 - var x497 p521Uint1 - x496, x497 = p521AddcarryxU64(x493, x258, 0x0) + var x497 uint64 + x496, x497 = bits.Add64(x495, x492, uint64(0x0)) var x498 uint64 - x498, _ = p521AddcarryxU64(x494, x260, x497) - x500 := ((x496 >> 58) | ((x498 << 6) & 0xffffffffffffffff)) - x501 := (x498 >> 58) - x502 := (x496 & 0x3ffffffffffffff) + var x499 uint64 + x498, x499 = bits.Add64(x493, x490, uint64(p521Uint1(x497))) + var x500 uint64 + var x501 uint64 + x500, x501 = bits.Add64(x491, x488, uint64(p521Uint1(x499))) + var x502 uint64 var x503 uint64 - var x504 p521Uint1 - x503, x504 = p521AddcarryxU64(x500, x226, 0x0) + x502, x503 = bits.Add64(x489, x486, uint64(p521Uint1(x501))) + var x504 uint64 var x505 uint64 - x505, _ = p521AddcarryxU64(x501, x228, x504) - x507 := ((x503 >> 57) | ((x505 << 7) & 0xffffffffffffffff)) - x508 := (x505 >> 57) - x509 := (x503 & 0x1ffffffffffffff) + x504, x505 = bits.Add64(x487, x484, uint64(p521Uint1(x503))) + var x506 uint64 + var x507 uint64 + x506, x507 = bits.Add64(x485, x482, uint64(p521Uint1(x505))) + var x508 uint64 + var x509 uint64 + x508, x509 = bits.Add64(x483, x480, uint64(p521Uint1(x507))) var x510 uint64 - var x511 p521Uint1 - x510, x511 = p521AddcarryxU64(x197, x507, 0x0) - x512 := (uint64(x511) + x508) - x513 := ((x510 >> 58) | ((x512 << 6) & 0xffffffffffffffff)) - x514 := (x510 & 0x3ffffffffffffff) - x515 := (x513 + x460) - x516 := p521Uint1((x515 >> 58)) - x517 := (x515 & 0x3ffffffffffffff) - x518 := (uint64(x516) + x467) - out1[0] = x514 - out1[1] = x517 - out1[2] = x518 - out1[3] = x474 - out1[4] = x481 - out1[5] = x488 - out1[6] = x495 - out1[7] = x502 - out1[8] = x509 + var x511 uint64 + x510, x511 = bits.Add64(x481, x478, uint64(p521Uint1(x509))) + var x513 uint64 + _, x513 = bits.Add64(x462, x494, uint64(0x0)) + var x514 uint64 + var x515 uint64 + x514, x515 = bits.Add64(x464, x496, uint64(p521Uint1(x513))) + var x516 uint64 + var x517 uint64 + x516, x517 = bits.Add64(x466, x498, uint64(p521Uint1(x515))) + var x518 uint64 + var x519 uint64 + x518, x519 = bits.Add64(x468, x500, uint64(p521Uint1(x517))) + var x520 uint64 + var x521 uint64 + x520, x521 = bits.Add64(x470, x502, uint64(p521Uint1(x519))) + var x522 uint64 + var x523 uint64 + x522, x523 = bits.Add64(x472, x504, uint64(p521Uint1(x521))) + var x524 uint64 + var x525 uint64 + x524, x525 = bits.Add64(x474, x506, uint64(p521Uint1(x523))) + var x526 uint64 + var x527 uint64 + x526, x527 = bits.Add64(x476, x508, uint64(p521Uint1(x525))) + var x528 uint64 + var x529 uint64 + x528, x529 = bits.Add64((uint64(p521Uint1(x477)) + (uint64(p521Uint1(x461)) + (uint64(p521Uint1(x443)) + x411))), x510, uint64(p521Uint1(x527))) + var x530 uint64 + var x531 uint64 + x530, x531 = bits.Add64(x514, arg1[8], uint64(0x0)) + var x532 uint64 + var x533 uint64 + x532, x533 = bits.Add64(x516, uint64(0x0), uint64(p521Uint1(x531))) + var x534 uint64 + var x535 uint64 + x534, x535 = bits.Add64(x518, uint64(0x0), uint64(p521Uint1(x533))) + var x536 uint64 + var x537 uint64 + x536, x537 = bits.Add64(x520, uint64(0x0), uint64(p521Uint1(x535))) + var x538 uint64 + var x539 uint64 + x538, x539 = bits.Add64(x522, uint64(0x0), uint64(p521Uint1(x537))) + var x540 uint64 + var x541 uint64 + x540, x541 = bits.Add64(x524, uint64(0x0), uint64(p521Uint1(x539))) + var x542 uint64 + var x543 uint64 + x542, x543 = bits.Add64(x526, uint64(0x0), uint64(p521Uint1(x541))) + var x544 uint64 + var x545 uint64 + x544, x545 = bits.Add64(x528, uint64(0x0), uint64(p521Uint1(x543))) + var x546 uint64 + var x547 uint64 + x547, x546 = bits.Mul64(x530, 0x1ff) + var x548 uint64 + var x549 uint64 + x549, x548 = bits.Mul64(x530, 0xffffffffffffffff) + var x550 uint64 + var x551 uint64 + x551, x550 = bits.Mul64(x530, 0xffffffffffffffff) + var x552 uint64 + var x553 uint64 + x553, x552 = bits.Mul64(x530, 0xffffffffffffffff) + var x554 uint64 + var x555 uint64 + x555, x554 = bits.Mul64(x530, 0xffffffffffffffff) + var x556 uint64 + var x557 uint64 + x557, x556 = bits.Mul64(x530, 0xffffffffffffffff) + var x558 uint64 + var x559 uint64 + x559, x558 = bits.Mul64(x530, 0xffffffffffffffff) + var x560 uint64 + var x561 uint64 + x561, x560 = bits.Mul64(x530, 0xffffffffffffffff) + var x562 uint64 + var x563 uint64 + x563, x562 = bits.Mul64(x530, 0xffffffffffffffff) + var x564 uint64 + var x565 uint64 + x564, x565 = bits.Add64(x563, x560, uint64(0x0)) + var x566 uint64 + var x567 uint64 + x566, x567 = bits.Add64(x561, x558, uint64(p521Uint1(x565))) + var x568 uint64 + var x569 uint64 + x568, x569 = bits.Add64(x559, x556, uint64(p521Uint1(x567))) + var x570 uint64 + var x571 uint64 + x570, x571 = bits.Add64(x557, x554, uint64(p521Uint1(x569))) + var x572 uint64 + var x573 uint64 + x572, x573 = bits.Add64(x555, x552, uint64(p521Uint1(x571))) + var x574 uint64 + var x575 uint64 + x574, x575 = bits.Add64(x553, x550, uint64(p521Uint1(x573))) + var x576 uint64 + var x577 uint64 + x576, x577 = bits.Add64(x551, x548, uint64(p521Uint1(x575))) + var x578 uint64 + var x579 uint64 + x578, x579 = bits.Add64(x549, x546, uint64(p521Uint1(x577))) + var x581 uint64 + _, x581 = bits.Add64(x530, x562, uint64(0x0)) + var x582 uint64 + var x583 uint64 + x582, x583 = bits.Add64(x532, x564, uint64(p521Uint1(x581))) + var x584 uint64 + var x585 uint64 + x584, x585 = bits.Add64(x534, x566, uint64(p521Uint1(x583))) + var x586 uint64 + var x587 uint64 + x586, x587 = bits.Add64(x536, x568, uint64(p521Uint1(x585))) + var x588 uint64 + var x589 uint64 + x588, x589 = bits.Add64(x538, x570, uint64(p521Uint1(x587))) + var x590 uint64 + var x591 uint64 + x590, x591 = bits.Add64(x540, x572, uint64(p521Uint1(x589))) + var x592 uint64 + var x593 uint64 + x592, x593 = bits.Add64(x542, x574, uint64(p521Uint1(x591))) + var x594 uint64 + var x595 uint64 + x594, x595 = bits.Add64(x544, x576, uint64(p521Uint1(x593))) + var x596 uint64 + var x597 uint64 + x596, x597 = bits.Add64((uint64(p521Uint1(x545)) + (uint64(p521Uint1(x529)) + (uint64(p521Uint1(x511)) + x479))), x578, uint64(p521Uint1(x595))) + x598 := (uint64(p521Uint1(x597)) + (uint64(p521Uint1(x579)) + x547)) + var x599 uint64 + var x600 uint64 + x599, x600 = bits.Sub64(x582, 0xffffffffffffffff, uint64(0x0)) + var x601 uint64 + var x602 uint64 + x601, x602 = bits.Sub64(x584, 0xffffffffffffffff, uint64(p521Uint1(x600))) + var x603 uint64 + var x604 uint64 + x603, x604 = bits.Sub64(x586, 0xffffffffffffffff, uint64(p521Uint1(x602))) + var x605 uint64 + var x606 uint64 + x605, x606 = bits.Sub64(x588, 0xffffffffffffffff, uint64(p521Uint1(x604))) + var x607 uint64 + var x608 uint64 + x607, x608 = bits.Sub64(x590, 0xffffffffffffffff, uint64(p521Uint1(x606))) + var x609 uint64 + var x610 uint64 + x609, x610 = bits.Sub64(x592, 0xffffffffffffffff, uint64(p521Uint1(x608))) + var x611 uint64 + var x612 uint64 + x611, x612 = bits.Sub64(x594, 0xffffffffffffffff, uint64(p521Uint1(x610))) + var x613 uint64 + var x614 uint64 + x613, x614 = bits.Sub64(x596, 0xffffffffffffffff, uint64(p521Uint1(x612))) + var x615 uint64 + var x616 uint64 + x615, x616 = bits.Sub64(x598, 0x1ff, uint64(p521Uint1(x614))) + var x618 uint64 + _, x618 = bits.Sub64(uint64(0x0), uint64(0x0), uint64(p521Uint1(x616))) + var x619 uint64 + p521CmovznzU64(&x619, p521Uint1(x618), x599, x582) + var x620 uint64 + p521CmovznzU64(&x620, p521Uint1(x618), x601, x584) + var x621 uint64 + p521CmovznzU64(&x621, p521Uint1(x618), x603, x586) + var x622 uint64 + p521CmovznzU64(&x622, p521Uint1(x618), x605, x588) + var x623 uint64 + p521CmovznzU64(&x623, p521Uint1(x618), x607, x590) + var x624 uint64 + p521CmovznzU64(&x624, p521Uint1(x618), x609, x592) + var x625 uint64 + p521CmovznzU64(&x625, p521Uint1(x618), x611, x594) + var x626 uint64 + p521CmovznzU64(&x626, p521Uint1(x618), x613, x596) + var x627 uint64 + p521CmovznzU64(&x627, p521Uint1(x618), x615, x598) + out1[0] = x619 + out1[1] = x620 + out1[2] = x621 + out1[3] = x622 + out1[4] = x623 + out1[5] = x624 + out1[6] = x625 + out1[7] = x626 + out1[8] = x627 } -// p521CarrySquare squares a field element and reduces the result. +// p521ToMontgomery translates a field element into the Montgomery domain. // +// Preconditions: +// 0 ≤ eval arg1 < m // Postconditions: -// eval out1 mod m = (eval arg1 * eval arg1) mod m +// eval (from_montgomery out1) mod m = eval arg1 mod m +// 0 ≤ eval out1 < m // -// Input Bounds: -// arg1: [[0x0 ~> 0xc00000000000000], [0x0 ~> 0xc00000000000000], [0x0 ~> 0xc00000000000000], [0x0 ~> 0xc00000000000000], [0x0 ~> 0xc00000000000000], [0x0 ~> 0xc00000000000000], [0x0 ~> 0xc00000000000000], [0x0 ~> 0xc00000000000000], [0x0 ~> 0x600000000000000]] -// Output Bounds: -// out1: [[0x0 ~> 0x400000000000000], [0x0 ~> 0x400000000000000], [0x0 ~> 0x400000000000000], [0x0 ~> 0x400000000000000], [0x0 ~> 0x400000000000000], [0x0 ~> 0x400000000000000], [0x0 ~> 0x400000000000000], [0x0 ~> 0x400000000000000], [0x0 ~> 0x200000000000000]] -func p521CarrySquare(out1 *[9]uint64, arg1 *[9]uint64) { - x1 := arg1[8] - x2 := (x1 * 0x2) - x3 := (arg1[8] * 0x2) - x4 := arg1[7] - x5 := (x4 * 0x2) - x6 := (arg1[7] * 0x2) - x7 := arg1[6] - x8 := (x7 * 0x2) - x9 := (arg1[6] * 0x2) - x10 := arg1[5] - x11 := (x10 * 0x2) - x12 := (arg1[5] * 0x2) - x13 := (arg1[4] * 0x2) - x14 := (arg1[3] * 0x2) - x15 := (arg1[2] * 0x2) - x16 := (arg1[1] * 0x2) +func p521ToMontgomery(out1 *p521MontgomeryDomainFieldElement, arg1 *p521NonMontgomeryDomainFieldElement) { + var x1 uint64 + var x2 uint64 + x2, x1 = bits.Mul64(arg1[0], 0x400000000000) + var x3 uint64 + var x4 uint64 + x4, x3 = bits.Mul64(arg1[1], 0x400000000000) + var x5 uint64 + var x6 uint64 + x5, x6 = bits.Add64(x2, x3, uint64(0x0)) + var x7 uint64 + var x8 uint64 + x8, x7 = bits.Mul64(x1, 0x1ff) + var x9 uint64 + var x10 uint64 + x10, x9 = bits.Mul64(x1, 0xffffffffffffffff) + var x11 uint64 + var x12 uint64 + x12, x11 = bits.Mul64(x1, 0xffffffffffffffff) + var x13 uint64 + var x14 uint64 + x14, x13 = bits.Mul64(x1, 0xffffffffffffffff) + var x15 uint64 + var x16 uint64 + x16, x15 = bits.Mul64(x1, 0xffffffffffffffff) var x17 uint64 var x18 uint64 - x18, x17 = bits.Mul64(arg1[8], (x1 * 0x2)) + x18, x17 = bits.Mul64(x1, 0xffffffffffffffff) var x19 uint64 var x20 uint64 - x20, x19 = bits.Mul64(arg1[7], (x2 * 0x2)) + x20, x19 = bits.Mul64(x1, 0xffffffffffffffff) var x21 uint64 var x22 uint64 - x22, x21 = bits.Mul64(arg1[7], (x4 * 0x2)) + x22, x21 = bits.Mul64(x1, 0xffffffffffffffff) var x23 uint64 var x24 uint64 - x24, x23 = bits.Mul64(arg1[6], (x2 * 0x2)) + x24, x23 = bits.Mul64(x1, 0xffffffffffffffff) var x25 uint64 var x26 uint64 - x26, x25 = bits.Mul64(arg1[6], (x5 * 0x2)) + x25, x26 = bits.Add64(x24, x21, uint64(0x0)) var x27 uint64 var x28 uint64 - x28, x27 = bits.Mul64(arg1[6], (x7 * 0x2)) + x27, x28 = bits.Add64(x22, x19, uint64(p521Uint1(x26))) var x29 uint64 var x30 uint64 - x30, x29 = bits.Mul64(arg1[5], (x2 * 0x2)) + x29, x30 = bits.Add64(x20, x17, uint64(p521Uint1(x28))) var x31 uint64 var x32 uint64 - x32, x31 = bits.Mul64(arg1[5], (x5 * 0x2)) + x31, x32 = bits.Add64(x18, x15, uint64(p521Uint1(x30))) var x33 uint64 var x34 uint64 - x34, x33 = bits.Mul64(arg1[5], (x8 * 0x2)) + x33, x34 = bits.Add64(x16, x13, uint64(p521Uint1(x32))) var x35 uint64 var x36 uint64 - x36, x35 = bits.Mul64(arg1[5], (x10 * 0x2)) + x35, x36 = bits.Add64(x14, x11, uint64(p521Uint1(x34))) var x37 uint64 var x38 uint64 - x38, x37 = bits.Mul64(arg1[4], (x2 * 0x2)) + x37, x38 = bits.Add64(x12, x9, uint64(p521Uint1(x36))) var x39 uint64 var x40 uint64 - x40, x39 = bits.Mul64(arg1[4], (x5 * 0x2)) - var x41 uint64 + x39, x40 = bits.Add64(x10, x7, uint64(p521Uint1(x38))) var x42 uint64 - x42, x41 = bits.Mul64(arg1[4], (x8 * 0x2)) + _, x42 = bits.Add64(x1, x23, uint64(0x0)) var x43 uint64 var x44 uint64 - x44, x43 = bits.Mul64(arg1[4], (x11 * 0x2)) + x43, x44 = bits.Add64(x5, x25, uint64(p521Uint1(x42))) var x45 uint64 var x46 uint64 - x46, x45 = bits.Mul64(arg1[4], arg1[4]) + x45, x46 = bits.Add64((uint64(p521Uint1(x6)) + x4), x27, uint64(p521Uint1(x44))) var x47 uint64 var x48 uint64 - x48, x47 = bits.Mul64(arg1[3], (x2 * 0x2)) + x47, x48 = bits.Add64(uint64(0x0), x29, uint64(p521Uint1(x46))) var x49 uint64 var x50 uint64 - x50, x49 = bits.Mul64(arg1[3], (x5 * 0x2)) + x49, x50 = bits.Add64(uint64(0x0), x31, uint64(p521Uint1(x48))) var x51 uint64 var x52 uint64 - x52, x51 = bits.Mul64(arg1[3], (x8 * 0x2)) + x51, x52 = bits.Add64(uint64(0x0), x33, uint64(p521Uint1(x50))) var x53 uint64 var x54 uint64 - x54, x53 = bits.Mul64(arg1[3], x12) + x53, x54 = bits.Add64(uint64(0x0), x35, uint64(p521Uint1(x52))) var x55 uint64 var x56 uint64 - x56, x55 = bits.Mul64(arg1[3], x13) + x55, x56 = bits.Add64(uint64(0x0), x37, uint64(p521Uint1(x54))) var x57 uint64 var x58 uint64 - x58, x57 = bits.Mul64(arg1[3], arg1[3]) + x57, x58 = bits.Add64(uint64(0x0), x39, uint64(p521Uint1(x56))) var x59 uint64 var x60 uint64 - x60, x59 = bits.Mul64(arg1[2], (x2 * 0x2)) + x60, x59 = bits.Mul64(arg1[2], 0x400000000000) var x61 uint64 var x62 uint64 - x62, x61 = bits.Mul64(arg1[2], (x5 * 0x2)) + x61, x62 = bits.Add64(x45, x59, uint64(0x0)) var x63 uint64 var x64 uint64 - x64, x63 = bits.Mul64(arg1[2], x9) + x63, x64 = bits.Add64(x47, x60, uint64(p521Uint1(x62))) var x65 uint64 var x66 uint64 - x66, x65 = bits.Mul64(arg1[2], x12) + x65, x66 = bits.Add64(x49, uint64(0x0), uint64(p521Uint1(x64))) var x67 uint64 var x68 uint64 - x68, x67 = bits.Mul64(arg1[2], x13) + x67, x68 = bits.Add64(x51, uint64(0x0), uint64(p521Uint1(x66))) var x69 uint64 var x70 uint64 - x70, x69 = bits.Mul64(arg1[2], x14) + x69, x70 = bits.Add64(x53, uint64(0x0), uint64(p521Uint1(x68))) var x71 uint64 var x72 uint64 - x72, x71 = bits.Mul64(arg1[2], arg1[2]) + x71, x72 = bits.Add64(x55, uint64(0x0), uint64(p521Uint1(x70))) var x73 uint64 var x74 uint64 - x74, x73 = bits.Mul64(arg1[1], (x2 * 0x2)) + x73, x74 = bits.Add64(x57, uint64(0x0), uint64(p521Uint1(x72))) var x75 uint64 var x76 uint64 - x76, x75 = bits.Mul64(arg1[1], x6) + x76, x75 = bits.Mul64(x43, 0x1ff) var x77 uint64 var x78 uint64 - x78, x77 = bits.Mul64(arg1[1], x9) + x78, x77 = bits.Mul64(x43, 0xffffffffffffffff) var x79 uint64 var x80 uint64 - x80, x79 = bits.Mul64(arg1[1], x12) + x80, x79 = bits.Mul64(x43, 0xffffffffffffffff) var x81 uint64 var x82 uint64 - x82, x81 = bits.Mul64(arg1[1], x13) + x82, x81 = bits.Mul64(x43, 0xffffffffffffffff) var x83 uint64 var x84 uint64 - x84, x83 = bits.Mul64(arg1[1], x14) + x84, x83 = bits.Mul64(x43, 0xffffffffffffffff) var x85 uint64 var x86 uint64 - x86, x85 = bits.Mul64(arg1[1], x15) + x86, x85 = bits.Mul64(x43, 0xffffffffffffffff) var x87 uint64 var x88 uint64 - x88, x87 = bits.Mul64(arg1[1], arg1[1]) + x88, x87 = bits.Mul64(x43, 0xffffffffffffffff) var x89 uint64 var x90 uint64 - x90, x89 = bits.Mul64(arg1[0], x3) + x90, x89 = bits.Mul64(x43, 0xffffffffffffffff) var x91 uint64 var x92 uint64 - x92, x91 = bits.Mul64(arg1[0], x6) + x92, x91 = bits.Mul64(x43, 0xffffffffffffffff) var x93 uint64 var x94 uint64 - x94, x93 = bits.Mul64(arg1[0], x9) + x93, x94 = bits.Add64(x92, x89, uint64(0x0)) var x95 uint64 var x96 uint64 - x96, x95 = bits.Mul64(arg1[0], x12) + x95, x96 = bits.Add64(x90, x87, uint64(p521Uint1(x94))) var x97 uint64 var x98 uint64 - x98, x97 = bits.Mul64(arg1[0], x13) + x97, x98 = bits.Add64(x88, x85, uint64(p521Uint1(x96))) var x99 uint64 var x100 uint64 - x100, x99 = bits.Mul64(arg1[0], x14) + x99, x100 = bits.Add64(x86, x83, uint64(p521Uint1(x98))) var x101 uint64 var x102 uint64 - x102, x101 = bits.Mul64(arg1[0], x15) + x101, x102 = bits.Add64(x84, x81, uint64(p521Uint1(x100))) var x103 uint64 var x104 uint64 - x104, x103 = bits.Mul64(arg1[0], x16) + x103, x104 = bits.Add64(x82, x79, uint64(p521Uint1(x102))) var x105 uint64 var x106 uint64 - x106, x105 = bits.Mul64(arg1[0], arg1[0]) + x105, x106 = bits.Add64(x80, x77, uint64(p521Uint1(x104))) var x107 uint64 - var x108 p521Uint1 - x107, x108 = p521AddcarryxU64(x51, x43, 0x0) - var x109 uint64 - x109, _ = p521AddcarryxU64(x52, x44, x108) + var x108 uint64 + x107, x108 = bits.Add64(x78, x75, uint64(p521Uint1(x106))) + var x110 uint64 + _, x110 = bits.Add64(x43, x91, uint64(0x0)) var x111 uint64 - var x112 p521Uint1 - x111, x112 = p521AddcarryxU64(x61, x107, 0x0) + var x112 uint64 + x111, x112 = bits.Add64(x61, x93, uint64(p521Uint1(x110))) var x113 uint64 - x113, _ = p521AddcarryxU64(x62, x109, x112) + var x114 uint64 + x113, x114 = bits.Add64(x63, x95, uint64(p521Uint1(x112))) var x115 uint64 - var x116 p521Uint1 - x115, x116 = p521AddcarryxU64(x73, x111, 0x0) + var x116 uint64 + x115, x116 = bits.Add64(x65, x97, uint64(p521Uint1(x114))) var x117 uint64 - x117, _ = p521AddcarryxU64(x74, x113, x116) + var x118 uint64 + x117, x118 = bits.Add64(x67, x99, uint64(p521Uint1(x116))) var x119 uint64 - var x120 p521Uint1 - x119, x120 = p521AddcarryxU64(x105, x115, 0x0) + var x120 uint64 + x119, x120 = bits.Add64(x69, x101, uint64(p521Uint1(x118))) var x121 uint64 - x121, _ = p521AddcarryxU64(x106, x117, x120) - x123 := ((x119 >> 58) | ((x121 << 6) & 0xffffffffffffffff)) - x124 := (x121 >> 58) - x125 := (x119 & 0x3ffffffffffffff) + var x122 uint64 + x121, x122 = bits.Add64(x71, x103, uint64(p521Uint1(x120))) + var x123 uint64 + var x124 uint64 + x123, x124 = bits.Add64(x73, x105, uint64(p521Uint1(x122))) + var x125 uint64 var x126 uint64 - var x127 p521Uint1 - x126, x127 = p521AddcarryxU64(x53, x45, 0x0) + x125, x126 = bits.Add64((uint64(p521Uint1(x74)) + (uint64(p521Uint1(x58)) + (uint64(p521Uint1(x40)) + x8))), x107, uint64(p521Uint1(x124))) + var x127 uint64 var x128 uint64 - x128, _ = p521AddcarryxU64(x54, x46, x127) + x128, x127 = bits.Mul64(arg1[3], 0x400000000000) + var x129 uint64 var x130 uint64 - var x131 p521Uint1 - x130, x131 = p521AddcarryxU64(x63, x126, 0x0) + x129, x130 = bits.Add64(x113, x127, uint64(0x0)) + var x131 uint64 var x132 uint64 - x132, _ = p521AddcarryxU64(x64, x128, x131) + x131, x132 = bits.Add64(x115, x128, uint64(p521Uint1(x130))) + var x133 uint64 var x134 uint64 - var x135 p521Uint1 - x134, x135 = p521AddcarryxU64(x75, x130, 0x0) + x133, x134 = bits.Add64(x117, uint64(0x0), uint64(p521Uint1(x132))) + var x135 uint64 var x136 uint64 - x136, _ = p521AddcarryxU64(x76, x132, x135) + x135, x136 = bits.Add64(x119, uint64(0x0), uint64(p521Uint1(x134))) + var x137 uint64 var x138 uint64 - var x139 p521Uint1 - x138, x139 = p521AddcarryxU64(x89, x134, 0x0) + x137, x138 = bits.Add64(x121, uint64(0x0), uint64(p521Uint1(x136))) + var x139 uint64 var x140 uint64 - x140, _ = p521AddcarryxU64(x90, x136, x139) + x139, x140 = bits.Add64(x123, uint64(0x0), uint64(p521Uint1(x138))) + var x141 uint64 var x142 uint64 - var x143 p521Uint1 - x142, x143 = p521AddcarryxU64(x55, x17, 0x0) + x141, x142 = bits.Add64(x125, uint64(0x0), uint64(p521Uint1(x140))) + var x143 uint64 var x144 uint64 - x144, _ = p521AddcarryxU64(x56, x18, x143) + x144, x143 = bits.Mul64(x111, 0x1ff) + var x145 uint64 var x146 uint64 - var x147 p521Uint1 - x146, x147 = p521AddcarryxU64(x65, x142, 0x0) + x146, x145 = bits.Mul64(x111, 0xffffffffffffffff) + var x147 uint64 var x148 uint64 - x148, _ = p521AddcarryxU64(x66, x144, x147) + x148, x147 = bits.Mul64(x111, 0xffffffffffffffff) + var x149 uint64 var x150 uint64 - var x151 p521Uint1 - x150, x151 = p521AddcarryxU64(x77, x146, 0x0) + x150, x149 = bits.Mul64(x111, 0xffffffffffffffff) + var x151 uint64 var x152 uint64 - x152, _ = p521AddcarryxU64(x78, x148, x151) + x152, x151 = bits.Mul64(x111, 0xffffffffffffffff) + var x153 uint64 var x154 uint64 - var x155 p521Uint1 - x154, x155 = p521AddcarryxU64(x91, x150, 0x0) + x154, x153 = bits.Mul64(x111, 0xffffffffffffffff) + var x155 uint64 var x156 uint64 - x156, _ = p521AddcarryxU64(x92, x152, x155) + x156, x155 = bits.Mul64(x111, 0xffffffffffffffff) + var x157 uint64 var x158 uint64 - var x159 p521Uint1 - x158, x159 = p521AddcarryxU64(x57, x19, 0x0) + x158, x157 = bits.Mul64(x111, 0xffffffffffffffff) + var x159 uint64 var x160 uint64 - x160, _ = p521AddcarryxU64(x58, x20, x159) + x160, x159 = bits.Mul64(x111, 0xffffffffffffffff) + var x161 uint64 var x162 uint64 - var x163 p521Uint1 - x162, x163 = p521AddcarryxU64(x67, x158, 0x0) + x161, x162 = bits.Add64(x160, x157, uint64(0x0)) + var x163 uint64 var x164 uint64 - x164, _ = p521AddcarryxU64(x68, x160, x163) + x163, x164 = bits.Add64(x158, x155, uint64(p521Uint1(x162))) + var x165 uint64 var x166 uint64 - var x167 p521Uint1 - x166, x167 = p521AddcarryxU64(x79, x162, 0x0) + x165, x166 = bits.Add64(x156, x153, uint64(p521Uint1(x164))) + var x167 uint64 var x168 uint64 - x168, _ = p521AddcarryxU64(x80, x164, x167) + x167, x168 = bits.Add64(x154, x151, uint64(p521Uint1(x166))) + var x169 uint64 var x170 uint64 - var x171 p521Uint1 - x170, x171 = p521AddcarryxU64(x93, x166, 0x0) + x169, x170 = bits.Add64(x152, x149, uint64(p521Uint1(x168))) + var x171 uint64 var x172 uint64 - x172, _ = p521AddcarryxU64(x94, x168, x171) + x171, x172 = bits.Add64(x150, x147, uint64(p521Uint1(x170))) + var x173 uint64 var x174 uint64 - var x175 p521Uint1 - x174, x175 = p521AddcarryxU64(x23, x21, 0x0) + x173, x174 = bits.Add64(x148, x145, uint64(p521Uint1(x172))) + var x175 uint64 var x176 uint64 - x176, _ = p521AddcarryxU64(x24, x22, x175) + x175, x176 = bits.Add64(x146, x143, uint64(p521Uint1(x174))) var x178 uint64 - var x179 p521Uint1 - x178, x179 = p521AddcarryxU64(x69, x174, 0x0) + _, x178 = bits.Add64(x111, x159, uint64(0x0)) + var x179 uint64 var x180 uint64 - x180, _ = p521AddcarryxU64(x70, x176, x179) + x179, x180 = bits.Add64(x129, x161, uint64(p521Uint1(x178))) + var x181 uint64 var x182 uint64 - var x183 p521Uint1 - x182, x183 = p521AddcarryxU64(x81, x178, 0x0) + x181, x182 = bits.Add64(x131, x163, uint64(p521Uint1(x180))) + var x183 uint64 var x184 uint64 - x184, _ = p521AddcarryxU64(x82, x180, x183) + x183, x184 = bits.Add64(x133, x165, uint64(p521Uint1(x182))) + var x185 uint64 var x186 uint64 - var x187 p521Uint1 - x186, x187 = p521AddcarryxU64(x95, x182, 0x0) + x185, x186 = bits.Add64(x135, x167, uint64(p521Uint1(x184))) + var x187 uint64 var x188 uint64 - x188, _ = p521AddcarryxU64(x96, x184, x187) + x187, x188 = bits.Add64(x137, x169, uint64(p521Uint1(x186))) + var x189 uint64 var x190 uint64 - var x191 p521Uint1 - x190, x191 = p521AddcarryxU64(x29, x25, 0x0) + x189, x190 = bits.Add64(x139, x171, uint64(p521Uint1(x188))) + var x191 uint64 var x192 uint64 - x192, _ = p521AddcarryxU64(x30, x26, x191) + x191, x192 = bits.Add64(x141, x173, uint64(p521Uint1(x190))) + var x193 uint64 var x194 uint64 - var x195 p521Uint1 - x194, x195 = p521AddcarryxU64(x71, x190, 0x0) + x193, x194 = bits.Add64((uint64(p521Uint1(x142)) + (uint64(p521Uint1(x126)) + (uint64(p521Uint1(x108)) + x76))), x175, uint64(p521Uint1(x192))) + var x195 uint64 var x196 uint64 - x196, _ = p521AddcarryxU64(x72, x192, x195) + x196, x195 = bits.Mul64(arg1[4], 0x400000000000) + var x197 uint64 var x198 uint64 - var x199 p521Uint1 - x198, x199 = p521AddcarryxU64(x83, x194, 0x0) + x197, x198 = bits.Add64(x181, x195, uint64(0x0)) + var x199 uint64 var x200 uint64 - x200, _ = p521AddcarryxU64(x84, x196, x199) + x199, x200 = bits.Add64(x183, x196, uint64(p521Uint1(x198))) + var x201 uint64 var x202 uint64 - var x203 p521Uint1 - x202, x203 = p521AddcarryxU64(x97, x198, 0x0) + x201, x202 = bits.Add64(x185, uint64(0x0), uint64(p521Uint1(x200))) + var x203 uint64 var x204 uint64 - x204, _ = p521AddcarryxU64(x98, x200, x203) + x203, x204 = bits.Add64(x187, uint64(0x0), uint64(p521Uint1(x202))) + var x205 uint64 var x206 uint64 - var x207 p521Uint1 - x206, x207 = p521AddcarryxU64(x31, x27, 0x0) + x205, x206 = bits.Add64(x189, uint64(0x0), uint64(p521Uint1(x204))) + var x207 uint64 var x208 uint64 - x208, _ = p521AddcarryxU64(x32, x28, x207) + x207, x208 = bits.Add64(x191, uint64(0x0), uint64(p521Uint1(x206))) + var x209 uint64 var x210 uint64 - var x211 p521Uint1 - x210, x211 = p521AddcarryxU64(x37, x206, 0x0) + x209, x210 = bits.Add64(x193, uint64(0x0), uint64(p521Uint1(x208))) + var x211 uint64 var x212 uint64 - x212, _ = p521AddcarryxU64(x38, x208, x211) + x212, x211 = bits.Mul64(x179, 0x1ff) + var x213 uint64 var x214 uint64 - var x215 p521Uint1 - x214, x215 = p521AddcarryxU64(x85, x210, 0x0) + x214, x213 = bits.Mul64(x179, 0xffffffffffffffff) + var x215 uint64 var x216 uint64 - x216, _ = p521AddcarryxU64(x86, x212, x215) + x216, x215 = bits.Mul64(x179, 0xffffffffffffffff) + var x217 uint64 var x218 uint64 - var x219 p521Uint1 - x218, x219 = p521AddcarryxU64(x99, x214, 0x0) + x218, x217 = bits.Mul64(x179, 0xffffffffffffffff) + var x219 uint64 var x220 uint64 - x220, _ = p521AddcarryxU64(x100, x216, x219) + x220, x219 = bits.Mul64(x179, 0xffffffffffffffff) + var x221 uint64 var x222 uint64 - var x223 p521Uint1 - x222, x223 = p521AddcarryxU64(x39, x33, 0x0) + x222, x221 = bits.Mul64(x179, 0xffffffffffffffff) + var x223 uint64 var x224 uint64 - x224, _ = p521AddcarryxU64(x40, x34, x223) + x224, x223 = bits.Mul64(x179, 0xffffffffffffffff) + var x225 uint64 var x226 uint64 - var x227 p521Uint1 - x226, x227 = p521AddcarryxU64(x47, x222, 0x0) + x226, x225 = bits.Mul64(x179, 0xffffffffffffffff) + var x227 uint64 var x228 uint64 - x228, _ = p521AddcarryxU64(x48, x224, x227) + x228, x227 = bits.Mul64(x179, 0xffffffffffffffff) + var x229 uint64 var x230 uint64 - var x231 p521Uint1 - x230, x231 = p521AddcarryxU64(x87, x226, 0x0) + x229, x230 = bits.Add64(x228, x225, uint64(0x0)) + var x231 uint64 var x232 uint64 - x232, _ = p521AddcarryxU64(x88, x228, x231) + x231, x232 = bits.Add64(x226, x223, uint64(p521Uint1(x230))) + var x233 uint64 var x234 uint64 - var x235 p521Uint1 - x234, x235 = p521AddcarryxU64(x101, x230, 0x0) + x233, x234 = bits.Add64(x224, x221, uint64(p521Uint1(x232))) + var x235 uint64 var x236 uint64 - x236, _ = p521AddcarryxU64(x102, x232, x235) + x235, x236 = bits.Add64(x222, x219, uint64(p521Uint1(x234))) + var x237 uint64 var x238 uint64 - var x239 p521Uint1 - x238, x239 = p521AddcarryxU64(x41, x35, 0x0) + x237, x238 = bits.Add64(x220, x217, uint64(p521Uint1(x236))) + var x239 uint64 var x240 uint64 - x240, _ = p521AddcarryxU64(x42, x36, x239) + x239, x240 = bits.Add64(x218, x215, uint64(p521Uint1(x238))) + var x241 uint64 var x242 uint64 - var x243 p521Uint1 - x242, x243 = p521AddcarryxU64(x49, x238, 0x0) + x241, x242 = bits.Add64(x216, x213, uint64(p521Uint1(x240))) + var x243 uint64 var x244 uint64 - x244, _ = p521AddcarryxU64(x50, x240, x243) + x243, x244 = bits.Add64(x214, x211, uint64(p521Uint1(x242))) var x246 uint64 - var x247 p521Uint1 - x246, x247 = p521AddcarryxU64(x59, x242, 0x0) + _, x246 = bits.Add64(x179, x227, uint64(0x0)) + var x247 uint64 var x248 uint64 - x248, _ = p521AddcarryxU64(x60, x244, x247) + x247, x248 = bits.Add64(x197, x229, uint64(p521Uint1(x246))) + var x249 uint64 var x250 uint64 - var x251 p521Uint1 - x250, x251 = p521AddcarryxU64(x103, x246, 0x0) + x249, x250 = bits.Add64(x199, x231, uint64(p521Uint1(x248))) + var x251 uint64 var x252 uint64 - x252, _ = p521AddcarryxU64(x104, x248, x251) + x251, x252 = bits.Add64(x201, x233, uint64(p521Uint1(x250))) + var x253 uint64 var x254 uint64 - var x255 p521Uint1 - x254, x255 = p521AddcarryxU64(x123, x250, 0x0) + x253, x254 = bits.Add64(x203, x235, uint64(p521Uint1(x252))) + var x255 uint64 var x256 uint64 - x256, _ = p521AddcarryxU64(x124, x252, x255) - x258 := ((x254 >> 58) | ((x256 << 6) & 0xffffffffffffffff)) - x259 := (x256 >> 58) - x260 := (x254 & 0x3ffffffffffffff) + x255, x256 = bits.Add64(x205, x237, uint64(p521Uint1(x254))) + var x257 uint64 + var x258 uint64 + x257, x258 = bits.Add64(x207, x239, uint64(p521Uint1(x256))) + var x259 uint64 + var x260 uint64 + x259, x260 = bits.Add64(x209, x241, uint64(p521Uint1(x258))) var x261 uint64 - var x262 p521Uint1 - x261, x262 = p521AddcarryxU64(x258, x234, 0x0) + var x262 uint64 + x261, x262 = bits.Add64((uint64(p521Uint1(x210)) + (uint64(p521Uint1(x194)) + (uint64(p521Uint1(x176)) + x144))), x243, uint64(p521Uint1(x260))) var x263 uint64 - x263, _ = p521AddcarryxU64(x259, x236, x262) - x265 := ((x261 >> 58) | ((x263 << 6) & 0xffffffffffffffff)) - x266 := (x263 >> 58) - x267 := (x261 & 0x3ffffffffffffff) + var x264 uint64 + x264, x263 = bits.Mul64(arg1[5], 0x400000000000) + var x265 uint64 + var x266 uint64 + x265, x266 = bits.Add64(x249, x263, uint64(0x0)) + var x267 uint64 var x268 uint64 - var x269 p521Uint1 - x268, x269 = p521AddcarryxU64(x265, x218, 0x0) + x267, x268 = bits.Add64(x251, x264, uint64(p521Uint1(x266))) + var x269 uint64 var x270 uint64 - x270, _ = p521AddcarryxU64(x266, x220, x269) - x272 := ((x268 >> 58) | ((x270 << 6) & 0xffffffffffffffff)) - x273 := (x270 >> 58) - x274 := (x268 & 0x3ffffffffffffff) + x269, x270 = bits.Add64(x253, uint64(0x0), uint64(p521Uint1(x268))) + var x271 uint64 + var x272 uint64 + x271, x272 = bits.Add64(x255, uint64(0x0), uint64(p521Uint1(x270))) + var x273 uint64 + var x274 uint64 + x273, x274 = bits.Add64(x257, uint64(0x0), uint64(p521Uint1(x272))) var x275 uint64 - var x276 p521Uint1 - x275, x276 = p521AddcarryxU64(x272, x202, 0x0) + var x276 uint64 + x275, x276 = bits.Add64(x259, uint64(0x0), uint64(p521Uint1(x274))) var x277 uint64 - x277, _ = p521AddcarryxU64(x273, x204, x276) - x279 := ((x275 >> 58) | ((x277 << 6) & 0xffffffffffffffff)) - x280 := (x277 >> 58) - x281 := (x275 & 0x3ffffffffffffff) + var x278 uint64 + x277, x278 = bits.Add64(x261, uint64(0x0), uint64(p521Uint1(x276))) + var x279 uint64 + var x280 uint64 + x280, x279 = bits.Mul64(x247, 0x1ff) + var x281 uint64 var x282 uint64 - var x283 p521Uint1 - x282, x283 = p521AddcarryxU64(x279, x186, 0x0) + x282, x281 = bits.Mul64(x247, 0xffffffffffffffff) + var x283 uint64 var x284 uint64 - x284, _ = p521AddcarryxU64(x280, x188, x283) - x286 := ((x282 >> 58) | ((x284 << 6) & 0xffffffffffffffff)) - x287 := (x284 >> 58) - x288 := (x282 & 0x3ffffffffffffff) + x284, x283 = bits.Mul64(x247, 0xffffffffffffffff) + var x285 uint64 + var x286 uint64 + x286, x285 = bits.Mul64(x247, 0xffffffffffffffff) + var x287 uint64 + var x288 uint64 + x288, x287 = bits.Mul64(x247, 0xffffffffffffffff) var x289 uint64 - var x290 p521Uint1 - x289, x290 = p521AddcarryxU64(x286, x170, 0x0) + var x290 uint64 + x290, x289 = bits.Mul64(x247, 0xffffffffffffffff) var x291 uint64 - x291, _ = p521AddcarryxU64(x287, x172, x290) - x293 := ((x289 >> 58) | ((x291 << 6) & 0xffffffffffffffff)) - x294 := (x291 >> 58) - x295 := (x289 & 0x3ffffffffffffff) + var x292 uint64 + x292, x291 = bits.Mul64(x247, 0xffffffffffffffff) + var x293 uint64 + var x294 uint64 + x294, x293 = bits.Mul64(x247, 0xffffffffffffffff) + var x295 uint64 var x296 uint64 - var x297 p521Uint1 - x296, x297 = p521AddcarryxU64(x293, x154, 0x0) + x296, x295 = bits.Mul64(x247, 0xffffffffffffffff) + var x297 uint64 var x298 uint64 - x298, _ = p521AddcarryxU64(x294, x156, x297) - x300 := ((x296 >> 58) | ((x298 << 6) & 0xffffffffffffffff)) - x301 := (x298 >> 58) - x302 := (x296 & 0x3ffffffffffffff) + x297, x298 = bits.Add64(x296, x293, uint64(0x0)) + var x299 uint64 + var x300 uint64 + x299, x300 = bits.Add64(x294, x291, uint64(p521Uint1(x298))) + var x301 uint64 + var x302 uint64 + x301, x302 = bits.Add64(x292, x289, uint64(p521Uint1(x300))) var x303 uint64 - var x304 p521Uint1 - x303, x304 = p521AddcarryxU64(x300, x138, 0x0) + var x304 uint64 + x303, x304 = bits.Add64(x290, x287, uint64(p521Uint1(x302))) var x305 uint64 - x305, _ = p521AddcarryxU64(x301, x140, x304) - x307 := ((x303 >> 57) | ((x305 << 7) & 0xffffffffffffffff)) - x308 := (x305 >> 57) - x309 := (x303 & 0x1ffffffffffffff) + var x306 uint64 + x305, x306 = bits.Add64(x288, x285, uint64(p521Uint1(x304))) + var x307 uint64 + var x308 uint64 + x307, x308 = bits.Add64(x286, x283, uint64(p521Uint1(x306))) + var x309 uint64 var x310 uint64 - var x311 p521Uint1 - x310, x311 = p521AddcarryxU64(x125, x307, 0x0) - x312 := (uint64(x311) + x308) - x313 := ((x310 >> 58) | ((x312 << 6) & 0xffffffffffffffff)) - x314 := (x310 & 0x3ffffffffffffff) - x315 := (x313 + x260) - x316 := p521Uint1((x315 >> 58)) - x317 := (x315 & 0x3ffffffffffffff) - x318 := (uint64(x316) + x267) - out1[0] = x314 - out1[1] = x317 - out1[2] = x318 - out1[3] = x274 - out1[4] = x281 - out1[5] = x288 - out1[6] = x295 - out1[7] = x302 - out1[8] = x309 -} - -// p521Carry reduces a field element. -// -// Postconditions: -// eval out1 mod m = eval arg1 mod m -// -// Input Bounds: -// arg1: [[0x0 ~> 0xc00000000000000], [0x0 ~> 0xc00000000000000], [0x0 ~> 0xc00000000000000], [0x0 ~> 0xc00000000000000], [0x0 ~> 0xc00000000000000], [0x0 ~> 0xc00000000000000], [0x0 ~> 0xc00000000000000], [0x0 ~> 0xc00000000000000], [0x0 ~> 0x600000000000000]] -// Output Bounds: -// out1: [[0x0 ~> 0x400000000000000], [0x0 ~> 0x400000000000000], [0x0 ~> 0x400000000000000], [0x0 ~> 0x400000000000000], [0x0 ~> 0x400000000000000], [0x0 ~> 0x400000000000000], [0x0 ~> 0x400000000000000], [0x0 ~> 0x400000000000000], [0x0 ~> 0x200000000000000]] -func p521Carry(out1 *[9]uint64, arg1 *[9]uint64) { - x1 := arg1[0] - x2 := ((x1 >> 58) + arg1[1]) - x3 := ((x2 >> 58) + arg1[2]) - x4 := ((x3 >> 58) + arg1[3]) - x5 := ((x4 >> 58) + arg1[4]) - x6 := ((x5 >> 58) + arg1[5]) - x7 := ((x6 >> 58) + arg1[6]) - x8 := ((x7 >> 58) + arg1[7]) - x9 := ((x8 >> 58) + arg1[8]) - x10 := ((x1 & 0x3ffffffffffffff) + (x9 >> 57)) - x11 := (uint64(p521Uint1((x10 >> 58))) + (x2 & 0x3ffffffffffffff)) - x12 := (x10 & 0x3ffffffffffffff) - x13 := (x11 & 0x3ffffffffffffff) - x14 := (uint64(p521Uint1((x11 >> 58))) + (x3 & 0x3ffffffffffffff)) - x15 := (x4 & 0x3ffffffffffffff) - x16 := (x5 & 0x3ffffffffffffff) - x17 := (x6 & 0x3ffffffffffffff) - x18 := (x7 & 0x3ffffffffffffff) - x19 := (x8 & 0x3ffffffffffffff) - x20 := (x9 & 0x1ffffffffffffff) - out1[0] = x12 - out1[1] = x13 - out1[2] = x14 - out1[3] = x15 - out1[4] = x16 - out1[5] = x17 - out1[6] = x18 - out1[7] = x19 - out1[8] = x20 -} - -// p521Add adds two field elements. -// -// Postconditions: -// eval out1 mod m = (eval arg1 + eval arg2) mod m -// -// Input Bounds: -// arg1: [[0x0 ~> 0x400000000000000], [0x0 ~> 0x400000000000000], [0x0 ~> 0x400000000000000], [0x0 ~> 0x400000000000000], [0x0 ~> 0x400000000000000], [0x0 ~> 0x400000000000000], [0x0 ~> 0x400000000000000], [0x0 ~> 0x400000000000000], [0x0 ~> 0x200000000000000]] -// arg2: [[0x0 ~> 0x400000000000000], [0x0 ~> 0x400000000000000], [0x0 ~> 0x400000000000000], [0x0 ~> 0x400000000000000], [0x0 ~> 0x400000000000000], [0x0 ~> 0x400000000000000], [0x0 ~> 0x400000000000000], [0x0 ~> 0x400000000000000], [0x0 ~> 0x200000000000000]] -// Output Bounds: -// out1: [[0x0 ~> 0xc00000000000000], [0x0 ~> 0xc00000000000000], [0x0 ~> 0xc00000000000000], [0x0 ~> 0xc00000000000000], [0x0 ~> 0xc00000000000000], [0x0 ~> 0xc00000000000000], [0x0 ~> 0xc00000000000000], [0x0 ~> 0xc00000000000000], [0x0 ~> 0x600000000000000]] -func p521Add(out1 *[9]uint64, arg1 *[9]uint64, arg2 *[9]uint64) { - x1 := (arg1[0] + arg2[0]) - x2 := (arg1[1] + arg2[1]) - x3 := (arg1[2] + arg2[2]) - x4 := (arg1[3] + arg2[3]) - x5 := (arg1[4] + arg2[4]) - x6 := (arg1[5] + arg2[5]) - x7 := (arg1[6] + arg2[6]) - x8 := (arg1[7] + arg2[7]) - x9 := (arg1[8] + arg2[8]) - out1[0] = x1 - out1[1] = x2 - out1[2] = x3 - out1[3] = x4 - out1[4] = x5 - out1[5] = x6 - out1[6] = x7 - out1[7] = x8 - out1[8] = x9 + x309, x310 = bits.Add64(x284, x281, uint64(p521Uint1(x308))) + var x311 uint64 + var x312 uint64 + x311, x312 = bits.Add64(x282, x279, uint64(p521Uint1(x310))) + var x314 uint64 + _, x314 = bits.Add64(x247, x295, uint64(0x0)) + var x315 uint64 + var x316 uint64 + x315, x316 = bits.Add64(x265, x297, uint64(p521Uint1(x314))) + var x317 uint64 + var x318 uint64 + x317, x318 = bits.Add64(x267, x299, uint64(p521Uint1(x316))) + var x319 uint64 + var x320 uint64 + x319, x320 = bits.Add64(x269, x301, uint64(p521Uint1(x318))) + var x321 uint64 + var x322 uint64 + x321, x322 = bits.Add64(x271, x303, uint64(p521Uint1(x320))) + var x323 uint64 + var x324 uint64 + x323, x324 = bits.Add64(x273, x305, uint64(p521Uint1(x322))) + var x325 uint64 + var x326 uint64 + x325, x326 = bits.Add64(x275, x307, uint64(p521Uint1(x324))) + var x327 uint64 + var x328 uint64 + x327, x328 = bits.Add64(x277, x309, uint64(p521Uint1(x326))) + var x329 uint64 + var x330 uint64 + x329, x330 = bits.Add64((uint64(p521Uint1(x278)) + (uint64(p521Uint1(x262)) + (uint64(p521Uint1(x244)) + x212))), x311, uint64(p521Uint1(x328))) + var x331 uint64 + var x332 uint64 + x332, x331 = bits.Mul64(arg1[6], 0x400000000000) + var x333 uint64 + var x334 uint64 + x333, x334 = bits.Add64(x317, x331, uint64(0x0)) + var x335 uint64 + var x336 uint64 + x335, x336 = bits.Add64(x319, x332, uint64(p521Uint1(x334))) + var x337 uint64 + var x338 uint64 + x337, x338 = bits.Add64(x321, uint64(0x0), uint64(p521Uint1(x336))) + var x339 uint64 + var x340 uint64 + x339, x340 = bits.Add64(x323, uint64(0x0), uint64(p521Uint1(x338))) + var x341 uint64 + var x342 uint64 + x341, x342 = bits.Add64(x325, uint64(0x0), uint64(p521Uint1(x340))) + var x343 uint64 + var x344 uint64 + x343, x344 = bits.Add64(x327, uint64(0x0), uint64(p521Uint1(x342))) + var x345 uint64 + var x346 uint64 + x345, x346 = bits.Add64(x329, uint64(0x0), uint64(p521Uint1(x344))) + var x347 uint64 + var x348 uint64 + x348, x347 = bits.Mul64(x315, 0x1ff) + var x349 uint64 + var x350 uint64 + x350, x349 = bits.Mul64(x315, 0xffffffffffffffff) + var x351 uint64 + var x352 uint64 + x352, x351 = bits.Mul64(x315, 0xffffffffffffffff) + var x353 uint64 + var x354 uint64 + x354, x353 = bits.Mul64(x315, 0xffffffffffffffff) + var x355 uint64 + var x356 uint64 + x356, x355 = bits.Mul64(x315, 0xffffffffffffffff) + var x357 uint64 + var x358 uint64 + x358, x357 = bits.Mul64(x315, 0xffffffffffffffff) + var x359 uint64 + var x360 uint64 + x360, x359 = bits.Mul64(x315, 0xffffffffffffffff) + var x361 uint64 + var x362 uint64 + x362, x361 = bits.Mul64(x315, 0xffffffffffffffff) + var x363 uint64 + var x364 uint64 + x364, x363 = bits.Mul64(x315, 0xffffffffffffffff) + var x365 uint64 + var x366 uint64 + x365, x366 = bits.Add64(x364, x361, uint64(0x0)) + var x367 uint64 + var x368 uint64 + x367, x368 = bits.Add64(x362, x359, uint64(p521Uint1(x366))) + var x369 uint64 + var x370 uint64 + x369, x370 = bits.Add64(x360, x357, uint64(p521Uint1(x368))) + var x371 uint64 + var x372 uint64 + x371, x372 = bits.Add64(x358, x355, uint64(p521Uint1(x370))) + var x373 uint64 + var x374 uint64 + x373, x374 = bits.Add64(x356, x353, uint64(p521Uint1(x372))) + var x375 uint64 + var x376 uint64 + x375, x376 = bits.Add64(x354, x351, uint64(p521Uint1(x374))) + var x377 uint64 + var x378 uint64 + x377, x378 = bits.Add64(x352, x349, uint64(p521Uint1(x376))) + var x379 uint64 + var x380 uint64 + x379, x380 = bits.Add64(x350, x347, uint64(p521Uint1(x378))) + var x382 uint64 + _, x382 = bits.Add64(x315, x363, uint64(0x0)) + var x383 uint64 + var x384 uint64 + x383, x384 = bits.Add64(x333, x365, uint64(p521Uint1(x382))) + var x385 uint64 + var x386 uint64 + x385, x386 = bits.Add64(x335, x367, uint64(p521Uint1(x384))) + var x387 uint64 + var x388 uint64 + x387, x388 = bits.Add64(x337, x369, uint64(p521Uint1(x386))) + var x389 uint64 + var x390 uint64 + x389, x390 = bits.Add64(x339, x371, uint64(p521Uint1(x388))) + var x391 uint64 + var x392 uint64 + x391, x392 = bits.Add64(x341, x373, uint64(p521Uint1(x390))) + var x393 uint64 + var x394 uint64 + x393, x394 = bits.Add64(x343, x375, uint64(p521Uint1(x392))) + var x395 uint64 + var x396 uint64 + x395, x396 = bits.Add64(x345, x377, uint64(p521Uint1(x394))) + var x397 uint64 + var x398 uint64 + x397, x398 = bits.Add64((uint64(p521Uint1(x346)) + (uint64(p521Uint1(x330)) + (uint64(p521Uint1(x312)) + x280))), x379, uint64(p521Uint1(x396))) + var x399 uint64 + var x400 uint64 + x400, x399 = bits.Mul64(arg1[7], 0x400000000000) + var x401 uint64 + var x402 uint64 + x401, x402 = bits.Add64(x385, x399, uint64(0x0)) + var x403 uint64 + var x404 uint64 + x403, x404 = bits.Add64(x387, x400, uint64(p521Uint1(x402))) + var x405 uint64 + var x406 uint64 + x405, x406 = bits.Add64(x389, uint64(0x0), uint64(p521Uint1(x404))) + var x407 uint64 + var x408 uint64 + x407, x408 = bits.Add64(x391, uint64(0x0), uint64(p521Uint1(x406))) + var x409 uint64 + var x410 uint64 + x409, x410 = bits.Add64(x393, uint64(0x0), uint64(p521Uint1(x408))) + var x411 uint64 + var x412 uint64 + x411, x412 = bits.Add64(x395, uint64(0x0), uint64(p521Uint1(x410))) + var x413 uint64 + var x414 uint64 + x413, x414 = bits.Add64(x397, uint64(0x0), uint64(p521Uint1(x412))) + var x415 uint64 + var x416 uint64 + x416, x415 = bits.Mul64(x383, 0x1ff) + var x417 uint64 + var x418 uint64 + x418, x417 = bits.Mul64(x383, 0xffffffffffffffff) + var x419 uint64 + var x420 uint64 + x420, x419 = bits.Mul64(x383, 0xffffffffffffffff) + var x421 uint64 + var x422 uint64 + x422, x421 = bits.Mul64(x383, 0xffffffffffffffff) + var x423 uint64 + var x424 uint64 + x424, x423 = bits.Mul64(x383, 0xffffffffffffffff) + var x425 uint64 + var x426 uint64 + x426, x425 = bits.Mul64(x383, 0xffffffffffffffff) + var x427 uint64 + var x428 uint64 + x428, x427 = bits.Mul64(x383, 0xffffffffffffffff) + var x429 uint64 + var x430 uint64 + x430, x429 = bits.Mul64(x383, 0xffffffffffffffff) + var x431 uint64 + var x432 uint64 + x432, x431 = bits.Mul64(x383, 0xffffffffffffffff) + var x433 uint64 + var x434 uint64 + x433, x434 = bits.Add64(x432, x429, uint64(0x0)) + var x435 uint64 + var x436 uint64 + x435, x436 = bits.Add64(x430, x427, uint64(p521Uint1(x434))) + var x437 uint64 + var x438 uint64 + x437, x438 = bits.Add64(x428, x425, uint64(p521Uint1(x436))) + var x439 uint64 + var x440 uint64 + x439, x440 = bits.Add64(x426, x423, uint64(p521Uint1(x438))) + var x441 uint64 + var x442 uint64 + x441, x442 = bits.Add64(x424, x421, uint64(p521Uint1(x440))) + var x443 uint64 + var x444 uint64 + x443, x444 = bits.Add64(x422, x419, uint64(p521Uint1(x442))) + var x445 uint64 + var x446 uint64 + x445, x446 = bits.Add64(x420, x417, uint64(p521Uint1(x444))) + var x447 uint64 + var x448 uint64 + x447, x448 = bits.Add64(x418, x415, uint64(p521Uint1(x446))) + var x450 uint64 + _, x450 = bits.Add64(x383, x431, uint64(0x0)) + var x451 uint64 + var x452 uint64 + x451, x452 = bits.Add64(x401, x433, uint64(p521Uint1(x450))) + var x453 uint64 + var x454 uint64 + x453, x454 = bits.Add64(x403, x435, uint64(p521Uint1(x452))) + var x455 uint64 + var x456 uint64 + x455, x456 = bits.Add64(x405, x437, uint64(p521Uint1(x454))) + var x457 uint64 + var x458 uint64 + x457, x458 = bits.Add64(x407, x439, uint64(p521Uint1(x456))) + var x459 uint64 + var x460 uint64 + x459, x460 = bits.Add64(x409, x441, uint64(p521Uint1(x458))) + var x461 uint64 + var x462 uint64 + x461, x462 = bits.Add64(x411, x443, uint64(p521Uint1(x460))) + var x463 uint64 + var x464 uint64 + x463, x464 = bits.Add64(x413, x445, uint64(p521Uint1(x462))) + var x465 uint64 + var x466 uint64 + x465, x466 = bits.Add64((uint64(p521Uint1(x414)) + (uint64(p521Uint1(x398)) + (uint64(p521Uint1(x380)) + x348))), x447, uint64(p521Uint1(x464))) + var x467 uint64 + var x468 uint64 + x468, x467 = bits.Mul64(arg1[8], 0x400000000000) + var x469 uint64 + var x470 uint64 + x469, x470 = bits.Add64(x453, x467, uint64(0x0)) + var x471 uint64 + var x472 uint64 + x471, x472 = bits.Add64(x455, x468, uint64(p521Uint1(x470))) + var x473 uint64 + var x474 uint64 + x473, x474 = bits.Add64(x457, uint64(0x0), uint64(p521Uint1(x472))) + var x475 uint64 + var x476 uint64 + x475, x476 = bits.Add64(x459, uint64(0x0), uint64(p521Uint1(x474))) + var x477 uint64 + var x478 uint64 + x477, x478 = bits.Add64(x461, uint64(0x0), uint64(p521Uint1(x476))) + var x479 uint64 + var x480 uint64 + x479, x480 = bits.Add64(x463, uint64(0x0), uint64(p521Uint1(x478))) + var x481 uint64 + var x482 uint64 + x481, x482 = bits.Add64(x465, uint64(0x0), uint64(p521Uint1(x480))) + var x483 uint64 + var x484 uint64 + x484, x483 = bits.Mul64(x451, 0x1ff) + var x485 uint64 + var x486 uint64 + x486, x485 = bits.Mul64(x451, 0xffffffffffffffff) + var x487 uint64 + var x488 uint64 + x488, x487 = bits.Mul64(x451, 0xffffffffffffffff) + var x489 uint64 + var x490 uint64 + x490, x489 = bits.Mul64(x451, 0xffffffffffffffff) + var x491 uint64 + var x492 uint64 + x492, x491 = bits.Mul64(x451, 0xffffffffffffffff) + var x493 uint64 + var x494 uint64 + x494, x493 = bits.Mul64(x451, 0xffffffffffffffff) + var x495 uint64 + var x496 uint64 + x496, x495 = bits.Mul64(x451, 0xffffffffffffffff) + var x497 uint64 + var x498 uint64 + x498, x497 = bits.Mul64(x451, 0xffffffffffffffff) + var x499 uint64 + var x500 uint64 + x500, x499 = bits.Mul64(x451, 0xffffffffffffffff) + var x501 uint64 + var x502 uint64 + x501, x502 = bits.Add64(x500, x497, uint64(0x0)) + var x503 uint64 + var x504 uint64 + x503, x504 = bits.Add64(x498, x495, uint64(p521Uint1(x502))) + var x505 uint64 + var x506 uint64 + x505, x506 = bits.Add64(x496, x493, uint64(p521Uint1(x504))) + var x507 uint64 + var x508 uint64 + x507, x508 = bits.Add64(x494, x491, uint64(p521Uint1(x506))) + var x509 uint64 + var x510 uint64 + x509, x510 = bits.Add64(x492, x489, uint64(p521Uint1(x508))) + var x511 uint64 + var x512 uint64 + x511, x512 = bits.Add64(x490, x487, uint64(p521Uint1(x510))) + var x513 uint64 + var x514 uint64 + x513, x514 = bits.Add64(x488, x485, uint64(p521Uint1(x512))) + var x515 uint64 + var x516 uint64 + x515, x516 = bits.Add64(x486, x483, uint64(p521Uint1(x514))) + var x518 uint64 + _, x518 = bits.Add64(x451, x499, uint64(0x0)) + var x519 uint64 + var x520 uint64 + x519, x520 = bits.Add64(x469, x501, uint64(p521Uint1(x518))) + var x521 uint64 + var x522 uint64 + x521, x522 = bits.Add64(x471, x503, uint64(p521Uint1(x520))) + var x523 uint64 + var x524 uint64 + x523, x524 = bits.Add64(x473, x505, uint64(p521Uint1(x522))) + var x525 uint64 + var x526 uint64 + x525, x526 = bits.Add64(x475, x507, uint64(p521Uint1(x524))) + var x527 uint64 + var x528 uint64 + x527, x528 = bits.Add64(x477, x509, uint64(p521Uint1(x526))) + var x529 uint64 + var x530 uint64 + x529, x530 = bits.Add64(x479, x511, uint64(p521Uint1(x528))) + var x531 uint64 + var x532 uint64 + x531, x532 = bits.Add64(x481, x513, uint64(p521Uint1(x530))) + var x533 uint64 + var x534 uint64 + x533, x534 = bits.Add64((uint64(p521Uint1(x482)) + (uint64(p521Uint1(x466)) + (uint64(p521Uint1(x448)) + x416))), x515, uint64(p521Uint1(x532))) + x535 := (uint64(p521Uint1(x534)) + (uint64(p521Uint1(x516)) + x484)) + var x536 uint64 + var x537 uint64 + x536, x537 = bits.Sub64(x519, 0xffffffffffffffff, uint64(0x0)) + var x538 uint64 + var x539 uint64 + x538, x539 = bits.Sub64(x521, 0xffffffffffffffff, uint64(p521Uint1(x537))) + var x540 uint64 + var x541 uint64 + x540, x541 = bits.Sub64(x523, 0xffffffffffffffff, uint64(p521Uint1(x539))) + var x542 uint64 + var x543 uint64 + x542, x543 = bits.Sub64(x525, 0xffffffffffffffff, uint64(p521Uint1(x541))) + var x544 uint64 + var x545 uint64 + x544, x545 = bits.Sub64(x527, 0xffffffffffffffff, uint64(p521Uint1(x543))) + var x546 uint64 + var x547 uint64 + x546, x547 = bits.Sub64(x529, 0xffffffffffffffff, uint64(p521Uint1(x545))) + var x548 uint64 + var x549 uint64 + x548, x549 = bits.Sub64(x531, 0xffffffffffffffff, uint64(p521Uint1(x547))) + var x550 uint64 + var x551 uint64 + x550, x551 = bits.Sub64(x533, 0xffffffffffffffff, uint64(p521Uint1(x549))) + var x552 uint64 + var x553 uint64 + x552, x553 = bits.Sub64(x535, 0x1ff, uint64(p521Uint1(x551))) + var x555 uint64 + _, x555 = bits.Sub64(uint64(0x0), uint64(0x0), uint64(p521Uint1(x553))) + var x556 uint64 + p521CmovznzU64(&x556, p521Uint1(x555), x536, x519) + var x557 uint64 + p521CmovznzU64(&x557, p521Uint1(x555), x538, x521) + var x558 uint64 + p521CmovznzU64(&x558, p521Uint1(x555), x540, x523) + var x559 uint64 + p521CmovznzU64(&x559, p521Uint1(x555), x542, x525) + var x560 uint64 + p521CmovznzU64(&x560, p521Uint1(x555), x544, x527) + var x561 uint64 + p521CmovznzU64(&x561, p521Uint1(x555), x546, x529) + var x562 uint64 + p521CmovznzU64(&x562, p521Uint1(x555), x548, x531) + var x563 uint64 + p521CmovznzU64(&x563, p521Uint1(x555), x550, x533) + var x564 uint64 + p521CmovznzU64(&x564, p521Uint1(x555), x552, x535) + out1[0] = x556 + out1[1] = x557 + out1[2] = x558 + out1[3] = x559 + out1[4] = x560 + out1[5] = x561 + out1[6] = x562 + out1[7] = x563 + out1[8] = x564 } -// p521Sub subtracts two field elements. +// p521Selectznz is a multi-limb conditional select. // // Postconditions: -// eval out1 mod m = (eval arg1 - eval arg2) mod m +// eval out1 = (if arg1 = 0 then eval arg2 else eval arg3) // // Input Bounds: -// arg1: [[0x0 ~> 0x400000000000000], [0x0 ~> 0x400000000000000], [0x0 ~> 0x400000000000000], [0x0 ~> 0x400000000000000], [0x0 ~> 0x400000000000000], [0x0 ~> 0x400000000000000], [0x0 ~> 0x400000000000000], [0x0 ~> 0x400000000000000], [0x0 ~> 0x200000000000000]] -// arg2: [[0x0 ~> 0x400000000000000], [0x0 ~> 0x400000000000000], [0x0 ~> 0x400000000000000], [0x0 ~> 0x400000000000000], [0x0 ~> 0x400000000000000], [0x0 ~> 0x400000000000000], [0x0 ~> 0x400000000000000], [0x0 ~> 0x400000000000000], [0x0 ~> 0x200000000000000]] +// arg1: [0x0 ~> 0x1] +// arg2: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]] +// arg3: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]] // Output Bounds: -// out1: [[0x0 ~> 0xc00000000000000], [0x0 ~> 0xc00000000000000], [0x0 ~> 0xc00000000000000], [0x0 ~> 0xc00000000000000], [0x0 ~> 0xc00000000000000], [0x0 ~> 0xc00000000000000], [0x0 ~> 0xc00000000000000], [0x0 ~> 0xc00000000000000], [0x0 ~> 0x600000000000000]] -func p521Sub(out1 *[9]uint64, arg1 *[9]uint64, arg2 *[9]uint64) { - x1 := ((0x7fffffffffffffe + arg1[0]) - arg2[0]) - x2 := ((0x7fffffffffffffe + arg1[1]) - arg2[1]) - x3 := ((0x7fffffffffffffe + arg1[2]) - arg2[2]) - x4 := ((0x7fffffffffffffe + arg1[3]) - arg2[3]) - x5 := ((0x7fffffffffffffe + arg1[4]) - arg2[4]) - x6 := ((0x7fffffffffffffe + arg1[5]) - arg2[5]) - x7 := ((0x7fffffffffffffe + arg1[6]) - arg2[6]) - x8 := ((0x7fffffffffffffe + arg1[7]) - arg2[7]) - x9 := ((0x3fffffffffffffe + arg1[8]) - arg2[8]) +// out1: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]] +func p521Selectznz(out1 *[9]uint64, arg1 p521Uint1, arg2 *[9]uint64, arg3 *[9]uint64) { + var x1 uint64 + p521CmovznzU64(&x1, arg1, arg2[0], arg3[0]) + var x2 uint64 + p521CmovznzU64(&x2, arg1, arg2[1], arg3[1]) + var x3 uint64 + p521CmovznzU64(&x3, arg1, arg2[2], arg3[2]) + var x4 uint64 + p521CmovznzU64(&x4, arg1, arg2[3], arg3[3]) + var x5 uint64 + p521CmovznzU64(&x5, arg1, arg2[4], arg3[4]) + var x6 uint64 + p521CmovznzU64(&x6, arg1, arg2[5], arg3[5]) + var x7 uint64 + p521CmovznzU64(&x7, arg1, arg2[6], arg3[6]) + var x8 uint64 + p521CmovznzU64(&x8, arg1, arg2[7], arg3[7]) + var x9 uint64 + p521CmovznzU64(&x9, arg1, arg2[8], arg3[8]) out1[0] = x1 out1[1] = x2 out1[2] = x3 @@ -1380,346 +5158,280 @@ func p521Sub(out1 *[9]uint64, arg1 *[9]uint64, arg2 *[9]uint64) { out1[8] = x9 } -// p521ToBytes serializes a field element to bytes in little-endian order. +// p521ToBytes serializes a field element NOT in the Montgomery domain to bytes in little-endian order. // +// Preconditions: +// 0 ≤ eval arg1 < m // Postconditions: // out1 = map (λ x, ⌊((eval arg1 mod m) mod 2^(8 * (x + 1))) / 2^(8 * x)⌋) [0..65] // // Input Bounds: -// arg1: [[0x0 ~> 0x400000000000000], [0x0 ~> 0x400000000000000], [0x0 ~> 0x400000000000000], [0x0 ~> 0x400000000000000], [0x0 ~> 0x400000000000000], [0x0 ~> 0x400000000000000], [0x0 ~> 0x400000000000000], [0x0 ~> 0x400000000000000], [0x0 ~> 0x200000000000000]] +// arg1: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0x1ff]] // Output Bounds: // out1: [[0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0x1]] func p521ToBytes(out1 *[66]uint8, arg1 *[9]uint64) { - var x1 uint64 - var x2 p521Uint1 - p521SubborrowxU58(&x1, &x2, 0x0, arg1[0], 0x3ffffffffffffff) - var x3 uint64 - var x4 p521Uint1 - p521SubborrowxU58(&x3, &x4, x2, arg1[1], 0x3ffffffffffffff) - var x5 uint64 - var x6 p521Uint1 - p521SubborrowxU58(&x5, &x6, x4, arg1[2], 0x3ffffffffffffff) - var x7 uint64 - var x8 p521Uint1 - p521SubborrowxU58(&x7, &x8, x6, arg1[3], 0x3ffffffffffffff) - var x9 uint64 - var x10 p521Uint1 - p521SubborrowxU58(&x9, &x10, x8, arg1[4], 0x3ffffffffffffff) - var x11 uint64 - var x12 p521Uint1 - p521SubborrowxU58(&x11, &x12, x10, arg1[5], 0x3ffffffffffffff) - var x13 uint64 - var x14 p521Uint1 - p521SubborrowxU58(&x13, &x14, x12, arg1[6], 0x3ffffffffffffff) - var x15 uint64 - var x16 p521Uint1 - p521SubborrowxU58(&x15, &x16, x14, arg1[7], 0x3ffffffffffffff) - var x17 uint64 - var x18 p521Uint1 - p521SubborrowxU57(&x17, &x18, x16, arg1[8], 0x1ffffffffffffff) - var x19 uint64 - p521CmovznzU64(&x19, x18, uint64(0x0), 0xffffffffffffffff) - var x20 uint64 - var x21 p521Uint1 - p521AddcarryxU58(&x20, &x21, 0x0, x1, (x19 & 0x3ffffffffffffff)) - var x22 uint64 - var x23 p521Uint1 - p521AddcarryxU58(&x22, &x23, x21, x3, (x19 & 0x3ffffffffffffff)) - var x24 uint64 - var x25 p521Uint1 - p521AddcarryxU58(&x24, &x25, x23, x5, (x19 & 0x3ffffffffffffff)) - var x26 uint64 - var x27 p521Uint1 - p521AddcarryxU58(&x26, &x27, x25, x7, (x19 & 0x3ffffffffffffff)) - var x28 uint64 - var x29 p521Uint1 - p521AddcarryxU58(&x28, &x29, x27, x9, (x19 & 0x3ffffffffffffff)) - var x30 uint64 - var x31 p521Uint1 - p521AddcarryxU58(&x30, &x31, x29, x11, (x19 & 0x3ffffffffffffff)) - var x32 uint64 - var x33 p521Uint1 - p521AddcarryxU58(&x32, &x33, x31, x13, (x19 & 0x3ffffffffffffff)) - var x34 uint64 - var x35 p521Uint1 - p521AddcarryxU58(&x34, &x35, x33, x15, (x19 & 0x3ffffffffffffff)) - var x36 uint64 - var x37 p521Uint1 - p521AddcarryxU57(&x36, &x37, x35, x17, (x19 & 0x1ffffffffffffff)) - x38 := (x34 << 6) - x39 := (x32 << 4) - x40 := (x30 << 2) - x41 := (x26 << 6) - x42 := (x24 << 4) - x43 := (x22 << 2) - x44 := (uint8(x20) & 0xff) - x45 := (x20 >> 8) + x1 := arg1[8] + x2 := arg1[7] + x3 := arg1[6] + x4 := arg1[5] + x5 := arg1[4] + x6 := arg1[3] + x7 := arg1[2] + x8 := arg1[1] + x9 := arg1[0] + x10 := (uint8(x9) & 0xff) + x11 := (x9 >> 8) + x12 := (uint8(x11) & 0xff) + x13 := (x11 >> 8) + x14 := (uint8(x13) & 0xff) + x15 := (x13 >> 8) + x16 := (uint8(x15) & 0xff) + x17 := (x15 >> 8) + x18 := (uint8(x17) & 0xff) + x19 := (x17 >> 8) + x20 := (uint8(x19) & 0xff) + x21 := (x19 >> 8) + x22 := (uint8(x21) & 0xff) + x23 := uint8((x21 >> 8)) + x24 := (uint8(x8) & 0xff) + x25 := (x8 >> 8) + x26 := (uint8(x25) & 0xff) + x27 := (x25 >> 8) + x28 := (uint8(x27) & 0xff) + x29 := (x27 >> 8) + x30 := (uint8(x29) & 0xff) + x31 := (x29 >> 8) + x32 := (uint8(x31) & 0xff) + x33 := (x31 >> 8) + x34 := (uint8(x33) & 0xff) + x35 := (x33 >> 8) + x36 := (uint8(x35) & 0xff) + x37 := uint8((x35 >> 8)) + x38 := (uint8(x7) & 0xff) + x39 := (x7 >> 8) + x40 := (uint8(x39) & 0xff) + x41 := (x39 >> 8) + x42 := (uint8(x41) & 0xff) + x43 := (x41 >> 8) + x44 := (uint8(x43) & 0xff) + x45 := (x43 >> 8) x46 := (uint8(x45) & 0xff) x47 := (x45 >> 8) x48 := (uint8(x47) & 0xff) x49 := (x47 >> 8) x50 := (uint8(x49) & 0xff) - x51 := (x49 >> 8) - x52 := (uint8(x51) & 0xff) - x53 := (x51 >> 8) + x51 := uint8((x49 >> 8)) + x52 := (uint8(x6) & 0xff) + x53 := (x6 >> 8) x54 := (uint8(x53) & 0xff) x55 := (x53 >> 8) x56 := (uint8(x55) & 0xff) - x57 := uint8((x55 >> 8)) - x58 := (x43 + uint64(x57)) - x59 := (uint8(x58) & 0xff) - x60 := (x58 >> 8) - x61 := (uint8(x60) & 0xff) - x62 := (x60 >> 8) - x63 := (uint8(x62) & 0xff) - x64 := (x62 >> 8) - x65 := (uint8(x64) & 0xff) - x66 := (x64 >> 8) - x67 := (uint8(x66) & 0xff) - x68 := (x66 >> 8) - x69 := (uint8(x68) & 0xff) - x70 := (x68 >> 8) - x71 := (uint8(x70) & 0xff) - x72 := uint8((x70 >> 8)) - x73 := (x42 + uint64(x72)) + x57 := (x55 >> 8) + x58 := (uint8(x57) & 0xff) + x59 := (x57 >> 8) + x60 := (uint8(x59) & 0xff) + x61 := (x59 >> 8) + x62 := (uint8(x61) & 0xff) + x63 := (x61 >> 8) + x64 := (uint8(x63) & 0xff) + x65 := uint8((x63 >> 8)) + x66 := (uint8(x5) & 0xff) + x67 := (x5 >> 8) + x68 := (uint8(x67) & 0xff) + x69 := (x67 >> 8) + x70 := (uint8(x69) & 0xff) + x71 := (x69 >> 8) + x72 := (uint8(x71) & 0xff) + x73 := (x71 >> 8) x74 := (uint8(x73) & 0xff) x75 := (x73 >> 8) x76 := (uint8(x75) & 0xff) x77 := (x75 >> 8) x78 := (uint8(x77) & 0xff) - x79 := (x77 >> 8) - x80 := (uint8(x79) & 0xff) - x81 := (x79 >> 8) + x79 := uint8((x77 >> 8)) + x80 := (uint8(x4) & 0xff) + x81 := (x4 >> 8) x82 := (uint8(x81) & 0xff) x83 := (x81 >> 8) x84 := (uint8(x83) & 0xff) x85 := (x83 >> 8) x86 := (uint8(x85) & 0xff) - x87 := uint8((x85 >> 8)) - x88 := (x41 + uint64(x87)) - x89 := (uint8(x88) & 0xff) - x90 := (x88 >> 8) - x91 := (uint8(x90) & 0xff) - x92 := (x90 >> 8) - x93 := (uint8(x92) & 0xff) - x94 := (x92 >> 8) - x95 := (uint8(x94) & 0xff) - x96 := (x94 >> 8) - x97 := (uint8(x96) & 0xff) - x98 := (x96 >> 8) - x99 := (uint8(x98) & 0xff) - x100 := (x98 >> 8) - x101 := (uint8(x100) & 0xff) - x102 := uint8((x100 >> 8)) - x103 := (uint8(x28) & 0xff) - x104 := (x28 >> 8) - x105 := (uint8(x104) & 0xff) - x106 := (x104 >> 8) - x107 := (uint8(x106) & 0xff) - x108 := (x106 >> 8) - x109 := (uint8(x108) & 0xff) - x110 := (x108 >> 8) - x111 := (uint8(x110) & 0xff) - x112 := (x110 >> 8) - x113 := (uint8(x112) & 0xff) - x114 := (x112 >> 8) - x115 := (uint8(x114) & 0xff) - x116 := uint8((x114 >> 8)) - x117 := (x40 + uint64(x116)) + x87 := (x85 >> 8) + x88 := (uint8(x87) & 0xff) + x89 := (x87 >> 8) + x90 := (uint8(x89) & 0xff) + x91 := (x89 >> 8) + x92 := (uint8(x91) & 0xff) + x93 := uint8((x91 >> 8)) + x94 := (uint8(x3) & 0xff) + x95 := (x3 >> 8) + x96 := (uint8(x95) & 0xff) + x97 := (x95 >> 8) + x98 := (uint8(x97) & 0xff) + x99 := (x97 >> 8) + x100 := (uint8(x99) & 0xff) + x101 := (x99 >> 8) + x102 := (uint8(x101) & 0xff) + x103 := (x101 >> 8) + x104 := (uint8(x103) & 0xff) + x105 := (x103 >> 8) + x106 := (uint8(x105) & 0xff) + x107 := uint8((x105 >> 8)) + x108 := (uint8(x2) & 0xff) + x109 := (x2 >> 8) + x110 := (uint8(x109) & 0xff) + x111 := (x109 >> 8) + x112 := (uint8(x111) & 0xff) + x113 := (x111 >> 8) + x114 := (uint8(x113) & 0xff) + x115 := (x113 >> 8) + x116 := (uint8(x115) & 0xff) + x117 := (x115 >> 8) x118 := (uint8(x117) & 0xff) x119 := (x117 >> 8) x120 := (uint8(x119) & 0xff) - x121 := (x119 >> 8) - x122 := (uint8(x121) & 0xff) - x123 := (x121 >> 8) - x124 := (uint8(x123) & 0xff) - x125 := (x123 >> 8) - x126 := (uint8(x125) & 0xff) - x127 := (x125 >> 8) - x128 := (uint8(x127) & 0xff) - x129 := (x127 >> 8) - x130 := (uint8(x129) & 0xff) - x131 := uint8((x129 >> 8)) - x132 := (x39 + uint64(x131)) - x133 := (uint8(x132) & 0xff) - x134 := (x132 >> 8) - x135 := (uint8(x134) & 0xff) - x136 := (x134 >> 8) - x137 := (uint8(x136) & 0xff) - x138 := (x136 >> 8) - x139 := (uint8(x138) & 0xff) - x140 := (x138 >> 8) - x141 := (uint8(x140) & 0xff) - x142 := (x140 >> 8) - x143 := (uint8(x142) & 0xff) - x144 := (x142 >> 8) - x145 := (uint8(x144) & 0xff) - x146 := uint8((x144 >> 8)) - x147 := (x38 + uint64(x146)) - x148 := (uint8(x147) & 0xff) - x149 := (x147 >> 8) - x150 := (uint8(x149) & 0xff) - x151 := (x149 >> 8) - x152 := (uint8(x151) & 0xff) - x153 := (x151 >> 8) - x154 := (uint8(x153) & 0xff) - x155 := (x153 >> 8) - x156 := (uint8(x155) & 0xff) - x157 := (x155 >> 8) - x158 := (uint8(x157) & 0xff) - x159 := (x157 >> 8) - x160 := (uint8(x159) & 0xff) - x161 := uint8((x159 >> 8)) - x162 := (uint8(x36) & 0xff) - x163 := (x36 >> 8) - x164 := (uint8(x163) & 0xff) - x165 := (x163 >> 8) - x166 := (uint8(x165) & 0xff) - x167 := (x165 >> 8) - x168 := (uint8(x167) & 0xff) - x169 := (x167 >> 8) - x170 := (uint8(x169) & 0xff) - x171 := (x169 >> 8) - x172 := (uint8(x171) & 0xff) - x173 := (x171 >> 8) - x174 := (uint8(x173) & 0xff) - x175 := p521Uint1((x173 >> 8)) - out1[0] = x44 - out1[1] = x46 - out1[2] = x48 - out1[3] = x50 - out1[4] = x52 - out1[5] = x54 - out1[6] = x56 - out1[7] = x59 - out1[8] = x61 - out1[9] = x63 - out1[10] = x65 - out1[11] = x67 - out1[12] = x69 - out1[13] = x71 - out1[14] = x74 - out1[15] = x76 - out1[16] = x78 - out1[17] = x80 - out1[18] = x82 - out1[19] = x84 - out1[20] = x86 - out1[21] = x89 - out1[22] = x91 - out1[23] = x93 - out1[24] = x95 - out1[25] = x97 - out1[26] = x99 - out1[27] = x101 - out1[28] = x102 - out1[29] = x103 - out1[30] = x105 - out1[31] = x107 - out1[32] = x109 - out1[33] = x111 - out1[34] = x113 - out1[35] = x115 - out1[36] = x118 - out1[37] = x120 - out1[38] = x122 - out1[39] = x124 - out1[40] = x126 - out1[41] = x128 - out1[42] = x130 - out1[43] = x133 - out1[44] = x135 - out1[45] = x137 - out1[46] = x139 - out1[47] = x141 - out1[48] = x143 - out1[49] = x145 - out1[50] = x148 - out1[51] = x150 - out1[52] = x152 - out1[53] = x154 - out1[54] = x156 - out1[55] = x158 - out1[56] = x160 - out1[57] = x161 - out1[58] = x162 - out1[59] = x164 - out1[60] = x166 - out1[61] = x168 - out1[62] = x170 - out1[63] = x172 - out1[64] = x174 - out1[65] = uint8(x175) + x121 := uint8((x119 >> 8)) + x122 := (uint8(x1) & 0xff) + x123 := p521Uint1((x1 >> 8)) + out1[0] = x10 + out1[1] = x12 + out1[2] = x14 + out1[3] = x16 + out1[4] = x18 + out1[5] = x20 + out1[6] = x22 + out1[7] = x23 + out1[8] = x24 + out1[9] = x26 + out1[10] = x28 + out1[11] = x30 + out1[12] = x32 + out1[13] = x34 + out1[14] = x36 + out1[15] = x37 + out1[16] = x38 + out1[17] = x40 + out1[18] = x42 + out1[19] = x44 + out1[20] = x46 + out1[21] = x48 + out1[22] = x50 + out1[23] = x51 + out1[24] = x52 + out1[25] = x54 + out1[26] = x56 + out1[27] = x58 + out1[28] = x60 + out1[29] = x62 + out1[30] = x64 + out1[31] = x65 + out1[32] = x66 + out1[33] = x68 + out1[34] = x70 + out1[35] = x72 + out1[36] = x74 + out1[37] = x76 + out1[38] = x78 + out1[39] = x79 + out1[40] = x80 + out1[41] = x82 + out1[42] = x84 + out1[43] = x86 + out1[44] = x88 + out1[45] = x90 + out1[46] = x92 + out1[47] = x93 + out1[48] = x94 + out1[49] = x96 + out1[50] = x98 + out1[51] = x100 + out1[52] = x102 + out1[53] = x104 + out1[54] = x106 + out1[55] = x107 + out1[56] = x108 + out1[57] = x110 + out1[58] = x112 + out1[59] = x114 + out1[60] = x116 + out1[61] = x118 + out1[62] = x120 + out1[63] = x121 + out1[64] = x122 + out1[65] = uint8(x123) } -// p521FromBytes deserializes a field element from bytes in little-endian order. +// p521FromBytes deserializes a field element NOT in the Montgomery domain from bytes in little-endian order. // +// Preconditions: +// 0 ≤ bytes_eval arg1 < m // Postconditions: // eval out1 mod m = bytes_eval arg1 mod m +// 0 ≤ eval out1 < m // // Input Bounds: // arg1: [[0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0x1]] // Output Bounds: -// out1: [[0x0 ~> 0x400000000000000], [0x0 ~> 0x400000000000000], [0x0 ~> 0x400000000000000], [0x0 ~> 0x400000000000000], [0x0 ~> 0x400000000000000], [0x0 ~> 0x400000000000000], [0x0 ~> 0x400000000000000], [0x0 ~> 0x400000000000000], [0x0 ~> 0x200000000000000]] +// out1: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0x1ff]] func p521FromBytes(out1 *[9]uint64, arg1 *[66]uint8) { - x1 := (uint64(p521Uint1(arg1[65])) << 56) - x2 := (uint64(arg1[64]) << 48) - x3 := (uint64(arg1[63]) << 40) - x4 := (uint64(arg1[62]) << 32) - x5 := (uint64(arg1[61]) << 24) - x6 := (uint64(arg1[60]) << 16) - x7 := (uint64(arg1[59]) << 8) - x8 := arg1[58] - x9 := (uint64(arg1[57]) << 50) - x10 := (uint64(arg1[56]) << 42) - x11 := (uint64(arg1[55]) << 34) - x12 := (uint64(arg1[54]) << 26) - x13 := (uint64(arg1[53]) << 18) - x14 := (uint64(arg1[52]) << 10) - x15 := (uint64(arg1[51]) << 2) - x16 := (uint64(arg1[50]) << 52) - x17 := (uint64(arg1[49]) << 44) - x18 := (uint64(arg1[48]) << 36) - x19 := (uint64(arg1[47]) << 28) - x20 := (uint64(arg1[46]) << 20) - x21 := (uint64(arg1[45]) << 12) - x22 := (uint64(arg1[44]) << 4) - x23 := (uint64(arg1[43]) << 54) - x24 := (uint64(arg1[42]) << 46) - x25 := (uint64(arg1[41]) << 38) - x26 := (uint64(arg1[40]) << 30) - x27 := (uint64(arg1[39]) << 22) - x28 := (uint64(arg1[38]) << 14) - x29 := (uint64(arg1[37]) << 6) - x30 := (uint64(arg1[36]) << 56) - x31 := (uint64(arg1[35]) << 48) - x32 := (uint64(arg1[34]) << 40) - x33 := (uint64(arg1[33]) << 32) - x34 := (uint64(arg1[32]) << 24) - x35 := (uint64(arg1[31]) << 16) - x36 := (uint64(arg1[30]) << 8) - x37 := arg1[29] - x38 := (uint64(arg1[28]) << 50) - x39 := (uint64(arg1[27]) << 42) - x40 := (uint64(arg1[26]) << 34) - x41 := (uint64(arg1[25]) << 26) - x42 := (uint64(arg1[24]) << 18) - x43 := (uint64(arg1[23]) << 10) - x44 := (uint64(arg1[22]) << 2) - x45 := (uint64(arg1[21]) << 52) - x46 := (uint64(arg1[20]) << 44) - x47 := (uint64(arg1[19]) << 36) - x48 := (uint64(arg1[18]) << 28) - x49 := (uint64(arg1[17]) << 20) - x50 := (uint64(arg1[16]) << 12) - x51 := (uint64(arg1[15]) << 4) - x52 := (uint64(arg1[14]) << 54) - x53 := (uint64(arg1[13]) << 46) - x54 := (uint64(arg1[12]) << 38) - x55 := (uint64(arg1[11]) << 30) - x56 := (uint64(arg1[10]) << 22) - x57 := (uint64(arg1[9]) << 14) - x58 := (uint64(arg1[8]) << 6) + x1 := (uint64(p521Uint1(arg1[65])) << 8) + x2 := arg1[64] + x3 := (uint64(arg1[63]) << 56) + x4 := (uint64(arg1[62]) << 48) + x5 := (uint64(arg1[61]) << 40) + x6 := (uint64(arg1[60]) << 32) + x7 := (uint64(arg1[59]) << 24) + x8 := (uint64(arg1[58]) << 16) + x9 := (uint64(arg1[57]) << 8) + x10 := arg1[56] + x11 := (uint64(arg1[55]) << 56) + x12 := (uint64(arg1[54]) << 48) + x13 := (uint64(arg1[53]) << 40) + x14 := (uint64(arg1[52]) << 32) + x15 := (uint64(arg1[51]) << 24) + x16 := (uint64(arg1[50]) << 16) + x17 := (uint64(arg1[49]) << 8) + x18 := arg1[48] + x19 := (uint64(arg1[47]) << 56) + x20 := (uint64(arg1[46]) << 48) + x21 := (uint64(arg1[45]) << 40) + x22 := (uint64(arg1[44]) << 32) + x23 := (uint64(arg1[43]) << 24) + x24 := (uint64(arg1[42]) << 16) + x25 := (uint64(arg1[41]) << 8) + x26 := arg1[40] + x27 := (uint64(arg1[39]) << 56) + x28 := (uint64(arg1[38]) << 48) + x29 := (uint64(arg1[37]) << 40) + x30 := (uint64(arg1[36]) << 32) + x31 := (uint64(arg1[35]) << 24) + x32 := (uint64(arg1[34]) << 16) + x33 := (uint64(arg1[33]) << 8) + x34 := arg1[32] + x35 := (uint64(arg1[31]) << 56) + x36 := (uint64(arg1[30]) << 48) + x37 := (uint64(arg1[29]) << 40) + x38 := (uint64(arg1[28]) << 32) + x39 := (uint64(arg1[27]) << 24) + x40 := (uint64(arg1[26]) << 16) + x41 := (uint64(arg1[25]) << 8) + x42 := arg1[24] + x43 := (uint64(arg1[23]) << 56) + x44 := (uint64(arg1[22]) << 48) + x45 := (uint64(arg1[21]) << 40) + x46 := (uint64(arg1[20]) << 32) + x47 := (uint64(arg1[19]) << 24) + x48 := (uint64(arg1[18]) << 16) + x49 := (uint64(arg1[17]) << 8) + x50 := arg1[16] + x51 := (uint64(arg1[15]) << 56) + x52 := (uint64(arg1[14]) << 48) + x53 := (uint64(arg1[13]) << 40) + x54 := (uint64(arg1[12]) << 32) + x55 := (uint64(arg1[11]) << 24) + x56 := (uint64(arg1[10]) << 16) + x57 := (uint64(arg1[9]) << 8) + x58 := arg1[8] x59 := (uint64(arg1[7]) << 56) x60 := (uint64(arg1[6]) << 48) x61 := (uint64(arg1[5]) << 40) @@ -1735,122 +5447,63 @@ func p521FromBytes(out1 *[9]uint64, arg1 *[66]uint8) { x71 := (x61 + x70) x72 := (x60 + x71) x73 := (x59 + x72) - x74 := (x73 & 0x3ffffffffffffff) - x75 := uint8((x73 >> 58)) - x76 := (x58 + uint64(x75)) - x77 := (x57 + x76) - x78 := (x56 + x77) - x79 := (x55 + x78) - x80 := (x54 + x79) - x81 := (x53 + x80) - x82 := (x52 + x81) - x83 := (x82 & 0x3ffffffffffffff) - x84 := uint8((x82 >> 58)) - x85 := (x51 + uint64(x84)) - x86 := (x50 + x85) - x87 := (x49 + x86) - x88 := (x48 + x87) - x89 := (x47 + x88) - x90 := (x46 + x89) - x91 := (x45 + x90) - x92 := (x91 & 0x3ffffffffffffff) - x93 := uint8((x91 >> 58)) - x94 := (x44 + uint64(x93)) - x95 := (x43 + x94) - x96 := (x42 + x95) - x97 := (x41 + x96) - x98 := (x40 + x97) - x99 := (x39 + x98) - x100 := (x38 + x99) - x101 := (x36 + uint64(x37)) - x102 := (x35 + x101) - x103 := (x34 + x102) - x104 := (x33 + x103) - x105 := (x32 + x104) - x106 := (x31 + x105) - x107 := (x30 + x106) - x108 := (x107 & 0x3ffffffffffffff) - x109 := uint8((x107 >> 58)) - x110 := (x29 + uint64(x109)) - x111 := (x28 + x110) - x112 := (x27 + x111) - x113 := (x26 + x112) - x114 := (x25 + x113) - x115 := (x24 + x114) - x116 := (x23 + x115) - x117 := (x116 & 0x3ffffffffffffff) - x118 := uint8((x116 >> 58)) - x119 := (x22 + uint64(x118)) - x120 := (x21 + x119) - x121 := (x20 + x120) - x122 := (x19 + x121) - x123 := (x18 + x122) - x124 := (x17 + x123) - x125 := (x16 + x124) - x126 := (x125 & 0x3ffffffffffffff) - x127 := uint8((x125 >> 58)) - x128 := (x15 + uint64(x127)) - x129 := (x14 + x128) - x130 := (x13 + x129) - x131 := (x12 + x130) - x132 := (x11 + x131) - x133 := (x10 + x132) - x134 := (x9 + x133) - x135 := (x7 + uint64(x8)) - x136 := (x6 + x135) - x137 := (x5 + x136) - x138 := (x4 + x137) - x139 := (x3 + x138) - x140 := (x2 + x139) - x141 := (x1 + x140) - out1[0] = x74 - out1[1] = x83 - out1[2] = x92 - out1[3] = x100 - out1[4] = x108 - out1[5] = x117 - out1[6] = x126 - out1[7] = x134 - out1[8] = x141 -} - -// p521Selectznz is a multi-limb conditional select. -// -// Postconditions: -// eval out1 = (if arg1 = 0 then eval arg2 else eval arg3) -// -// Input Bounds: -// arg1: [0x0 ~> 0x1] -// arg2: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]] -// arg3: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]] -// Output Bounds: -// out1: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]] -func p521Selectznz(out1 *[9]uint64, arg1 p521Uint1, arg2 *[9]uint64, arg3 *[9]uint64) { - var x1 uint64 - p521CmovznzU64(&x1, arg1, arg2[0], arg3[0]) - var x2 uint64 - p521CmovznzU64(&x2, arg1, arg2[1], arg3[1]) - var x3 uint64 - p521CmovznzU64(&x3, arg1, arg2[2], arg3[2]) - var x4 uint64 - p521CmovznzU64(&x4, arg1, arg2[3], arg3[3]) - var x5 uint64 - p521CmovznzU64(&x5, arg1, arg2[4], arg3[4]) - var x6 uint64 - p521CmovznzU64(&x6, arg1, arg2[5], arg3[5]) - var x7 uint64 - p521CmovznzU64(&x7, arg1, arg2[6], arg3[6]) - var x8 uint64 - p521CmovznzU64(&x8, arg1, arg2[7], arg3[7]) - var x9 uint64 - p521CmovznzU64(&x9, arg1, arg2[8], arg3[8]) - out1[0] = x1 - out1[1] = x2 - out1[2] = x3 - out1[3] = x4 - out1[4] = x5 - out1[5] = x6 - out1[6] = x7 - out1[7] = x8 - out1[8] = x9 + x74 := (x57 + uint64(x58)) + x75 := (x56 + x74) + x76 := (x55 + x75) + x77 := (x54 + x76) + x78 := (x53 + x77) + x79 := (x52 + x78) + x80 := (x51 + x79) + x81 := (x49 + uint64(x50)) + x82 := (x48 + x81) + x83 := (x47 + x82) + x84 := (x46 + x83) + x85 := (x45 + x84) + x86 := (x44 + x85) + x87 := (x43 + x86) + x88 := (x41 + uint64(x42)) + x89 := (x40 + x88) + x90 := (x39 + x89) + x91 := (x38 + x90) + x92 := (x37 + x91) + x93 := (x36 + x92) + x94 := (x35 + x93) + x95 := (x33 + uint64(x34)) + x96 := (x32 + x95) + x97 := (x31 + x96) + x98 := (x30 + x97) + x99 := (x29 + x98) + x100 := (x28 + x99) + x101 := (x27 + x100) + x102 := (x25 + uint64(x26)) + x103 := (x24 + x102) + x104 := (x23 + x103) + x105 := (x22 + x104) + x106 := (x21 + x105) + x107 := (x20 + x106) + x108 := (x19 + x107) + x109 := (x17 + uint64(x18)) + x110 := (x16 + x109) + x111 := (x15 + x110) + x112 := (x14 + x111) + x113 := (x13 + x112) + x114 := (x12 + x113) + x115 := (x11 + x114) + x116 := (x9 + uint64(x10)) + x117 := (x8 + x116) + x118 := (x7 + x117) + x119 := (x6 + x118) + x120 := (x5 + x119) + x121 := (x4 + x120) + x122 := (x3 + x121) + x123 := (x1 + uint64(x2)) + out1[0] = x73 + out1[1] = x80 + out1[2] = x87 + out1[3] = x94 + out1[4] = x101 + out1[5] = x108 + out1[6] = x115 + out1[7] = x122 + out1[8] = x123 } diff --git a/libgo/go/crypto/elliptic/internal/fiat/p521_invert.go b/libgo/go/crypto/elliptic/internal/fiat/p521_invert.go new file mode 100644 index 0000000..407711a --- /dev/null +++ b/libgo/go/crypto/elliptic/internal/fiat/p521_invert.go @@ -0,0 +1,89 @@ +// Copyright 2021 The Go Authors. All rights reserved. +// Use of this source code is governed by a BSD-style +// license that can be found in the LICENSE file. + +// Code generated by addchain. DO NOT EDIT. + +package fiat + +// Invert sets e = 1/x, and returns e. +// +// If x == 0, Invert returns e = 0. +func (e *P521Element) Invert(x *P521Element) *P521Element { + // Inversion is implemented as exponentiation with exponent p − 2. + // The sequence of 13 multiplications and 520 squarings is derived from the + // following addition chain generated with github.com/mmcloughlin/addchain v0.3.0. + // + // _10 = 2*1 + // _11 = 1 + _10 + // _1100 = _11 << 2 + // _1111 = _11 + _1100 + // _11110000 = _1111 << 4 + // _11111111 = _1111 + _11110000 + // x16 = _11111111 << 8 + _11111111 + // x32 = x16 << 16 + x16 + // x64 = x32 << 32 + x32 + // x65 = 2*x64 + 1 + // x129 = x65 << 64 + x64 + // x130 = 2*x129 + 1 + // x259 = x130 << 129 + x129 + // x260 = 2*x259 + 1 + // x519 = x260 << 259 + x259 + // return x519 << 2 + 1 + // + + var z = new(P521Element).Set(e) + var t0 = new(P521Element) + + z.Square(x) + z.Mul(x, z) + t0.Square(z) + for s := 1; s < 2; s++ { + t0.Square(t0) + } + z.Mul(z, t0) + t0.Square(z) + for s := 1; s < 4; s++ { + t0.Square(t0) + } + z.Mul(z, t0) + t0.Square(z) + for s := 1; s < 8; s++ { + t0.Square(t0) + } + z.Mul(z, t0) + t0.Square(z) + for s := 1; s < 16; s++ { + t0.Square(t0) + } + z.Mul(z, t0) + t0.Square(z) + for s := 1; s < 32; s++ { + t0.Square(t0) + } + z.Mul(z, t0) + t0.Square(z) + t0.Mul(x, t0) + for s := 0; s < 64; s++ { + t0.Square(t0) + } + z.Mul(z, t0) + t0.Square(z) + t0.Mul(x, t0) + for s := 0; s < 129; s++ { + t0.Square(t0) + } + z.Mul(z, t0) + t0.Square(z) + t0.Mul(x, t0) + for s := 0; s < 259; s++ { + t0.Square(t0) + } + z.Mul(z, t0) + for s := 0; s < 2; s++ { + z.Square(z) + } + z.Mul(x, z) + + return e.Set(z) +} diff --git a/libgo/go/crypto/elliptic/internal/fiat/p521_test.go b/libgo/go/crypto/elliptic/internal/fiat/p521_test.go deleted file mode 100644 index 661bde3..0000000 --- a/libgo/go/crypto/elliptic/internal/fiat/p521_test.go +++ /dev/null @@ -1,37 +0,0 @@ -// Copyright 2021 The Go Authors. All rights reserved. -// Use of this source code is governed by a BSD-style -// license that can be found in the LICENSE file. - -package fiat_test - -import ( - "crypto/elliptic/internal/fiat" - "crypto/rand" - "testing" -) - -func p521Random(t *testing.T) *fiat.P521Element { - buf := make([]byte, 66) - if _, err := rand.Read(buf); err != nil { - t.Fatal(err) - } - buf[65] &= 1 - e, err := new(fiat.P521Element).SetBytes(buf) - if err != nil { - t.Fatal(err) - } - return e -} - -func TestP521Invert(t *testing.T) { - a := p521Random(t) - inv := new(fiat.P521Element).Invert(a) - one := new(fiat.P521Element).Mul(a, inv) - if new(fiat.P521Element).One().Equal(one) != 1 { - t.Errorf("a * 1/a != 1; got %x for %x", one.Bytes(), a.Bytes()) - } - inv.Invert(new(fiat.P521Element)) - if new(fiat.P521Element).Equal(inv) != 1 { - t.Errorf("1/0 != 0; got %x", inv.Bytes()) - } -} diff --git a/libgo/go/crypto/elliptic/internal/nistec/nistec_test.go b/libgo/go/crypto/elliptic/internal/nistec/nistec_test.go new file mode 100644 index 0000000..63a2e47 --- /dev/null +++ b/libgo/go/crypto/elliptic/internal/nistec/nistec_test.go @@ -0,0 +1,98 @@ +// Copyright 2021 The Go Authors. All rights reserved. +// Use of this source code is governed by a BSD-style +// license that can be found in the LICENSE file. + +package nistec_test + +import ( + "crypto/elliptic/internal/nistec" + "math/rand" + "os" + "runtime" + "strings" + "testing" +) + +func TestAllocations(t *testing.T) { + if runtime.Compiler == "gccgo" { + t.Skip("gofrontend escape analysis not good enough") + } + if strings.HasSuffix(os.Getenv("GO_BUILDER_NAME"), "-noopt") { + t.Skip("skipping allocations test without relevant optimizations") + } + t.Run("P224", func(t *testing.T) { + if allocs := testing.AllocsPerRun(100, func() { + p := nistec.NewP224Generator() + scalar := make([]byte, 66) + rand.Read(scalar) + p.ScalarMult(p, scalar) + out := p.Bytes() + if _, err := p.SetBytes(out); err != nil { + t.Fatal(err) + } + }); allocs > 0 { + t.Errorf("expected zero allocations, got %0.1f", allocs) + } + }) + t.Run("P384", func(t *testing.T) { + if allocs := testing.AllocsPerRun(100, func() { + p := nistec.NewP384Generator() + scalar := make([]byte, 66) + rand.Read(scalar) + p.ScalarMult(p, scalar) + out := p.Bytes() + if _, err := p.SetBytes(out); err != nil { + t.Fatal(err) + } + }); allocs > 0 { + t.Errorf("expected zero allocations, got %0.1f", allocs) + } + }) + t.Run("P521", func(t *testing.T) { + if allocs := testing.AllocsPerRun(100, func() { + p := nistec.NewP521Generator() + scalar := make([]byte, 66) + rand.Read(scalar) + p.ScalarMult(p, scalar) + out := p.Bytes() + if _, err := p.SetBytes(out); err != nil { + t.Fatal(err) + } + }); allocs > 0 { + t.Errorf("expected zero allocations, got %0.1f", allocs) + } + }) +} + +func BenchmarkScalarMult(b *testing.B) { + b.Run("P224", func(b *testing.B) { + scalar := make([]byte, 66) + rand.Read(scalar) + p := nistec.NewP224Generator() + b.ReportAllocs() + b.ResetTimer() + for i := 0; i < b.N; i++ { + p.ScalarMult(p, scalar) + } + }) + b.Run("P384", func(b *testing.B) { + scalar := make([]byte, 66) + rand.Read(scalar) + p := nistec.NewP384Generator() + b.ReportAllocs() + b.ResetTimer() + for i := 0; i < b.N; i++ { + p.ScalarMult(p, scalar) + } + }) + b.Run("P521", func(b *testing.B) { + scalar := make([]byte, 66) + rand.Read(scalar) + p := nistec.NewP521Generator() + b.ReportAllocs() + b.ResetTimer() + for i := 0; i < b.N; i++ { + p.ScalarMult(p, scalar) + } + }) +} diff --git a/libgo/go/crypto/elliptic/internal/nistec/p224.go b/libgo/go/crypto/elliptic/internal/nistec/p224.go new file mode 100644 index 0000000..74dbc18 --- /dev/null +++ b/libgo/go/crypto/elliptic/internal/nistec/p224.go @@ -0,0 +1,293 @@ +// Copyright 2021 The Go Authors. All rights reserved. +// Use of this source code is governed by a BSD-style +// license that can be found in the LICENSE file. + +package nistec + +import ( + "crypto/elliptic/internal/fiat" + "crypto/subtle" + "errors" +) + +var p224B, _ = new(fiat.P224Element).SetBytes([]byte{0xb4, 0x05, 0x0a, 0x85, + 0x0c, 0x04, 0xb3, 0xab, 0xf5, 0x41, 0x32, 0x56, 0x50, 0x44, 0xb0, 0xb7, + 0xd7, 0xbf, 0xd8, 0xba, 0x27, 0x0b, 0x39, 0x43, 0x23, 0x55, 0xff, 0xb4}) + +var p224G, _ = NewP224Point().SetBytes([]byte{0x04, + 0xb7, 0x0e, 0x0c, 0xbd, 0x6b, 0xb4, 0xbf, 0x7f, 0x32, 0x13, 0x90, 0xb9, + 0x4a, 0x03, 0xc1, 0xd3, 0x56, 0xc2, 0x11, 0x22, 0x34, 0x32, 0x80, 0xd6, + 0x11, 0x5c, 0x1d, 0x21, 0xbd, 0x37, 0x63, 0x88, 0xb5, 0xf7, 0x23, 0xfb, + 0x4c, 0x22, 0xdf, 0xe6, 0xcd, 0x43, 0x75, 0xa0, 0x5a, 0x07, 0x47, 0x64, + 0x44, 0xd5, 0x81, 0x99, 0x85, 0x0, 0x7e, 0x34}) + +const p224ElementLength = 28 + +// P224Point is a P-224 point. The zero value is NOT valid. +type P224Point struct { + // The point is represented in projective coordinates (X:Y:Z), + // where x = X/Z and y = Y/Z. + x, y, z *fiat.P224Element +} + +// NewP224Point returns a new P224Point representing the point at infinity point. +func NewP224Point() *P224Point { + return &P224Point{ + x: new(fiat.P224Element), + y: new(fiat.P224Element).One(), + z: new(fiat.P224Element), + } +} + +// NewP224Generator returns a new P224Point set to the canonical generator. +func NewP224Generator() *P224Point { + return (&P224Point{ + x: new(fiat.P224Element), + y: new(fiat.P224Element), + z: new(fiat.P224Element), + }).Set(p224G) +} + +// Set sets p = q and returns p. +func (p *P224Point) Set(q *P224Point) *P224Point { + p.x.Set(q.x) + p.y.Set(q.y) + p.z.Set(q.z) + return p +} + +// SetBytes sets p to the compressed, uncompressed, or infinity value encoded in +// b, as specified in SEC 1, Version 2.0, Section 2.3.4. If the point is not on +// the curve, it returns nil and an error, and the receiver is unchanged. +// Otherwise, it returns p. +func (p *P224Point) SetBytes(b []byte) (*P224Point, error) { + switch { + // Point at infinity. + case len(b) == 1 && b[0] == 0: + return p.Set(NewP224Point()), nil + + // Uncompressed form. + case len(b) == 1+2*p224ElementLength && b[0] == 4: + x, err := new(fiat.P224Element).SetBytes(b[1 : 1+p224ElementLength]) + if err != nil { + return nil, err + } + y, err := new(fiat.P224Element).SetBytes(b[1+p224ElementLength:]) + if err != nil { + return nil, err + } + if err := p224CheckOnCurve(x, y); err != nil { + return nil, err + } + p.x.Set(x) + p.y.Set(y) + p.z.One() + return p, nil + + // Compressed form + case len(b) == 1+p224ElementLength && b[0] == 0: + return nil, errors.New("unimplemented") // TODO(filippo) + + default: + return nil, errors.New("invalid P224 point encoding") + } +} + +func p224CheckOnCurve(x, y *fiat.P224Element) error { + // x³ - 3x + b. + x3 := new(fiat.P224Element).Square(x) + x3.Mul(x3, x) + + threeX := new(fiat.P224Element).Add(x, x) + threeX.Add(threeX, x) + + x3.Sub(x3, threeX) + x3.Add(x3, p224B) + + // y² = x³ - 3x + b + y2 := new(fiat.P224Element).Square(y) + + if x3.Equal(y2) != 1 { + return errors.New("P224 point not on curve") + } + return nil +} + +// Bytes returns the uncompressed or infinity encoding of p, as specified in +// SEC 1, Version 2.0, Section 2.3.3. Note that the encoding of the point at +// infinity is shorter than all other encodings. +func (p *P224Point) Bytes() []byte { + // This function is outlined to make the allocations inline in the caller + // rather than happen on the heap. + var out [133]byte + return p.bytes(&out) +} + +func (p *P224Point) bytes(out *[133]byte) []byte { + if p.z.IsZero() == 1 { + return append(out[:0], 0) + } + + zinv := new(fiat.P224Element).Invert(p.z) + xx := new(fiat.P224Element).Mul(p.x, zinv) + yy := new(fiat.P224Element).Mul(p.y, zinv) + + buf := append(out[:0], 4) + buf = append(buf, xx.Bytes()...) + buf = append(buf, yy.Bytes()...) + return buf +} + +// Add sets q = p1 + p2, and returns q. The points may overlap. +func (q *P224Point) Add(p1, p2 *P224Point) *P224Point { + // Complete addition formula for a = -3 from "Complete addition formulas for + // prime order elliptic curves" (https://eprint.iacr.org/2015/1060), §A.2. + + t0 := new(fiat.P224Element).Mul(p1.x, p2.x) // t0 := X1 * X2 + t1 := new(fiat.P224Element).Mul(p1.y, p2.y) // t1 := Y1 * Y2 + t2 := new(fiat.P224Element).Mul(p1.z, p2.z) // t2 := Z1 * Z2 + t3 := new(fiat.P224Element).Add(p1.x, p1.y) // t3 := X1 + Y1 + t4 := new(fiat.P224Element).Add(p2.x, p2.y) // t4 := X2 + Y2 + t3.Mul(t3, t4) // t3 := t3 * t4 + t4.Add(t0, t1) // t4 := t0 + t1 + t3.Sub(t3, t4) // t3 := t3 - t4 + t4.Add(p1.y, p1.z) // t4 := Y1 + Z1 + x3 := new(fiat.P224Element).Add(p2.y, p2.z) // X3 := Y2 + Z2 + t4.Mul(t4, x3) // t4 := t4 * X3 + x3.Add(t1, t2) // X3 := t1 + t2 + t4.Sub(t4, x3) // t4 := t4 - X3 + x3.Add(p1.x, p1.z) // X3 := X1 + Z1 + y3 := new(fiat.P224Element).Add(p2.x, p2.z) // Y3 := X2 + Z2 + x3.Mul(x3, y3) // X3 := X3 * Y3 + y3.Add(t0, t2) // Y3 := t0 + t2 + y3.Sub(x3, y3) // Y3 := X3 - Y3 + z3 := new(fiat.P224Element).Mul(p224B, t2) // Z3 := b * t2 + x3.Sub(y3, z3) // X3 := Y3 - Z3 + z3.Add(x3, x3) // Z3 := X3 + X3 + x3.Add(x3, z3) // X3 := X3 + Z3 + z3.Sub(t1, x3) // Z3 := t1 - X3 + x3.Add(t1, x3) // X3 := t1 + X3 + y3.Mul(p224B, y3) // Y3 := b * Y3 + t1.Add(t2, t2) // t1 := t2 + t2 + t2.Add(t1, t2) // t2 := t1 + t2 + y3.Sub(y3, t2) // Y3 := Y3 - t2 + y3.Sub(y3, t0) // Y3 := Y3 - t0 + t1.Add(y3, y3) // t1 := Y3 + Y3 + y3.Add(t1, y3) // Y3 := t1 + Y3 + t1.Add(t0, t0) // t1 := t0 + t0 + t0.Add(t1, t0) // t0 := t1 + t0 + t0.Sub(t0, t2) // t0 := t0 - t2 + t1.Mul(t4, y3) // t1 := t4 * Y3 + t2.Mul(t0, y3) // t2 := t0 * Y3 + y3.Mul(x3, z3) // Y3 := X3 * Z3 + y3.Add(y3, t2) // Y3 := Y3 + t2 + x3.Mul(t3, x3) // X3 := t3 * X3 + x3.Sub(x3, t1) // X3 := X3 - t1 + z3.Mul(t4, z3) // Z3 := t4 * Z3 + t1.Mul(t3, t0) // t1 := t3 * t0 + z3.Add(z3, t1) // Z3 := Z3 + t1 + + q.x.Set(x3) + q.y.Set(y3) + q.z.Set(z3) + return q +} + +// Double sets q = p + p, and returns q. The points may overlap. +func (q *P224Point) Double(p *P224Point) *P224Point { + // Complete addition formula for a = -3 from "Complete addition formulas for + // prime order elliptic curves" (https://eprint.iacr.org/2015/1060), §A.2. + + t0 := new(fiat.P224Element).Square(p.x) // t0 := X ^ 2 + t1 := new(fiat.P224Element).Square(p.y) // t1 := Y ^ 2 + t2 := new(fiat.P224Element).Square(p.z) // t2 := Z ^ 2 + t3 := new(fiat.P224Element).Mul(p.x, p.y) // t3 := X * Y + t3.Add(t3, t3) // t3 := t3 + t3 + z3 := new(fiat.P224Element).Mul(p.x, p.z) // Z3 := X * Z + z3.Add(z3, z3) // Z3 := Z3 + Z3 + y3 := new(fiat.P224Element).Mul(p224B, t2) // Y3 := b * t2 + y3.Sub(y3, z3) // Y3 := Y3 - Z3 + x3 := new(fiat.P224Element).Add(y3, y3) // X3 := Y3 + Y3 + y3.Add(x3, y3) // Y3 := X3 + Y3 + x3.Sub(t1, y3) // X3 := t1 - Y3 + y3.Add(t1, y3) // Y3 := t1 + Y3 + y3.Mul(x3, y3) // Y3 := X3 * Y3 + x3.Mul(x3, t3) // X3 := X3 * t3 + t3.Add(t2, t2) // t3 := t2 + t2 + t2.Add(t2, t3) // t2 := t2 + t3 + z3.Mul(p224B, z3) // Z3 := b * Z3 + z3.Sub(z3, t2) // Z3 := Z3 - t2 + z3.Sub(z3, t0) // Z3 := Z3 - t0 + t3.Add(z3, z3) // t3 := Z3 + Z3 + z3.Add(z3, t3) // Z3 := Z3 + t3 + t3.Add(t0, t0) // t3 := t0 + t0 + t0.Add(t3, t0) // t0 := t3 + t0 + t0.Sub(t0, t2) // t0 := t0 - t2 + t0.Mul(t0, z3) // t0 := t0 * Z3 + y3.Add(y3, t0) // Y3 := Y3 + t0 + t0.Mul(p.y, p.z) // t0 := Y * Z + t0.Add(t0, t0) // t0 := t0 + t0 + z3.Mul(t0, z3) // Z3 := t0 * Z3 + x3.Sub(x3, z3) // X3 := X3 - Z3 + z3.Mul(t0, t1) // Z3 := t0 * t1 + z3.Add(z3, z3) // Z3 := Z3 + Z3 + z3.Add(z3, z3) // Z3 := Z3 + Z3 + + q.x.Set(x3) + q.y.Set(y3) + q.z.Set(z3) + return q +} + +// Select sets q to p1 if cond == 1, and to p2 if cond == 0. +func (q *P224Point) Select(p1, p2 *P224Point, cond int) *P224Point { + q.x.Select(p1.x, p2.x, cond) + q.y.Select(p1.y, p2.y, cond) + q.z.Select(p1.z, p2.z, cond) + return q +} + +// ScalarMult sets p = scalar * q, and returns p. +func (p *P224Point) ScalarMult(q *P224Point, scalar []byte) *P224Point { + // table holds the first 16 multiples of q. The explicit newP224Point calls + // get inlined, letting the allocations live on the stack. + var table = [16]*P224Point{ + NewP224Point(), NewP224Point(), NewP224Point(), NewP224Point(), + NewP224Point(), NewP224Point(), NewP224Point(), NewP224Point(), + NewP224Point(), NewP224Point(), NewP224Point(), NewP224Point(), + NewP224Point(), NewP224Point(), NewP224Point(), NewP224Point(), + } + for i := 1; i < 16; i++ { + table[i].Add(table[i-1], q) + } + + // Instead of doing the classic double-and-add chain, we do it with a + // four-bit window: we double four times, and then add [0-15]P. + t := NewP224Point() + p.Set(NewP224Point()) + for _, byte := range scalar { + p.Double(p) + p.Double(p) + p.Double(p) + p.Double(p) + + for i := uint8(0); i < 16; i++ { + cond := subtle.ConstantTimeByteEq(byte>>4, i) + t.Select(table[i], t, cond) + } + p.Add(p, t) + + p.Double(p) + p.Double(p) + p.Double(p) + p.Double(p) + + for i := uint8(0); i < 16; i++ { + cond := subtle.ConstantTimeByteEq(byte&0b1111, i) + t.Select(table[i], t, cond) + } + p.Add(p, t) + } + + return p +} diff --git a/libgo/go/crypto/elliptic/internal/nistec/p384.go b/libgo/go/crypto/elliptic/internal/nistec/p384.go new file mode 100644 index 0000000..24a166d --- /dev/null +++ b/libgo/go/crypto/elliptic/internal/nistec/p384.go @@ -0,0 +1,298 @@ +// Copyright 2021 The Go Authors. All rights reserved. +// Use of this source code is governed by a BSD-style +// license that can be found in the LICENSE file. + +package nistec + +import ( + "crypto/elliptic/internal/fiat" + "crypto/subtle" + "errors" +) + +var p384B, _ = new(fiat.P384Element).SetBytes([]byte{ + 0xb3, 0x31, 0x2f, 0xa7, 0xe2, 0x3e, 0xe7, 0xe4, 0x98, 0x8e, 0x05, 0x6b, + 0xe3, 0xf8, 0x2d, 0x19, 0x18, 0x1d, 0x9c, 0x6e, 0xfe, 0x81, 0x41, 0x12, + 0x03, 0x14, 0x08, 0x8f, 0x50, 0x13, 0x87, 0x5a, 0xc6, 0x56, 0x39, 0x8d, + 0x8a, 0x2e, 0xd1, 0x9d, 0x2a, 0x85, 0xc8, 0xed, 0xd3, 0xec, 0x2a, 0xef}) + +var p384G, _ = NewP384Point().SetBytes([]byte{0x4, + 0xaa, 0x87, 0xca, 0x22, 0xbe, 0x8b, 0x05, 0x37, 0x8e, 0xb1, 0xc7, 0x1e, + 0xf3, 0x20, 0xad, 0x74, 0x6e, 0x1d, 0x3b, 0x62, 0x8b, 0xa7, 0x9b, 0x98, + 0x59, 0xf7, 0x41, 0xe0, 0x82, 0x54, 0x2a, 0x38, 0x55, 0x02, 0xf2, 0x5d, + 0xbf, 0x55, 0x29, 0x6c, 0x3a, 0x54, 0x5e, 0x38, 0x72, 0x76, 0x0a, 0xb7, + 0x36, 0x17, 0xde, 0x4a, 0x96, 0x26, 0x2c, 0x6f, 0x5d, 0x9e, 0x98, 0xbf, + 0x92, 0x92, 0xdc, 0x29, 0xf8, 0xf4, 0x1d, 0xbd, 0x28, 0x9a, 0x14, 0x7c, + 0xe9, 0xda, 0x31, 0x13, 0xb5, 0xf0, 0xb8, 0xc0, 0x0a, 0x60, 0xb1, 0xce, + 0x1d, 0x7e, 0x81, 0x9d, 0x7a, 0x43, 0x1d, 0x7c, 0x90, 0xea, 0x0e, 0x5f}) + +const p384ElementLength = 48 + +// P384Point is a P-384 point. The zero value is NOT valid. +type P384Point struct { + // The point is represented in projective coordinates (X:Y:Z), + // where x = X/Z and y = Y/Z. + x, y, z *fiat.P384Element +} + +// NewP384Point returns a new P384Point representing the point at infinity point. +func NewP384Point() *P384Point { + return &P384Point{ + x: new(fiat.P384Element), + y: new(fiat.P384Element).One(), + z: new(fiat.P384Element), + } +} + +// NewP384Generator returns a new P384Point set to the canonical generator. +func NewP384Generator() *P384Point { + return (&P384Point{ + x: new(fiat.P384Element), + y: new(fiat.P384Element), + z: new(fiat.P384Element), + }).Set(p384G) +} + +// Set sets p = q and returns p. +func (p *P384Point) Set(q *P384Point) *P384Point { + p.x.Set(q.x) + p.y.Set(q.y) + p.z.Set(q.z) + return p +} + +// SetBytes sets p to the compressed, uncompressed, or infinity value encoded in +// b, as specified in SEC 1, Version 2.0, Section 2.3.4. If the point is not on +// the curve, it returns nil and an error, and the receiver is unchanged. +// Otherwise, it returns p. +func (p *P384Point) SetBytes(b []byte) (*P384Point, error) { + switch { + // Point at infinity. + case len(b) == 1 && b[0] == 0: + return p.Set(NewP384Point()), nil + + // Uncompressed form. + case len(b) == 1+2*p384ElementLength && b[0] == 4: + x, err := new(fiat.P384Element).SetBytes(b[1 : 1+p384ElementLength]) + if err != nil { + return nil, err + } + y, err := new(fiat.P384Element).SetBytes(b[1+p384ElementLength:]) + if err != nil { + return nil, err + } + if err := p384CheckOnCurve(x, y); err != nil { + return nil, err + } + p.x.Set(x) + p.y.Set(y) + p.z.One() + return p, nil + + // Compressed form + case len(b) == 1+p384ElementLength && b[0] == 0: + return nil, errors.New("unimplemented") // TODO(filippo) + + default: + return nil, errors.New("invalid P384 point encoding") + } +} + +func p384CheckOnCurve(x, y *fiat.P384Element) error { + // x³ - 3x + b. + x3 := new(fiat.P384Element).Square(x) + x3.Mul(x3, x) + + threeX := new(fiat.P384Element).Add(x, x) + threeX.Add(threeX, x) + + x3.Sub(x3, threeX) + x3.Add(x3, p384B) + + // y² = x³ - 3x + b + y2 := new(fiat.P384Element).Square(y) + + if x3.Equal(y2) != 1 { + return errors.New("P384 point not on curve") + } + return nil +} + +// Bytes returns the uncompressed or infinity encoding of p, as specified in +// SEC 1, Version 2.0, Section 2.3.3. Note that the encoding of the point at +// infinity is shorter than all other encodings. +func (p *P384Point) Bytes() []byte { + // This function is outlined to make the allocations inline in the caller + // rather than happen on the heap. + var out [133]byte + return p.bytes(&out) +} + +func (p *P384Point) bytes(out *[133]byte) []byte { + if p.z.IsZero() == 1 { + return append(out[:0], 0) + } + + zinv := new(fiat.P384Element).Invert(p.z) + xx := new(fiat.P384Element).Mul(p.x, zinv) + yy := new(fiat.P384Element).Mul(p.y, zinv) + + buf := append(out[:0], 4) + buf = append(buf, xx.Bytes()...) + buf = append(buf, yy.Bytes()...) + return buf +} + +// Add sets q = p1 + p2, and returns q. The points may overlap. +func (q *P384Point) Add(p1, p2 *P384Point) *P384Point { + // Complete addition formula for a = -3 from "Complete addition formulas for + // prime order elliptic curves" (https://eprint.iacr.org/2015/1060), §A.2. + + t0 := new(fiat.P384Element).Mul(p1.x, p2.x) // t0 := X1 * X2 + t1 := new(fiat.P384Element).Mul(p1.y, p2.y) // t1 := Y1 * Y2 + t2 := new(fiat.P384Element).Mul(p1.z, p2.z) // t2 := Z1 * Z2 + t3 := new(fiat.P384Element).Add(p1.x, p1.y) // t3 := X1 + Y1 + t4 := new(fiat.P384Element).Add(p2.x, p2.y) // t4 := X2 + Y2 + t3.Mul(t3, t4) // t3 := t3 * t4 + t4.Add(t0, t1) // t4 := t0 + t1 + t3.Sub(t3, t4) // t3 := t3 - t4 + t4.Add(p1.y, p1.z) // t4 := Y1 + Z1 + x3 := new(fiat.P384Element).Add(p2.y, p2.z) // X3 := Y2 + Z2 + t4.Mul(t4, x3) // t4 := t4 * X3 + x3.Add(t1, t2) // X3 := t1 + t2 + t4.Sub(t4, x3) // t4 := t4 - X3 + x3.Add(p1.x, p1.z) // X3 := X1 + Z1 + y3 := new(fiat.P384Element).Add(p2.x, p2.z) // Y3 := X2 + Z2 + x3.Mul(x3, y3) // X3 := X3 * Y3 + y3.Add(t0, t2) // Y3 := t0 + t2 + y3.Sub(x3, y3) // Y3 := X3 - Y3 + z3 := new(fiat.P384Element).Mul(p384B, t2) // Z3 := b * t2 + x3.Sub(y3, z3) // X3 := Y3 - Z3 + z3.Add(x3, x3) // Z3 := X3 + X3 + x3.Add(x3, z3) // X3 := X3 + Z3 + z3.Sub(t1, x3) // Z3 := t1 - X3 + x3.Add(t1, x3) // X3 := t1 + X3 + y3.Mul(p384B, y3) // Y3 := b * Y3 + t1.Add(t2, t2) // t1 := t2 + t2 + t2.Add(t1, t2) // t2 := t1 + t2 + y3.Sub(y3, t2) // Y3 := Y3 - t2 + y3.Sub(y3, t0) // Y3 := Y3 - t0 + t1.Add(y3, y3) // t1 := Y3 + Y3 + y3.Add(t1, y3) // Y3 := t1 + Y3 + t1.Add(t0, t0) // t1 := t0 + t0 + t0.Add(t1, t0) // t0 := t1 + t0 + t0.Sub(t0, t2) // t0 := t0 - t2 + t1.Mul(t4, y3) // t1 := t4 * Y3 + t2.Mul(t0, y3) // t2 := t0 * Y3 + y3.Mul(x3, z3) // Y3 := X3 * Z3 + y3.Add(y3, t2) // Y3 := Y3 + t2 + x3.Mul(t3, x3) // X3 := t3 * X3 + x3.Sub(x3, t1) // X3 := X3 - t1 + z3.Mul(t4, z3) // Z3 := t4 * Z3 + t1.Mul(t3, t0) // t1 := t3 * t0 + z3.Add(z3, t1) // Z3 := Z3 + t1 + + q.x.Set(x3) + q.y.Set(y3) + q.z.Set(z3) + return q +} + +// Double sets q = p + p, and returns q. The points may overlap. +func (q *P384Point) Double(p *P384Point) *P384Point { + // Complete addition formula for a = -3 from "Complete addition formulas for + // prime order elliptic curves" (https://eprint.iacr.org/2015/1060), §A.2. + + t0 := new(fiat.P384Element).Square(p.x) // t0 := X ^ 2 + t1 := new(fiat.P384Element).Square(p.y) // t1 := Y ^ 2 + t2 := new(fiat.P384Element).Square(p.z) // t2 := Z ^ 2 + t3 := new(fiat.P384Element).Mul(p.x, p.y) // t3 := X * Y + t3.Add(t3, t3) // t3 := t3 + t3 + z3 := new(fiat.P384Element).Mul(p.x, p.z) // Z3 := X * Z + z3.Add(z3, z3) // Z3 := Z3 + Z3 + y3 := new(fiat.P384Element).Mul(p384B, t2) // Y3 := b * t2 + y3.Sub(y3, z3) // Y3 := Y3 - Z3 + x3 := new(fiat.P384Element).Add(y3, y3) // X3 := Y3 + Y3 + y3.Add(x3, y3) // Y3 := X3 + Y3 + x3.Sub(t1, y3) // X3 := t1 - Y3 + y3.Add(t1, y3) // Y3 := t1 + Y3 + y3.Mul(x3, y3) // Y3 := X3 * Y3 + x3.Mul(x3, t3) // X3 := X3 * t3 + t3.Add(t2, t2) // t3 := t2 + t2 + t2.Add(t2, t3) // t2 := t2 + t3 + z3.Mul(p384B, z3) // Z3 := b * Z3 + z3.Sub(z3, t2) // Z3 := Z3 - t2 + z3.Sub(z3, t0) // Z3 := Z3 - t0 + t3.Add(z3, z3) // t3 := Z3 + Z3 + z3.Add(z3, t3) // Z3 := Z3 + t3 + t3.Add(t0, t0) // t3 := t0 + t0 + t0.Add(t3, t0) // t0 := t3 + t0 + t0.Sub(t0, t2) // t0 := t0 - t2 + t0.Mul(t0, z3) // t0 := t0 * Z3 + y3.Add(y3, t0) // Y3 := Y3 + t0 + t0.Mul(p.y, p.z) // t0 := Y * Z + t0.Add(t0, t0) // t0 := t0 + t0 + z3.Mul(t0, z3) // Z3 := t0 * Z3 + x3.Sub(x3, z3) // X3 := X3 - Z3 + z3.Mul(t0, t1) // Z3 := t0 * t1 + z3.Add(z3, z3) // Z3 := Z3 + Z3 + z3.Add(z3, z3) // Z3 := Z3 + Z3 + + q.x.Set(x3) + q.y.Set(y3) + q.z.Set(z3) + return q +} + +// Select sets q to p1 if cond == 1, and to p2 if cond == 0. +func (q *P384Point) Select(p1, p2 *P384Point, cond int) *P384Point { + q.x.Select(p1.x, p2.x, cond) + q.y.Select(p1.y, p2.y, cond) + q.z.Select(p1.z, p2.z, cond) + return q +} + +// ScalarMult sets p = scalar * q, and returns p. +func (p *P384Point) ScalarMult(q *P384Point, scalar []byte) *P384Point { + // table holds the first 16 multiples of q. The explicit newP384Point calls + // get inlined, letting the allocations live on the stack. + var table = [16]*P384Point{ + NewP384Point(), NewP384Point(), NewP384Point(), NewP384Point(), + NewP384Point(), NewP384Point(), NewP384Point(), NewP384Point(), + NewP384Point(), NewP384Point(), NewP384Point(), NewP384Point(), + NewP384Point(), NewP384Point(), NewP384Point(), NewP384Point(), + } + for i := 1; i < 16; i++ { + table[i].Add(table[i-1], q) + } + + // Instead of doing the classic double-and-add chain, we do it with a + // four-bit window: we double four times, and then add [0-15]P. + t := NewP384Point() + p.Set(NewP384Point()) + for _, byte := range scalar { + p.Double(p) + p.Double(p) + p.Double(p) + p.Double(p) + + for i := uint8(0); i < 16; i++ { + cond := subtle.ConstantTimeByteEq(byte>>4, i) + t.Select(table[i], t, cond) + } + p.Add(p, t) + + p.Double(p) + p.Double(p) + p.Double(p) + p.Double(p) + + for i := uint8(0); i < 16; i++ { + cond := subtle.ConstantTimeByteEq(byte&0b1111, i) + t.Select(table[i], t, cond) + } + p.Add(p, t) + } + + return p +} diff --git a/libgo/go/crypto/elliptic/internal/nistec/p521.go b/libgo/go/crypto/elliptic/internal/nistec/p521.go new file mode 100644 index 0000000..cdbd195 --- /dev/null +++ b/libgo/go/crypto/elliptic/internal/nistec/p521.go @@ -0,0 +1,310 @@ +// Copyright 2021 The Go Authors. All rights reserved. +// Use of this source code is governed by a BSD-style +// license that can be found in the LICENSE file. + +// Package nistec implements the NIST P elliptic curves from FIPS 186-4. +// +// This package uses fiat-crypto for its backend field arithmetic (not math/big) +// and exposes constant-time, heap allocation-free, byte slice-based safe APIs. +// Group operations use modern and safe complete addition formulas. The point at +// infinity is handled and encoded according to SEC 1, Version 2.0, and invalid +// curve points can't be represented. +package nistec + +import ( + "crypto/elliptic/internal/fiat" + "crypto/subtle" + "errors" +) + +var p521B, _ = new(fiat.P521Element).SetBytes([]byte{ + 0x00, 0x51, 0x95, 0x3e, 0xb9, 0x61, 0x8e, 0x1c, 0x9a, 0x1f, 0x92, 0x9a, + 0x21, 0xa0, 0xb6, 0x85, 0x40, 0xee, 0xa2, 0xda, 0x72, 0x5b, 0x99, 0xb3, + 0x15, 0xf3, 0xb8, 0xb4, 0x89, 0x91, 0x8e, 0xf1, 0x09, 0xe1, 0x56, 0x19, + 0x39, 0x51, 0xec, 0x7e, 0x93, 0x7b, 0x16, 0x52, 0xc0, 0xbd, 0x3b, 0xb1, + 0xbf, 0x07, 0x35, 0x73, 0xdf, 0x88, 0x3d, 0x2c, 0x34, 0xf1, 0xef, 0x45, + 0x1f, 0xd4, 0x6b, 0x50, 0x3f, 0x00}) + +var p521G, _ = NewP521Point().SetBytes([]byte{0x04, + 0x00, 0xc6, 0x85, 0x8e, 0x06, 0xb7, 0x04, 0x04, 0xe9, 0xcd, 0x9e, 0x3e, + 0xcb, 0x66, 0x23, 0x95, 0xb4, 0x42, 0x9c, 0x64, 0x81, 0x39, 0x05, 0x3f, + 0xb5, 0x21, 0xf8, 0x28, 0xaf, 0x60, 0x6b, 0x4d, 0x3d, 0xba, 0xa1, 0x4b, + 0x5e, 0x77, 0xef, 0xe7, 0x59, 0x28, 0xfe, 0x1d, 0xc1, 0x27, 0xa2, 0xff, + 0xa8, 0xde, 0x33, 0x48, 0xb3, 0xc1, 0x85, 0x6a, 0x42, 0x9b, 0xf9, 0x7e, + 0x7e, 0x31, 0xc2, 0xe5, 0xbd, 0x66, 0x01, 0x18, 0x39, 0x29, 0x6a, 0x78, + 0x9a, 0x3b, 0xc0, 0x04, 0x5c, 0x8a, 0x5f, 0xb4, 0x2c, 0x7d, 0x1b, 0xd9, + 0x98, 0xf5, 0x44, 0x49, 0x57, 0x9b, 0x44, 0x68, 0x17, 0xaf, 0xbd, 0x17, + 0x27, 0x3e, 0x66, 0x2c, 0x97, 0xee, 0x72, 0x99, 0x5e, 0xf4, 0x26, 0x40, + 0xc5, 0x50, 0xb9, 0x01, 0x3f, 0xad, 0x07, 0x61, 0x35, 0x3c, 0x70, 0x86, + 0xa2, 0x72, 0xc2, 0x40, 0x88, 0xbe, 0x94, 0x76, 0x9f, 0xd1, 0x66, 0x50}) + +const p521ElementLength = 66 + +// P521Point is a P-521 point. The zero value is NOT valid. +type P521Point struct { + // The point is represented in projective coordinates (X:Y:Z), + // where x = X/Z and y = Y/Z. + x, y, z *fiat.P521Element +} + +// NewP521Point returns a new P521Point representing the point at infinity point. +func NewP521Point() *P521Point { + return &P521Point{ + x: new(fiat.P521Element), + y: new(fiat.P521Element).One(), + z: new(fiat.P521Element), + } +} + +// NewP521Generator returns a new P521Point set to the canonical generator. +func NewP521Generator() *P521Point { + return (&P521Point{ + x: new(fiat.P521Element), + y: new(fiat.P521Element), + z: new(fiat.P521Element), + }).Set(p521G) +} + +// Set sets p = q and returns p. +func (p *P521Point) Set(q *P521Point) *P521Point { + p.x.Set(q.x) + p.y.Set(q.y) + p.z.Set(q.z) + return p +} + +// SetBytes sets p to the compressed, uncompressed, or infinity value encoded in +// b, as specified in SEC 1, Version 2.0, Section 2.3.4. If the point is not on +// the curve, it returns nil and an error, and the receiver is unchanged. +// Otherwise, it returns p. +func (p *P521Point) SetBytes(b []byte) (*P521Point, error) { + switch { + // Point at infinity. + case len(b) == 1 && b[0] == 0: + return p.Set(NewP521Point()), nil + + // Uncompressed form. + case len(b) == 1+2*p521ElementLength && b[0] == 4: + x, err := new(fiat.P521Element).SetBytes(b[1 : 1+p521ElementLength]) + if err != nil { + return nil, err + } + y, err := new(fiat.P521Element).SetBytes(b[1+p521ElementLength:]) + if err != nil { + return nil, err + } + if err := p521CheckOnCurve(x, y); err != nil { + return nil, err + } + p.x.Set(x) + p.y.Set(y) + p.z.One() + return p, nil + + // Compressed form + case len(b) == 1+p521ElementLength && b[0] == 0: + return nil, errors.New("unimplemented") // TODO(filippo) + + default: + return nil, errors.New("invalid P521 point encoding") + } +} + +func p521CheckOnCurve(x, y *fiat.P521Element) error { + // x³ - 3x + b. + x3 := new(fiat.P521Element).Square(x) + x3.Mul(x3, x) + + threeX := new(fiat.P521Element).Add(x, x) + threeX.Add(threeX, x) + + x3.Sub(x3, threeX) + x3.Add(x3, p521B) + + // y² = x³ - 3x + b + y2 := new(fiat.P521Element).Square(y) + + if x3.Equal(y2) != 1 { + return errors.New("P521 point not on curve") + } + return nil +} + +// Bytes returns the uncompressed or infinity encoding of p, as specified in +// SEC 1, Version 2.0, Section 2.3.3. Note that the encoding of the point at +// infinity is shorter than all other encodings. +func (p *P521Point) Bytes() []byte { + // This function is outlined to make the allocations inline in the caller + // rather than happen on the heap. + var out [133]byte + return p.bytes(&out) +} + +func (p *P521Point) bytes(out *[133]byte) []byte { + if p.z.IsZero() == 1 { + return append(out[:0], 0) + } + + zinv := new(fiat.P521Element).Invert(p.z) + xx := new(fiat.P521Element).Mul(p.x, zinv) + yy := new(fiat.P521Element).Mul(p.y, zinv) + + buf := append(out[:0], 4) + buf = append(buf, xx.Bytes()...) + buf = append(buf, yy.Bytes()...) + return buf +} + +// Add sets q = p1 + p2, and returns q. The points may overlap. +func (q *P521Point) Add(p1, p2 *P521Point) *P521Point { + // Complete addition formula for a = -3 from "Complete addition formulas for + // prime order elliptic curves" (https://eprint.iacr.org/2015/1060), §A.2. + + t0 := new(fiat.P521Element).Mul(p1.x, p2.x) // t0 := X1 * X2 + t1 := new(fiat.P521Element).Mul(p1.y, p2.y) // t1 := Y1 * Y2 + t2 := new(fiat.P521Element).Mul(p1.z, p2.z) // t2 := Z1 * Z2 + t3 := new(fiat.P521Element).Add(p1.x, p1.y) // t3 := X1 + Y1 + t4 := new(fiat.P521Element).Add(p2.x, p2.y) // t4 := X2 + Y2 + t3.Mul(t3, t4) // t3 := t3 * t4 + t4.Add(t0, t1) // t4 := t0 + t1 + t3.Sub(t3, t4) // t3 := t3 - t4 + t4.Add(p1.y, p1.z) // t4 := Y1 + Z1 + x3 := new(fiat.P521Element).Add(p2.y, p2.z) // X3 := Y2 + Z2 + t4.Mul(t4, x3) // t4 := t4 * X3 + x3.Add(t1, t2) // X3 := t1 + t2 + t4.Sub(t4, x3) // t4 := t4 - X3 + x3.Add(p1.x, p1.z) // X3 := X1 + Z1 + y3 := new(fiat.P521Element).Add(p2.x, p2.z) // Y3 := X2 + Z2 + x3.Mul(x3, y3) // X3 := X3 * Y3 + y3.Add(t0, t2) // Y3 := t0 + t2 + y3.Sub(x3, y3) // Y3 := X3 - Y3 + z3 := new(fiat.P521Element).Mul(p521B, t2) // Z3 := b * t2 + x3.Sub(y3, z3) // X3 := Y3 - Z3 + z3.Add(x3, x3) // Z3 := X3 + X3 + x3.Add(x3, z3) // X3 := X3 + Z3 + z3.Sub(t1, x3) // Z3 := t1 - X3 + x3.Add(t1, x3) // X3 := t1 + X3 + y3.Mul(p521B, y3) // Y3 := b * Y3 + t1.Add(t2, t2) // t1 := t2 + t2 + t2.Add(t1, t2) // t2 := t1 + t2 + y3.Sub(y3, t2) // Y3 := Y3 - t2 + y3.Sub(y3, t0) // Y3 := Y3 - t0 + t1.Add(y3, y3) // t1 := Y3 + Y3 + y3.Add(t1, y3) // Y3 := t1 + Y3 + t1.Add(t0, t0) // t1 := t0 + t0 + t0.Add(t1, t0) // t0 := t1 + t0 + t0.Sub(t0, t2) // t0 := t0 - t2 + t1.Mul(t4, y3) // t1 := t4 * Y3 + t2.Mul(t0, y3) // t2 := t0 * Y3 + y3.Mul(x3, z3) // Y3 := X3 * Z3 + y3.Add(y3, t2) // Y3 := Y3 + t2 + x3.Mul(t3, x3) // X3 := t3 * X3 + x3.Sub(x3, t1) // X3 := X3 - t1 + z3.Mul(t4, z3) // Z3 := t4 * Z3 + t1.Mul(t3, t0) // t1 := t3 * t0 + z3.Add(z3, t1) // Z3 := Z3 + t1 + + q.x.Set(x3) + q.y.Set(y3) + q.z.Set(z3) + return q +} + +// Double sets q = p + p, and returns q. The points may overlap. +func (q *P521Point) Double(p *P521Point) *P521Point { + // Complete addition formula for a = -3 from "Complete addition formulas for + // prime order elliptic curves" (https://eprint.iacr.org/2015/1060), §A.2. + + t0 := new(fiat.P521Element).Square(p.x) // t0 := X ^ 2 + t1 := new(fiat.P521Element).Square(p.y) // t1 := Y ^ 2 + t2 := new(fiat.P521Element).Square(p.z) // t2 := Z ^ 2 + t3 := new(fiat.P521Element).Mul(p.x, p.y) // t3 := X * Y + t3.Add(t3, t3) // t3 := t3 + t3 + z3 := new(fiat.P521Element).Mul(p.x, p.z) // Z3 := X * Z + z3.Add(z3, z3) // Z3 := Z3 + Z3 + y3 := new(fiat.P521Element).Mul(p521B, t2) // Y3 := b * t2 + y3.Sub(y3, z3) // Y3 := Y3 - Z3 + x3 := new(fiat.P521Element).Add(y3, y3) // X3 := Y3 + Y3 + y3.Add(x3, y3) // Y3 := X3 + Y3 + x3.Sub(t1, y3) // X3 := t1 - Y3 + y3.Add(t1, y3) // Y3 := t1 + Y3 + y3.Mul(x3, y3) // Y3 := X3 * Y3 + x3.Mul(x3, t3) // X3 := X3 * t3 + t3.Add(t2, t2) // t3 := t2 + t2 + t2.Add(t2, t3) // t2 := t2 + t3 + z3.Mul(p521B, z3) // Z3 := b * Z3 + z3.Sub(z3, t2) // Z3 := Z3 - t2 + z3.Sub(z3, t0) // Z3 := Z3 - t0 + t3.Add(z3, z3) // t3 := Z3 + Z3 + z3.Add(z3, t3) // Z3 := Z3 + t3 + t3.Add(t0, t0) // t3 := t0 + t0 + t0.Add(t3, t0) // t0 := t3 + t0 + t0.Sub(t0, t2) // t0 := t0 - t2 + t0.Mul(t0, z3) // t0 := t0 * Z3 + y3.Add(y3, t0) // Y3 := Y3 + t0 + t0.Mul(p.y, p.z) // t0 := Y * Z + t0.Add(t0, t0) // t0 := t0 + t0 + z3.Mul(t0, z3) // Z3 := t0 * Z3 + x3.Sub(x3, z3) // X3 := X3 - Z3 + z3.Mul(t0, t1) // Z3 := t0 * t1 + z3.Add(z3, z3) // Z3 := Z3 + Z3 + z3.Add(z3, z3) // Z3 := Z3 + Z3 + + q.x.Set(x3) + q.y.Set(y3) + q.z.Set(z3) + return q +} + +// Select sets q to p1 if cond == 1, and to p2 if cond == 0. +func (q *P521Point) Select(p1, p2 *P521Point, cond int) *P521Point { + q.x.Select(p1.x, p2.x, cond) + q.y.Select(p1.y, p2.y, cond) + q.z.Select(p1.z, p2.z, cond) + return q +} + +// ScalarMult sets p = scalar * q, and returns p. +func (p *P521Point) ScalarMult(q *P521Point, scalar []byte) *P521Point { + // table holds the first 16 multiples of q. The explicit newP521Point calls + // get inlined, letting the allocations live on the stack. + var table = [16]*P521Point{ + NewP521Point(), NewP521Point(), NewP521Point(), NewP521Point(), + NewP521Point(), NewP521Point(), NewP521Point(), NewP521Point(), + NewP521Point(), NewP521Point(), NewP521Point(), NewP521Point(), + NewP521Point(), NewP521Point(), NewP521Point(), NewP521Point(), + } + for i := 1; i < 16; i++ { + table[i].Add(table[i-1], q) + } + + // Instead of doing the classic double-and-add chain, we do it with a + // four-bit window: we double four times, and then add [0-15]P. + t := NewP521Point() + p.Set(NewP521Point()) + for _, byte := range scalar { + p.Double(p) + p.Double(p) + p.Double(p) + p.Double(p) + + for i := uint8(0); i < 16; i++ { + cond := subtle.ConstantTimeByteEq(byte>>4, i) + t.Select(table[i], t, cond) + } + p.Add(p, t) + + p.Double(p) + p.Double(p) + p.Double(p) + p.Double(p) + + for i := uint8(0); i < 16; i++ { + cond := subtle.ConstantTimeByteEq(byte&0b1111, i) + t.Select(table[i], t, cond) + } + p.Add(p, t) + } + + return p +} diff --git a/libgo/go/crypto/elliptic/p224.go b/libgo/go/crypto/elliptic/p224.go index 8c76021..a8533b8 100644 --- a/libgo/go/crypto/elliptic/p224.go +++ b/libgo/go/crypto/elliptic/p224.go @@ -1,778 +1,136 @@ -// Copyright 2012 The Go Authors. All rights reserved. +// Copyright 2013 The Go Authors. All rights reserved. // Use of this source code is governed by a BSD-style // license that can be found in the LICENSE file. package elliptic -// This is a constant-time, 32-bit implementation of P224. See FIPS 186-3, -// section D.2.2. -// -// See https://www.imperialviolet.org/2010/12/04/ecc.html ([1]) for background. - import ( + "crypto/elliptic/internal/nistec" + "crypto/rand" "math/big" ) -var p224 p224Curve - -type p224Curve struct { - *CurveParams - gx, gy, b p224FieldElement -} - -func initP224() { - // See FIPS 186-3, section D.2.2 - p224.CurveParams = &CurveParams{Name: "P-224"} - p224.P, _ = new(big.Int).SetString("26959946667150639794667015087019630673557916260026308143510066298881", 10) - p224.N, _ = new(big.Int).SetString("26959946667150639794667015087019625940457807714424391721682722368061", 10) - p224.B, _ = new(big.Int).SetString("b4050a850c04b3abf54132565044b0b7d7bfd8ba270b39432355ffb4", 16) - p224.Gx, _ = new(big.Int).SetString("b70e0cbd6bb4bf7f321390b94a03c1d356c21122343280d6115c1d21", 16) - p224.Gy, _ = new(big.Int).SetString("bd376388b5f723fb4c22dfe6cd4375a05a07476444d5819985007e34", 16) - p224.BitSize = 224 - - p224FromBig(&p224.gx, p224.Gx) - p224FromBig(&p224.gy, p224.Gy) - p224FromBig(&p224.b, p224.B) -} - -// P224 returns a Curve which implements P-224 (see FIPS 186-3, section D.2.2). -// -// The cryptographic operations are implemented using constant-time algorithms. -func P224() Curve { - initonce.Do(initAll) - return p224 -} - -func (curve p224Curve) Params() *CurveParams { - return curve.CurveParams -} - -func (curve p224Curve) IsOnCurve(bigX, bigY *big.Int) bool { - var x, y p224FieldElement - p224FromBig(&x, bigX) - p224FromBig(&y, bigY) - - // y² = x³ - 3x + b - var tmp p224LargeFieldElement - var x3 p224FieldElement - p224Square(&x3, &x, &tmp) - p224Mul(&x3, &x3, &x, &tmp) - - for i := 0; i < 8; i++ { - x[i] *= 3 - } - p224Sub(&x3, &x3, &x) - p224Reduce(&x3) - p224Add(&x3, &x3, &curve.b) - p224Contract(&x3, &x3) - - p224Square(&y, &y, &tmp) - p224Contract(&y, &y) - - for i := 0; i < 8; i++ { - if y[i] != x3[i] { - return false - } - } - return true -} - -func (p224Curve) Add(bigX1, bigY1, bigX2, bigY2 *big.Int) (x, y *big.Int) { - var x1, y1, z1, x2, y2, z2, x3, y3, z3 p224FieldElement - - p224FromBig(&x1, bigX1) - p224FromBig(&y1, bigY1) - if bigX1.Sign() != 0 || bigY1.Sign() != 0 { - z1[0] = 1 - } - p224FromBig(&x2, bigX2) - p224FromBig(&y2, bigY2) - if bigX2.Sign() != 0 || bigY2.Sign() != 0 { - z2[0] = 1 - } - - p224AddJacobian(&x3, &y3, &z3, &x1, &y1, &z1, &x2, &y2, &z2) - return p224ToAffine(&x3, &y3, &z3) -} - -func (p224Curve) Double(bigX1, bigY1 *big.Int) (x, y *big.Int) { - var x1, y1, z1, x2, y2, z2 p224FieldElement - - p224FromBig(&x1, bigX1) - p224FromBig(&y1, bigY1) - z1[0] = 1 - - p224DoubleJacobian(&x2, &y2, &z2, &x1, &y1, &z1) - return p224ToAffine(&x2, &y2, &z2) -} - -func (p224Curve) ScalarMult(bigX1, bigY1 *big.Int, scalar []byte) (x, y *big.Int) { - var x1, y1, z1, x2, y2, z2 p224FieldElement - - p224FromBig(&x1, bigX1) - p224FromBig(&y1, bigY1) - z1[0] = 1 - - p224ScalarMult(&x2, &y2, &z2, &x1, &y1, &z1, scalar) - return p224ToAffine(&x2, &y2, &z2) -} - -func (curve p224Curve) ScalarBaseMult(scalar []byte) (x, y *big.Int) { - var z1, x2, y2, z2 p224FieldElement - - z1[0] = 1 - p224ScalarMult(&x2, &y2, &z2, &curve.gx, &curve.gy, &z1, scalar) - return p224ToAffine(&x2, &y2, &z2) -} - -// Field element functions. -// -// The field that we're dealing with is ℤ/pℤ where p = 2**224 - 2**96 + 1. -// -// Field elements are represented by a FieldElement, which is a typedef to an -// array of 8 uint32's. The value of a FieldElement, a, is: -// a[0] + 2**28·a[1] + 2**56·a[1] + ... + 2**196·a[7] +// p224Curve is a Curve implementation based on nistec.P224Point. // -// Using 28-bit limbs means that there's only 4 bits of headroom, which is less -// than we would really like. But it has the useful feature that we hit 2**224 -// exactly, making the reflections during a reduce much nicer. -type p224FieldElement [8]uint32 - -// p224P is the order of the field, represented as a p224FieldElement. -var p224P = [8]uint32{1, 0, 0, 0xffff000, 0xfffffff, 0xfffffff, 0xfffffff, 0xfffffff} - -// p224IsZero returns 1 if a == 0 mod p and 0 otherwise. -// -// a[i] < 2**29 -func p224IsZero(a *p224FieldElement) uint32 { - // Since a p224FieldElement contains 224 bits there are two possible - // representations of 0: 0 and p. - var minimal p224FieldElement - p224Contract(&minimal, a) - - var isZero, isP uint32 - for i, v := range minimal { - isZero |= v - isP |= v - p224P[i] - } - - // If either isZero or isP is 0, then we should return 1. - isZero |= isZero >> 16 - isZero |= isZero >> 8 - isZero |= isZero >> 4 - isZero |= isZero >> 2 - isZero |= isZero >> 1 - - isP |= isP >> 16 - isP |= isP >> 8 - isP |= isP >> 4 - isP |= isP >> 2 - isP |= isP >> 1 - - // For isZero and isP, the LSB is 0 iff all the bits are zero. - result := isZero & isP - result = (^result) & 1 - - return result -} - -// p224Add computes *out = a+b +// It's a wrapper that exposes the big.Int-based Curve interface and encodes the +// legacy idiosyncrasies it requires, such as invalid and infinity point +// handling. // -// a[i] + b[i] < 2**32 -func p224Add(out, a, b *p224FieldElement) { - for i := 0; i < 8; i++ { - out[i] = a[i] + b[i] - } -} - -const two31p3 = 1<<31 + 1<<3 -const two31m3 = 1<<31 - 1<<3 -const two31m15m3 = 1<<31 - 1<<15 - 1<<3 - -// p224ZeroModP31 is 0 mod p where bit 31 is set in all limbs so that we can -// subtract smaller amounts without underflow. See the section "Subtraction" in -// [1] for reasoning. -var p224ZeroModP31 = []uint32{two31p3, two31m3, two31m3, two31m15m3, two31m3, two31m3, two31m3, two31m3} - -// p224Sub computes *out = a-b -// -// a[i], b[i] < 2**30 -// out[i] < 2**32 -func p224Sub(out, a, b *p224FieldElement) { - for i := 0; i < 8; i++ { - out[i] = a[i] + p224ZeroModP31[i] - b[i] - } -} - -// LargeFieldElement also represents an element of the field. The limbs are -// still spaced 28-bits apart and in little-endian order. So the limbs are at -// 0, 28, 56, ..., 392 bits, each 64-bits wide. -type p224LargeFieldElement [15]uint64 - -const two63p35 = 1<<63 + 1<<35 -const two63m35 = 1<<63 - 1<<35 -const two63m35m19 = 1<<63 - 1<<35 - 1<<19 - -// p224ZeroModP63 is 0 mod p where bit 63 is set in all limbs. See the section -// "Subtraction" in [1] for why. -var p224ZeroModP63 = [8]uint64{two63p35, two63m35, two63m35, two63m35, two63m35m19, two63m35, two63m35, two63m35} - -const bottom12Bits = 0xfff -const bottom28Bits = 0xfffffff - -// p224Mul computes *out = a*b -// -// a[i] < 2**29, b[i] < 2**30 (or vice versa) -// out[i] < 2**29 -func p224Mul(out, a, b *p224FieldElement, tmp *p224LargeFieldElement) { - for i := 0; i < 15; i++ { - tmp[i] = 0 - } - - for i := 0; i < 8; i++ { - for j := 0; j < 8; j++ { - tmp[i+j] += uint64(a[i]) * uint64(b[j]) - } - } - - p224ReduceLarge(out, tmp) -} - -// Square computes *out = a*a -// -// a[i] < 2**29 -// out[i] < 2**29 -func p224Square(out, a *p224FieldElement, tmp *p224LargeFieldElement) { - for i := 0; i < 15; i++ { - tmp[i] = 0 - } - - for i := 0; i < 8; i++ { - for j := 0; j <= i; j++ { - r := uint64(a[i]) * uint64(a[j]) - if i == j { - tmp[i+j] += r - } else { - tmp[i+j] += r << 1 - } - } - } - - p224ReduceLarge(out, tmp) +// To interact with the nistec package, points are encoded into and decoded from +// properly formatted byte slices. All big.Int use is limited to this package. +// Encoding and decoding is 1/1000th of the runtime of a scalar multiplication, +// so the overhead is acceptable. +type p224Curve struct { + params *CurveParams } -// ReduceLarge converts a p224LargeFieldElement to a p224FieldElement. -// -// in[i] < 2**62 -func p224ReduceLarge(out *p224FieldElement, in *p224LargeFieldElement) { - for i := 0; i < 8; i++ { - in[i] += p224ZeroModP63[i] - } - - // Eliminate the coefficients at 2**224 and greater. - for i := 14; i >= 8; i-- { - in[i-8] -= in[i] - in[i-5] += (in[i] & 0xffff) << 12 - in[i-4] += in[i] >> 16 - } - in[8] = 0 - // in[0..8] < 2**64 - - // As the values become small enough, we start to store them in |out| - // and use 32-bit operations. - for i := 1; i < 8; i++ { - in[i+1] += in[i] >> 28 - out[i] = uint32(in[i] & bottom28Bits) - } - in[0] -= in[8] - out[3] += uint32(in[8]&0xffff) << 12 - out[4] += uint32(in[8] >> 16) - // in[0] < 2**64 - // out[3] < 2**29 - // out[4] < 2**29 - // out[1,2,5..7] < 2**28 - - out[0] = uint32(in[0] & bottom28Bits) - out[1] += uint32((in[0] >> 28) & bottom28Bits) - out[2] += uint32(in[0] >> 56) - // out[0] < 2**28 - // out[1..4] < 2**29 - // out[5..7] < 2**28 -} +var p224 p224Curve +var _ Curve = p224 -// Reduce reduces the coefficients of a to smaller bounds. -// -// On entry: a[i] < 2**31 + 2**30 -// On exit: a[i] < 2**29 -func p224Reduce(a *p224FieldElement) { - for i := 0; i < 7; i++ { - a[i+1] += a[i] >> 28 - a[i] &= bottom28Bits +func initP224() { + p224.params = &CurveParams{ + Name: "P-224", + BitSize: 224, + // FIPS 186-4, section D.1.2.2 + P: bigFromDecimal("26959946667150639794667015087019630673557916260026308143510066298881"), + N: bigFromDecimal("26959946667150639794667015087019625940457807714424391721682722368061"), + B: bigFromHex("b4050a850c04b3abf54132565044b0b7d7bfd8ba270b39432355ffb4"), + Gx: bigFromHex("b70e0cbd6bb4bf7f321390b94a03c1d356c21122343280d6115c1d21"), + Gy: bigFromHex("bd376388b5f723fb4c22dfe6cd4375a05a07476444d5819985007e34"), } - top := a[7] >> 28 - a[7] &= bottom28Bits - - // top < 2**4 - mask := top - mask |= mask >> 2 - mask |= mask >> 1 - mask <<= 31 - mask = uint32(int32(mask) >> 31) - // Mask is all ones if top != 0, all zero otherwise - - a[0] -= top - a[3] += top << 12 - - // We may have just made a[0] negative but, if we did, then we must - // have added something to a[3], this it's > 2**12. Therefore we can - // carry down to a[0]. - a[3] -= 1 & mask - a[2] += mask & (1<<28 - 1) - a[1] += mask & (1<<28 - 1) - a[0] += mask & (1 << 28) } -// p224Invert calculates *out = in**-1 by computing in**(2**224 - 2**96 - 1), -// i.e. Fermat's little theorem. -func p224Invert(out, in *p224FieldElement) { - var f1, f2, f3, f4 p224FieldElement - var c p224LargeFieldElement - - p224Square(&f1, in, &c) // 2 - p224Mul(&f1, &f1, in, &c) // 2**2 - 1 - p224Square(&f1, &f1, &c) // 2**3 - 2 - p224Mul(&f1, &f1, in, &c) // 2**3 - 1 - p224Square(&f2, &f1, &c) // 2**4 - 2 - p224Square(&f2, &f2, &c) // 2**5 - 4 - p224Square(&f2, &f2, &c) // 2**6 - 8 - p224Mul(&f1, &f1, &f2, &c) // 2**6 - 1 - p224Square(&f2, &f1, &c) // 2**7 - 2 - for i := 0; i < 5; i++ { // 2**12 - 2**6 - p224Square(&f2, &f2, &c) - } - p224Mul(&f2, &f2, &f1, &c) // 2**12 - 1 - p224Square(&f3, &f2, &c) // 2**13 - 2 - for i := 0; i < 11; i++ { // 2**24 - 2**12 - p224Square(&f3, &f3, &c) - } - p224Mul(&f2, &f3, &f2, &c) // 2**24 - 1 - p224Square(&f3, &f2, &c) // 2**25 - 2 - for i := 0; i < 23; i++ { // 2**48 - 2**24 - p224Square(&f3, &f3, &c) - } - p224Mul(&f3, &f3, &f2, &c) // 2**48 - 1 - p224Square(&f4, &f3, &c) // 2**49 - 2 - for i := 0; i < 47; i++ { // 2**96 - 2**48 - p224Square(&f4, &f4, &c) - } - p224Mul(&f3, &f3, &f4, &c) // 2**96 - 1 - p224Square(&f4, &f3, &c) // 2**97 - 2 - for i := 0; i < 23; i++ { // 2**120 - 2**24 - p224Square(&f4, &f4, &c) - } - p224Mul(&f2, &f4, &f2, &c) // 2**120 - 1 - for i := 0; i < 6; i++ { // 2**126 - 2**6 - p224Square(&f2, &f2, &c) - } - p224Mul(&f1, &f1, &f2, &c) // 2**126 - 1 - p224Square(&f1, &f1, &c) // 2**127 - 2 - p224Mul(&f1, &f1, in, &c) // 2**127 - 1 - for i := 0; i < 97; i++ { // 2**224 - 2**97 - p224Square(&f1, &f1, &c) - } - p224Mul(out, &f1, &f3, &c) // 2**224 - 2**96 - 1 +func (curve p224Curve) Params() *CurveParams { + return curve.params } -// p224Contract converts a FieldElement to its unique, minimal form. -// -// On entry, in[i] < 2**29 -// On exit, out[i] < 2**28 and out < p -func p224Contract(out, in *p224FieldElement) { - copy(out[:], in[:]) - - // First, carry the bits above 28 to the higher limb. - for i := 0; i < 7; i++ { - out[i+1] += out[i] >> 28 - out[i] &= bottom28Bits - } - top := out[7] >> 28 - out[7] &= bottom28Bits - - // Use the reduction identity to carry the overflow. - // - // a + top * 2²²⁴ = a + top * 2⁹⁶ - top - out[0] -= top - out[3] += top << 12 - - // We may just have made out[0] negative. So we carry down. If we made - // out[0] negative then we know that out[3] is sufficiently positive - // because we just added to it. - for i := 0; i < 3; i++ { - mask := uint32(int32(out[i]) >> 31) - out[i] += (1 << 28) & mask - out[i+1] -= 1 & mask - } - - // We might have pushed out[3] over 2**28 so we perform another, partial, - // carry chain. - for i := 3; i < 7; i++ { - out[i+1] += out[i] >> 28 - out[i] &= bottom28Bits - } - top = out[7] >> 28 - out[7] &= bottom28Bits - - // Eliminate top while maintaining the same value mod p. - out[0] -= top - out[3] += top << 12 - - // There are two cases to consider for out[3]: - // 1) The first time that we eliminated top, we didn't push out[3] over - // 2**28. In this case, the partial carry chain didn't change any values - // and top is now zero. - // 2) We did push out[3] over 2**28 the first time that we eliminated top. - // The first value of top was in [0..2], therefore, after overflowing - // and being reduced by the second carry chain, out[3] <= 2<<12 - 1. - // In both cases, out[3] cannot have overflowed when we eliminated top for - // the second time. - - // Again, we may just have made out[0] negative, so do the same carry down. - // As before, if we made out[0] negative then we know that out[3] is - // sufficiently positive. - for i := 0; i < 3; i++ { - mask := uint32(int32(out[i]) >> 31) - out[i] += (1 << 28) & mask - out[i+1] -= 1 & mask - } - - // Now we see if the value is >= p and, if so, subtract p. - - // First we build a mask from the top four limbs, which must all be - // equal to bottom28Bits if the whole value is >= p. If top4AllOnes - // ends up with any zero bits in the bottom 28 bits, then this wasn't - // true. - top4AllOnes := uint32(0xffffffff) - for i := 4; i < 8; i++ { - top4AllOnes &= out[i] - } - top4AllOnes |= 0xf0000000 - // Now we replicate any zero bits to all the bits in top4AllOnes. - top4AllOnes &= top4AllOnes >> 16 - top4AllOnes &= top4AllOnes >> 8 - top4AllOnes &= top4AllOnes >> 4 - top4AllOnes &= top4AllOnes >> 2 - top4AllOnes &= top4AllOnes >> 1 - top4AllOnes = uint32(int32(top4AllOnes<<31) >> 31) - - // Now we test whether the bottom three limbs are non-zero. - bottom3NonZero := out[0] | out[1] | out[2] - bottom3NonZero |= bottom3NonZero >> 16 - bottom3NonZero |= bottom3NonZero >> 8 - bottom3NonZero |= bottom3NonZero >> 4 - bottom3NonZero |= bottom3NonZero >> 2 - bottom3NonZero |= bottom3NonZero >> 1 - bottom3NonZero = uint32(int32(bottom3NonZero<<31) >> 31) - - // Assuming top4AllOnes != 0, everything depends on the value of out[3]. - // If it's > 0xffff000 then the whole value is > p - // If it's = 0xffff000 and bottom3NonZero != 0, then the whole value is >= p - // If it's < 0xffff000, then the whole value is < p - n := 0xffff000 - out[3] - out3Equal := n - out3Equal |= out3Equal >> 16 - out3Equal |= out3Equal >> 8 - out3Equal |= out3Equal >> 4 - out3Equal |= out3Equal >> 2 - out3Equal |= out3Equal >> 1 - out3Equal = ^uint32(int32(out3Equal<<31) >> 31) - - // If out[3] > 0xffff000 then n's MSB will be one. - out3GT := uint32(int32(n) >> 31) - - mask := top4AllOnes & ((out3Equal & bottom3NonZero) | out3GT) - out[0] -= 1 & mask - out[3] -= 0xffff000 & mask - out[4] -= 0xfffffff & mask - out[5] -= 0xfffffff & mask - out[6] -= 0xfffffff & mask - out[7] -= 0xfffffff & mask - - // Do one final carry down, in case we made out[0] negative. One of - // out[0..3] needs to be positive and able to absorb the -1 or the value - // would have been < p, and the subtraction wouldn't have happened. - for i := 0; i < 3; i++ { - mask := uint32(int32(out[i]) >> 31) - out[i] += (1 << 28) & mask - out[i+1] -= 1 & mask +func (curve p224Curve) IsOnCurve(x, y *big.Int) bool { + // IsOnCurve is documented to reject (0, 0), the conventional point at + // infinity, which however is accepted by p224PointFromAffine. + if x.Sign() == 0 && y.Sign() == 0 { + return false } + _, ok := p224PointFromAffine(x, y) + return ok } -// Group element functions. -// -// These functions deal with group elements. The group is an elliptic curve -// group with a = -3 defined in FIPS 186-3, section D.2.2. - -// p224AddJacobian computes *out = a+b where a != b. -func p224AddJacobian(x3, y3, z3, x1, y1, z1, x2, y2, z2 *p224FieldElement) { - // See https://hyperelliptic.org/EFD/g1p/auto-shortw-jacobian-3.html#addition-p224Add-2007-bl - var z1z1, z2z2, u1, u2, s1, s2, h, i, j, r, v p224FieldElement - var c p224LargeFieldElement - - z1IsZero := p224IsZero(z1) - z2IsZero := p224IsZero(z2) - - // Z1Z1 = Z1² - p224Square(&z1z1, z1, &c) - // Z2Z2 = Z2² - p224Square(&z2z2, z2, &c) - // U1 = X1*Z2Z2 - p224Mul(&u1, x1, &z2z2, &c) - // U2 = X2*Z1Z1 - p224Mul(&u2, x2, &z1z1, &c) - // S1 = Y1*Z2*Z2Z2 - p224Mul(&s1, z2, &z2z2, &c) - p224Mul(&s1, y1, &s1, &c) - // S2 = Y2*Z1*Z1Z1 - p224Mul(&s2, z1, &z1z1, &c) - p224Mul(&s2, y2, &s2, &c) - // H = U2-U1 - p224Sub(&h, &u2, &u1) - p224Reduce(&h) - xEqual := p224IsZero(&h) - // I = (2*H)² - for j := 0; j < 8; j++ { - i[j] = h[j] << 1 - } - p224Reduce(&i) - p224Square(&i, &i, &c) - // J = H*I - p224Mul(&j, &h, &i, &c) - // r = 2*(S2-S1) - p224Sub(&r, &s2, &s1) - p224Reduce(&r) - yEqual := p224IsZero(&r) - if xEqual == 1 && yEqual == 1 && z1IsZero == 0 && z2IsZero == 0 { - p224DoubleJacobian(x3, y3, z3, x1, y1, z1) - return - } - for i := 0; i < 8; i++ { - r[i] <<= 1 +func p224PointFromAffine(x, y *big.Int) (p *nistec.P224Point, ok bool) { + // (0, 0) is by convention the point at infinity, which can't be represented + // in affine coordinates. Marshal incorrectly encodes it as an uncompressed + // point, which SetBytes would correctly reject. See Issue 37294. + if x.Sign() == 0 && y.Sign() == 0 { + return nistec.NewP224Point(), true } - p224Reduce(&r) - // V = U1*I - p224Mul(&v, &u1, &i, &c) - // Z3 = ((Z1+Z2)²-Z1Z1-Z2Z2)*H - p224Add(&z1z1, &z1z1, &z2z2) - p224Add(&z2z2, z1, z2) - p224Reduce(&z2z2) - p224Square(&z2z2, &z2z2, &c) - p224Sub(z3, &z2z2, &z1z1) - p224Reduce(z3) - p224Mul(z3, z3, &h, &c) - // X3 = r²-J-2*V - for i := 0; i < 8; i++ { - z1z1[i] = v[i] << 1 + if x.BitLen() > 224 || y.BitLen() > 224 { + return nil, false } - p224Add(&z1z1, &j, &z1z1) - p224Reduce(&z1z1) - p224Square(x3, &r, &c) - p224Sub(x3, x3, &z1z1) - p224Reduce(x3) - // Y3 = r*(V-X3)-2*S1*J - for i := 0; i < 8; i++ { - s1[i] <<= 1 + p, err := nistec.NewP224Point().SetBytes(Marshal(P224(), x, y)) + if err != nil { + return nil, false } - p224Mul(&s1, &s1, &j, &c) - p224Sub(&z1z1, &v, x3) - p224Reduce(&z1z1) - p224Mul(&z1z1, &z1z1, &r, &c) - p224Sub(y3, &z1z1, &s1) - p224Reduce(y3) - - p224CopyConditional(x3, x2, z1IsZero) - p224CopyConditional(x3, x1, z2IsZero) - p224CopyConditional(y3, y2, z1IsZero) - p224CopyConditional(y3, y1, z2IsZero) - p224CopyConditional(z3, z2, z1IsZero) - p224CopyConditional(z3, z1, z2IsZero) + return p, true } -// p224DoubleJacobian computes *out = a+a. -func p224DoubleJacobian(x3, y3, z3, x1, y1, z1 *p224FieldElement) { - var delta, gamma, beta, alpha, t p224FieldElement - var c p224LargeFieldElement - - p224Square(&delta, z1, &c) - p224Square(&gamma, y1, &c) - p224Mul(&beta, x1, &gamma, &c) - - // alpha = 3*(X1-delta)*(X1+delta) - p224Add(&t, x1, &delta) - for i := 0; i < 8; i++ { - t[i] += t[i] << 1 - } - p224Reduce(&t) - p224Sub(&alpha, x1, &delta) - p224Reduce(&alpha) - p224Mul(&alpha, &alpha, &t, &c) - - // Z3 = (Y1+Z1)²-gamma-delta - p224Add(z3, y1, z1) - p224Reduce(z3) - p224Square(z3, z3, &c) - p224Sub(z3, z3, &gamma) - p224Reduce(z3) - p224Sub(z3, z3, &delta) - p224Reduce(z3) - - // X3 = alpha²-8*beta - for i := 0; i < 8; i++ { - delta[i] = beta[i] << 3 - } - p224Reduce(&delta) - p224Square(x3, &alpha, &c) - p224Sub(x3, x3, &delta) - p224Reduce(x3) - - // Y3 = alpha*(4*beta-X3)-8*gamma² - for i := 0; i < 8; i++ { - beta[i] <<= 2 +func p224PointToAffine(p *nistec.P224Point) (x, y *big.Int) { + out := p.Bytes() + if len(out) == 1 && out[0] == 0 { + // This is the correct encoding of the point at infinity, which + // Unmarshal does not support. See Issue 37294. + return new(big.Int), new(big.Int) } - p224Sub(&beta, &beta, x3) - p224Reduce(&beta) - p224Square(&gamma, &gamma, &c) - for i := 0; i < 8; i++ { - gamma[i] <<= 3 + x, y = Unmarshal(P224(), out) + if x == nil { + panic("crypto/elliptic: internal error: Unmarshal rejected a valid point encoding") } - p224Reduce(&gamma) - p224Mul(y3, &alpha, &beta, &c) - p224Sub(y3, y3, &gamma) - p224Reduce(y3) + return x, y } -// p224CopyConditional sets *out = *in iff the least-significant-bit of control -// is true, and it runs in constant time. -func p224CopyConditional(out, in *p224FieldElement, control uint32) { - control <<= 31 - control = uint32(int32(control) >> 31) - - for i := 0; i < 8; i++ { - out[i] ^= (out[i] ^ in[i]) & control +// p224RandomPoint returns a random point on the curve. It's used when Add, +// Double, or ScalarMult are fed a point not on the curve, which is undefined +// behavior. Originally, we used to do the math on it anyway (which allows +// invalid curve attacks) and relied on the caller and Unmarshal to avoid this +// happening in the first place. Now, we just can't construct a nistec.P224Point +// for an invalid pair of coordinates, because that API is safer. If we panic, +// we risk introducing a DoS. If we return nil, we risk a panic. If we return +// the input, ecdsa.Verify might fail open. The safest course seems to be to +// return a valid, random point, which hopefully won't help the attacker. +func p224RandomPoint() (x, y *big.Int) { + _, x, y, err := GenerateKey(P224(), rand.Reader) + if err != nil { + panic("crypto/elliptic: failed to generate random point") } + return x, y } -func p224ScalarMult(outX, outY, outZ, inX, inY, inZ *p224FieldElement, scalar []byte) { - var xx, yy, zz p224FieldElement - for i := 0; i < 8; i++ { - outX[i] = 0 - outY[i] = 0 - outZ[i] = 0 +func (p224Curve) Add(x1, y1, x2, y2 *big.Int) (*big.Int, *big.Int) { + p1, ok := p224PointFromAffine(x1, y1) + if !ok { + return p224RandomPoint() } - - for _, byte := range scalar { - for bitNum := uint(0); bitNum < 8; bitNum++ { - p224DoubleJacobian(outX, outY, outZ, outX, outY, outZ) - bit := uint32((byte >> (7 - bitNum)) & 1) - p224AddJacobian(&xx, &yy, &zz, inX, inY, inZ, outX, outY, outZ) - p224CopyConditional(outX, &xx, bit) - p224CopyConditional(outY, &yy, bit) - p224CopyConditional(outZ, &zz, bit) - } + p2, ok := p224PointFromAffine(x2, y2) + if !ok { + return p224RandomPoint() } + return p224PointToAffine(p1.Add(p1, p2)) } -// p224ToAffine converts from Jacobian to affine form. -func p224ToAffine(x, y, z *p224FieldElement) (*big.Int, *big.Int) { - var zinv, zinvsq, outx, outy p224FieldElement - var tmp p224LargeFieldElement - - if isPointAtInfinity := p224IsZero(z); isPointAtInfinity == 1 { - return new(big.Int), new(big.Int) +func (p224Curve) Double(x1, y1 *big.Int) (*big.Int, *big.Int) { + p, ok := p224PointFromAffine(x1, y1) + if !ok { + return p224RandomPoint() } - - p224Invert(&zinv, z) - p224Square(&zinvsq, &zinv, &tmp) - p224Mul(x, x, &zinvsq, &tmp) - p224Mul(&zinvsq, &zinvsq, &zinv, &tmp) - p224Mul(y, y, &zinvsq, &tmp) - - p224Contract(&outx, x) - p224Contract(&outy, y) - return p224ToBig(&outx), p224ToBig(&outy) + return p224PointToAffine(p.Double(p)) } -// get28BitsFromEnd returns the least-significant 28 bits from buf>>shift, -// where buf is interpreted as a big-endian number. -func get28BitsFromEnd(buf []byte, shift uint) (uint32, []byte) { - var ret uint32 - - for i := uint(0); i < 4; i++ { - var b byte - if l := len(buf); l > 0 { - b = buf[l-1] - // We don't remove the byte if we're about to return and we're not - // reading all of it. - if i != 3 || shift == 4 { - buf = buf[:l-1] - } - } - ret |= uint32(b) << (8 * i) >> shift +func (p224Curve) ScalarMult(Bx, By *big.Int, scalar []byte) (*big.Int, *big.Int) { + p, ok := p224PointFromAffine(Bx, By) + if !ok { + return p224RandomPoint() } - ret &= bottom28Bits - return ret, buf + return p224PointToAffine(p.ScalarMult(p, scalar)) } -// p224FromBig sets *out = *in. -func p224FromBig(out *p224FieldElement, in *big.Int) { - bytes := in.Bytes() - out[0], bytes = get28BitsFromEnd(bytes, 0) - out[1], bytes = get28BitsFromEnd(bytes, 4) - out[2], bytes = get28BitsFromEnd(bytes, 0) - out[3], bytes = get28BitsFromEnd(bytes, 4) - out[4], bytes = get28BitsFromEnd(bytes, 0) - out[5], bytes = get28BitsFromEnd(bytes, 4) - out[6], bytes = get28BitsFromEnd(bytes, 0) - out[7], bytes = get28BitsFromEnd(bytes, 4) -} - -// p224ToBig returns in as a big.Int. -func p224ToBig(in *p224FieldElement) *big.Int { - var buf [28]byte - buf[27] = byte(in[0]) - buf[26] = byte(in[0] >> 8) - buf[25] = byte(in[0] >> 16) - buf[24] = byte(((in[0] >> 24) & 0x0f) | (in[1]<<4)&0xf0) - - buf[23] = byte(in[1] >> 4) - buf[22] = byte(in[1] >> 12) - buf[21] = byte(in[1] >> 20) - - buf[20] = byte(in[2]) - buf[19] = byte(in[2] >> 8) - buf[18] = byte(in[2] >> 16) - buf[17] = byte(((in[2] >> 24) & 0x0f) | (in[3]<<4)&0xf0) - - buf[16] = byte(in[3] >> 4) - buf[15] = byte(in[3] >> 12) - buf[14] = byte(in[3] >> 20) - - buf[13] = byte(in[4]) - buf[12] = byte(in[4] >> 8) - buf[11] = byte(in[4] >> 16) - buf[10] = byte(((in[4] >> 24) & 0x0f) | (in[5]<<4)&0xf0) - - buf[9] = byte(in[5] >> 4) - buf[8] = byte(in[5] >> 12) - buf[7] = byte(in[5] >> 20) - - buf[6] = byte(in[6]) - buf[5] = byte(in[6] >> 8) - buf[4] = byte(in[6] >> 16) - buf[3] = byte(((in[6] >> 24) & 0x0f) | (in[7]<<4)&0xf0) - - buf[2] = byte(in[7] >> 4) - buf[1] = byte(in[7] >> 12) - buf[0] = byte(in[7] >> 20) - - return new(big.Int).SetBytes(buf[:]) +func (p224Curve) ScalarBaseMult(scalar []byte) (*big.Int, *big.Int) { + p := nistec.NewP224Generator() + return p224PointToAffine(p.ScalarMult(p, scalar)) } diff --git a/libgo/go/crypto/elliptic/p224_test.go b/libgo/go/crypto/elliptic/p224_test.go index b213b27..7971f63 100644 --- a/libgo/go/crypto/elliptic/p224_test.go +++ b/libgo/go/crypto/elliptic/p224_test.go @@ -8,313 +8,9 @@ import ( "encoding/hex" "fmt" "math/big" - "math/bits" - "math/rand" - "reflect" "testing" - "testing/quick" ) -var toFromBigTests = []string{ - "0", - "1", - "23", - "b70e0cb46bb4bf7f321390b94a03c1d356c01122343280d6105c1d21", - "706a46d476dcb76798e6046d89474788d164c18032d268fd10704fa6", -} - -func p224AlternativeToBig(in *p224FieldElement) *big.Int { - ret := new(big.Int) - tmp := new(big.Int) - - for i := len(in) - 1; i >= 0; i-- { - ret.Lsh(ret, 28) - tmp.SetInt64(int64(in[i])) - ret.Add(ret, tmp) - } - ret.Mod(ret, P224().Params().P) - return ret -} - -func TestP224ToFromBig(t *testing.T) { - for i, test := range toFromBigTests { - n, _ := new(big.Int).SetString(test, 16) - var x p224FieldElement - p224FromBig(&x, n) - m := p224ToBig(&x) - if n.Cmp(m) != 0 { - t.Errorf("#%d: %x != %x", i, n, m) - } - q := p224AlternativeToBig(&x) - if n.Cmp(q) != 0 { - t.Errorf("#%d: %x != %x (alternative)", i, n, q) - } - } -} - -// quickCheckConfig32 will make each quickcheck test run (32 * -quickchecks) -// times. The default value of -quickchecks is 100. -var quickCheckConfig32 = &quick.Config{MaxCountScale: 32} - -// weirdLimbs can be combined to generate a range of edge-case field elements. -var weirdLimbs = [...]uint32{ - 0, 1, (1 << 29) - 1, - (1 << 12), (1 << 12) - 1, - (1 << 28), (1 << 28) - 1, -} - -func generateLimb(rand *rand.Rand) uint32 { - const bottom29Bits = 0x1fffffff - n := rand.Intn(len(weirdLimbs) + 3) - switch n { - case len(weirdLimbs): - // Random value. - return uint32(rand.Int31n(1 << 29)) - case len(weirdLimbs) + 1: - // Sum of two values. - k := generateLimb(rand) + generateLimb(rand) - return k & bottom29Bits - case len(weirdLimbs) + 2: - // Difference of two values. - k := generateLimb(rand) - generateLimb(rand) - return k & bottom29Bits - default: - return weirdLimbs[n] - } -} - -func (p224FieldElement) Generate(rand *rand.Rand, size int) reflect.Value { - return reflect.ValueOf(p224FieldElement{ - generateLimb(rand), - generateLimb(rand), - generateLimb(rand), - generateLimb(rand), - generateLimb(rand), - generateLimb(rand), - generateLimb(rand), - generateLimb(rand), - }) -} - -func isInBounds(x *p224FieldElement) bool { - return bits.Len32(x[0]) <= 29 && - bits.Len32(x[1]) <= 29 && - bits.Len32(x[2]) <= 29 && - bits.Len32(x[3]) <= 29 && - bits.Len32(x[4]) <= 29 && - bits.Len32(x[5]) <= 29 && - bits.Len32(x[6]) <= 29 && - bits.Len32(x[7]) <= 29 -} - -func TestP224Mul(t *testing.T) { - mulMatchesBigInt := func(a, b, out p224FieldElement) bool { - var tmp p224LargeFieldElement - p224Mul(&out, &a, &b, &tmp) - - exp := new(big.Int).Mul(p224AlternativeToBig(&a), p224AlternativeToBig(&b)) - exp.Mod(exp, P224().Params().P) - got := p224AlternativeToBig(&out) - if exp.Cmp(got) != 0 || !isInBounds(&out) { - t.Logf("a = %x", a) - t.Logf("b = %x", b) - t.Logf("p224Mul(a, b) = %x = %v", out, got) - t.Logf("a * b = %v", exp) - return false - } - - return true - } - - a := p224FieldElement{0xfffffff, 0xfffffff, 0xf00ffff, 0x20f, 0x0, 0x0, 0x0, 0x0} - b := p224FieldElement{1, 0, 0, 0, 0, 0, 0, 0} - if !mulMatchesBigInt(a, b, p224FieldElement{}) { - t.Fail() - } - - if err := quick.Check(mulMatchesBigInt, quickCheckConfig32); err != nil { - t.Error(err) - } -} - -func TestP224Square(t *testing.T) { - squareMatchesBigInt := func(a, out p224FieldElement) bool { - var tmp p224LargeFieldElement - p224Square(&out, &a, &tmp) - - exp := p224AlternativeToBig(&a) - exp.Mul(exp, exp) - exp.Mod(exp, P224().Params().P) - got := p224AlternativeToBig(&out) - if exp.Cmp(got) != 0 || !isInBounds(&out) { - t.Logf("a = %x", a) - t.Logf("p224Square(a, b) = %x = %v", out, got) - t.Logf("a * a = %v", exp) - return false - } - - return true - } - - if err := quick.Check(squareMatchesBigInt, quickCheckConfig32); err != nil { - t.Error(err) - } -} - -func TestP224Add(t *testing.T) { - addMatchesBigInt := func(a, b, out p224FieldElement) bool { - p224Add(&out, &a, &b) - - exp := new(big.Int).Add(p224AlternativeToBig(&a), p224AlternativeToBig(&b)) - exp.Mod(exp, P224().Params().P) - got := p224AlternativeToBig(&out) - if exp.Cmp(got) != 0 { - t.Logf("a = %x", a) - t.Logf("b = %x", b) - t.Logf("p224Add(a, b) = %x = %v", out, got) - t.Logf("a + b = %v", exp) - return false - } - - return true - } - - if err := quick.Check(addMatchesBigInt, quickCheckConfig32); err != nil { - t.Error(err) - } -} - -func TestP224Reduce(t *testing.T) { - reduceMatchesBigInt := func(a p224FieldElement) bool { - out := a - // TODO: generate higher values for functions like p224Reduce that are - // expected to work with higher input bounds. - p224Reduce(&out) - - exp := p224AlternativeToBig(&a) - got := p224AlternativeToBig(&out) - if exp.Cmp(got) != 0 || !isInBounds(&out) { - t.Logf("a = %x = %v", a, exp) - t.Logf("p224Reduce(a) = %x = %v", out, got) - return false - } - - return true - } - - if err := quick.Check(reduceMatchesBigInt, quickCheckConfig32); err != nil { - t.Error(err) - } -} - -func TestP224Contract(t *testing.T) { - contractMatchesBigInt := func(a, out p224FieldElement) bool { - p224Contract(&out, &a) - - exp := p224AlternativeToBig(&a) - got := p224AlternativeToBig(&out) - if exp.Cmp(got) != 0 { - t.Logf("a = %x = %v", a, exp) - t.Logf("p224Contract(a) = %x = %v", out, got) - return false - } - - // Check that out < P. - for i := range p224P { - k := 8 - i - 1 - if out[k] > p224P[k] { - t.Logf("p224Contract(a) = %x", out) - return false - } - if out[k] < p224P[k] { - return true - } - } - t.Logf("p224Contract(a) = %x", out) - return false - } - - if !contractMatchesBigInt(p224P, p224FieldElement{}) { - t.Error("p224Contract(p) is broken") - } - pMinus1 := p224FieldElement{0, 0, 0, 0xffff000, 0xfffffff, 0xfffffff, 0xfffffff, 0xfffffff} - if !contractMatchesBigInt(pMinus1, p224FieldElement{}) { - t.Error("p224Contract(p - 1) is broken") - } - // Check that we can handle input above p, but lowest limb zero. - a := p224FieldElement{0, 1, 0, 0xffff000, 0xfffffff, 0xfffffff, 0xfffffff, 0xfffffff} - if !contractMatchesBigInt(a, p224FieldElement{}) { - t.Error("p224Contract(p + 2²⁸) is broken") - } - // Check that we can handle input above p, but lowest three limbs zero. - b := p224FieldElement{0, 0, 0, 0xffff001, 0xfffffff, 0xfffffff, 0xfffffff, 0xfffffff} - if !contractMatchesBigInt(b, p224FieldElement{}) { - t.Error("p224Contract(p + 2⁸⁴) is broken") - } - - if err := quick.Check(contractMatchesBigInt, quickCheckConfig32); err != nil { - t.Error(err) - } -} - -func TestP224IsZero(t *testing.T) { - if got := p224IsZero(&p224FieldElement{}); got != 1 { - t.Errorf("p224IsZero(0) = %d, expected 1", got) - } - if got := p224IsZero((*p224FieldElement)(&p224P)); got != 1 { - t.Errorf("p224IsZero(p) = %d, expected 1", got) - } - if got := p224IsZero(&p224FieldElement{1}); got != 0 { - t.Errorf("p224IsZero(1) = %d, expected 0", got) - } - - isZeroMatchesBigInt := func(a p224FieldElement) bool { - isZero := p224IsZero(&a) - - big := p224AlternativeToBig(&a) - if big.Sign() == 0 && isZero != 1 { - return false - } - if big.Sign() != 0 && isZero != 0 { - return false - } - return true - } - - if err := quick.Check(isZeroMatchesBigInt, quickCheckConfig32); err != nil { - t.Error(err) - } -} - -func TestP224Invert(t *testing.T) { - var out p224FieldElement - - p224Invert(&out, &p224FieldElement{}) - if got := p224IsZero(&out); got != 1 { - t.Errorf("p224Invert(0) = %x, expected 0", out) - } - - p224Invert(&out, (*p224FieldElement)(&p224P)) - if got := p224IsZero(&out); got != 1 { - t.Errorf("p224Invert(p) = %x, expected 0", out) - } - - p224Invert(&out, &p224FieldElement{1}) - p224Contract(&out, &out) - if out != (p224FieldElement{1}) { - t.Errorf("p224Invert(1) = %x, expected 1", out) - } - - var tmp p224LargeFieldElement - a := p224FieldElement{1, 2, 3, 4, 5, 6, 7, 8} - p224Invert(&out, &a) - p224Mul(&out, &out, &a, &tmp) - p224Contract(&out, &out) - if out != (p224FieldElement{1}) { - t.Errorf("p224Invert(a) * a = %x, expected 1", out) - } -} - type baseMultTest struct { k string x, y string @@ -602,7 +298,7 @@ func TestP224BaseMult(t *testing.T) { func TestP224GenericBaseMult(t *testing.T) { // We use the P224 CurveParams directly in order to test the generic implementation. - p224 := P224().Params() + p224 := genericParamsForCurve(P224()) for i, e := range p224BaseMultTests { k, ok := new(big.Int).SetString(e.k, 10) if !ok { diff --git a/libgo/go/crypto/elliptic/p256.go b/libgo/go/crypto/elliptic/p256.go index b05febd..1fbeb68 100644 --- a/libgo/go/crypto/elliptic/p256.go +++ b/libgo/go/crypto/elliptic/p256.go @@ -3,7 +3,6 @@ // license that can be found in the LICENSE file. //-go:build !amd64 && !arm64 -// -build !amd64,!arm64 package elliptic @@ -210,6 +209,8 @@ var p256Precomputed = [p256Limbs * 2 * 15 * 2]uint32{ // Field element operations: +const bottom28Bits = 0xfffffff + // nonZeroToAllOnes returns: // 0xffffffff for 0 < x <= 2**31 // 0 for x == 0 or x > 2**31. @@ -270,6 +271,7 @@ const ( two30m2 = 1<<30 - 1<<2 two30p13m2 = 1<<30 + 1<<13 - 1<<2 two31m2 = 1<<31 - 1<<2 + two31m3 = 1<<31 - 1<<3 two31p24m2 = 1<<31 + 1<<24 - 1<<2 two30m27m2 = 1<<30 - 1<<27 - 1<<2 ) diff --git a/libgo/go/crypto/elliptic/p256_asm.go b/libgo/go/crypto/elliptic/p256_asm.go index f530178..ac00429 100644 --- a/libgo/go/crypto/elliptic/p256_asm.go +++ b/libgo/go/crypto/elliptic/p256_asm.go @@ -10,8 +10,7 @@ // https://link.springer.com/article/10.1007%2Fs13389-014-0090-x // https://eprint.iacr.org/2013/816.pdf -//go:build ignore -// +build ignore +//go:build ignore && (amd64 || arm64) package elliptic @@ -19,6 +18,8 @@ import ( "math/big" ) +//go:generate go run -tags=tablegen gen_p256_table.go + type ( p256Curve struct { *CurveParams @@ -79,7 +80,7 @@ func p256LittleToBig(res []byte, in []uint64) func p256Select(point, table []uint64, idx int) //go:noescape -func p256SelectBase(point, table []uint64, idx int) +func p256SelectBase(point *[12]uint64, table string, idx int) // Montgomery multiplication modulo Ord(G) //go:noescape @@ -410,7 +411,7 @@ func boothW6(in uint) (int, int) { func (p *p256Point) p256BaseMult(scalar []uint64) { wvalue := (scalar[0] << 1) & 0x7f sel, sign := boothW6(uint(wvalue)) - p256SelectBase(p.xyz[0:8], p256Precomputed[0][0:], sel) + p256SelectBase(&p.xyz, p256Precomputed, sel) p256NegCond(p.xyz[4:8], sign) // (This is one, in the Montgomery domain.) @@ -437,7 +438,7 @@ func (p *p256Point) p256BaseMult(scalar []uint64) { } index += 6 sel, sign = boothW6(uint(wvalue)) - p256SelectBase(t0.xyz[0:8], p256Precomputed[i][0:], sel) + p256SelectBase(&t0.xyz, p256Precomputed[i*32*8*8:], sel) p256PointAddAffineAsm(p.xyz[0:12], p.xyz[0:12], t0.xyz[0:8], sign, sel, zero) zero |= sel } diff --git a/libgo/go/crypto/elliptic/p256_asm_table.go b/libgo/go/crypto/elliptic/p256_asm_table.go index 1d957bb..c0814ba5 100644 --- a/libgo/go/crypto/elliptic/p256_asm_table.go +++ b/libgo/go/crypto/elliptic/p256_asm_table.go @@ -2,1472 +2,1429 @@ // Use of this source code is governed by a BSD-style // license that can be found in the LICENSE file. -//go:build ignore -// +build ignore +// Generated by gen_p256_table.go. DO NOT EDIT. + +//go:build ignore && (amd64 || arm64) package elliptic -var p256Precomputed = &[43][32 * 8]uint64{ - { - 8784043285714375740, 8483257759279461889, 8789745728267363600, 1770019616739251654, 15992936863339206154, 10037038012062884956, 15197544864945402661, 9615747158586711429, - 9583737883674400333, 12279877754802111101, 8296198976379850969, 17778859909846088251, 3401986641240187301, 1525831644595056632, 1849003687033449918, 8702493044913179195, - 18423170064697770279, 12693387071620743675, 7398701556189346968, 2779682216903406718, 12703629940499916779, 6358598532389273114, 8683512038509439374, 15415938252666293255, - 8408419572923862476, 5066733120953500019, 926242532005776114, 6301489109130024811, 3285079390283344806, 1685054835664548935, 7740622190510199342, 9561507292862134371, - 13698695174800826869, 10442832251048252285, 10672604962207744524, 14485711676978308040, 16947216143812808464, 8342189264337602603, 3837253281927274344, 8331789856935110934, - 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16009534514129505275, 12481249112231139039, 10309390659262581143, 5782517315325366794, 16717384553294759530, 4578392002424884134, 239005024949492645, - 1836857790164349346, 11263074778654917115, 4786985732596838094, 10525445084936097674, 1484357665966453236, 3110871407036679558, 1668700683093601768, 2736269131339849752, - 9249362594190920246, 8088172462140746331, 4080107866285682736, 16205599538438551353, 18312943145606312277, 9100632964181080418, 3969991115337154345, 5340098959750368315, - 12122448407048035645, 2891250339380982359, 12794212052932523400, 7166035112141500392, 15777441312724841162, 4552528682229856831, 2210391301762911476, 16410254680957321386, - 6910044784455706429, 11951245774670922855, 207795885948948810, 3884359690300962405, 4578772752480772344, 2948797025787714138, 16774444535658202808, 1388183483009000463, - 16561979129019905420, 1881862411760441386, 15441950514711322010, 12933020223458438856, 5570341451312029630, 18172638959728259059, 9074261777549091198, 6171200053222754816, - 10126435102176037237, 1545112930055760251, 11563139991870561593, 10766754172364938834, 5116781688621052838, 14471715119500781375, 4724882615229687192, 10031687030722046325, - 15016829467434780812, 6777508689306592732, 3811682306063049290, 11475361222871876387, 6080948654298953274, 11612742274762615033, 5268311600240325047, 9147351973710519861, - 12130203770930472759, 3880998309361490881, 8807462332494735511, 9291388074337055133, 18165312304248982432, 12733144434841535979, 18090195697688236271, 5825342884125782172, - 13034385644450400616, 16498936039876211302, 13019014556329727588, 17911110193068084415, 2034190024798401134, 1526884555531436223, 8108814142164064795, 4075908755148182733, - 6404489603451030675, 16601749455344583377, 12907740667428956072, 8446383351289364752, 698035388979141580, 3593914367189873571, 6744392605914028800, 18168078953147292456, - 14484703498492722699, 6030798911934842161, 15931002029256202288, 13491601992324491240, 8585568434702372483, 9113555433818303018, 6375455514164501736, 1476639189214882947, - 5209683814158663472, 16895526973128357178, 10457488910391635027, 17530003042232440701, 4030542539553991812, 9445656287872984963, 4212489101708176016, 837886727556721620, - 2983790309644332360, 11276772732994425347, 1310621139116895737, 3131558545024164284, 3529698629777893989, 13271773334458143370, 8171825923423406479, 305718858162497191, - 12347543988562572522, 4315642616923374215, 17586477762860427847, 1037334149869395772, 18311071546005132724, 1489505092175764848, 8926409949339059078, 10260307609945070716, - 1253128470325829265, 917180526219408600, 10471425074479693158, 12658678264459355332, 8502334428811982364, 3789675096428271759, 4531393894096863308, 12176495757901795513, - 15081766794595471636, 3944913291385975654, 14507832069904091484, 3624606168811123851, 11476968507677098110, 1056328247986567681, 15246608002200052960, 6566558379177875405, - 652315099041528631, 4287214618428297946, 11730560225433863449, 7935915607867430686, 15979159466809939008, 9209839549459543141, 9501045239358734673, 15490773728258884277, - 14281001444503113096, 9253803478538227873, 3842669056581745692, 18399990656305827164, 11841387504710944221, 16052361836589007383, 831115622826254867, 8219898649601530197, - 2339128600785774471, 1426373723429876004, 3299581455481810683, 16966544600853047157, 8419320331267538738, 8376963013864643226, 1996128805959565963, 2376766970819731241, - 10963611841695254911, 2914831079289063424, 15884256460390936367, 8724520571578171796, 329402220949313078, 8905943304651682982, 1280899166177109409, 6980213851983339340, - 5524321102331478758, 2149164875175284006, 10897639484514200325, 14605181792035620644, 316829907946955098, 13776780818927038502, 18167912441745301047, 16845612593885106452, - 15817940025107036888, 14405005201957074368, 11647077937228007305, 13795438792777593442, 9813339145840642083, 13196196205982926907, 5981408724994946624, 12303812818084690125, - 11821409230485627325, 1934768678832528678, 15798397330147151183, 2089418311766868031, 16206123311846842647, 10276976147555604745, 14858750786699873336, 2500482310681473276, - 9502861285700748804, 12163827978530279544, 9383068907817479934, 5717811606328725851, 12416198015020836733, 15689586164720677894, 14337921697724349521, 9392403465642971279, - 6696074876763293236, 10302972695440286968, 16647054763285662245, 7841147641486000427, 10612636854719975349, 3592516733641215266, 14172459823963607855, 1290213042793222575, - }, -} +const p256Precomputed = "" + + + "\x3c\x14\xa9\x18\xd4\x30\xe7\x79" + "\x01\xb6\xed\x5f\xfc\x95\xba\x75" + "\x10\x25\x62\x77\x2b\x73\xfb\x79" + "\xc6\x55\x37\xa5\x76\x5f\x90\x18" + "\x0a\x56\x95\xce\x57\x53\xf2\xdd" + "\x5c\xe4\x19\xba\xe4\xb8\x4a\x8b" + "\x25\xf3\x21\xdd\x88\x86\xe8\xd2" + "\x85\x5d\x88\x25\x18\xff\x71\x85" + + "\x4d\xd6\xdd\x10\xd4\x46\x00\x85" + "\x7d\x82\x33\xa4\xc1\xe3\x6a\xaa" + "\xd9\x90\x14\x8d\x03\x05\x22\x73" + "\x3b\x3a\xcf\x3d\xe4\x32\xbb\xf6" + "\xa5\xe1\xbe\x61\xd3\x48\x36\x2f" + "\xf8\x6f\x23\xeb\xcb\xd7\x2c\x15" + "\xbe\x2d\x04\x92\x0e\xfb\xa8\x19" + "\x3b\x8a\x5b\x0a\x51\x77\xc5\x78" + + "\x27\xc1\xeb\x4e\x90\x3f\xac\xff" + "\xfb\x81\x7d\x08\x4a\xf8\x27\xb0" + "\x98\xbc\xcb\x87\xdd\x77\xad\x66" + "\x7e\x74\xff\xb6\x3f\x6a\x93\x26" + "\xeb\xa7\x83\xc9\x1f\x5c\x4c\xb0" + "\x1a\xfe\x61\x08\xad\x47\x3e\x58" + "\x8e\xe9\x2e\x1a\x31\x08\x82\x78" + "\x07\xcc\x87\xe5\x29\x6a\xf0\xd5" + + "\xcc\x8d\x91\x46\x0d\xb5\xb0\x74" + "\x73\xc1\x23\xc6\xed\xa6\x50\x46" + "\xf2\x0a\x10\xe8\xac\xac\xda\x0c" + "\x6b\x17\xb0\x41\xf5\x62\x73\x57" + "\xa6\xab\xcb\xe4\x4c\xf2\x96\x2d" + "\x47\xf4\xd6\xfa\x71\x84\x62\x17" + "\x2e\xd2\xdd\xe5\xde\x36\x6c\x6b" + "\x63\xb8\x5a\x4c\x39\x4c\xb1\x84" + + "\xf5\x61\x5c\xc4\xae\x8a\x1b\xbe" + "\x7d\x53\xb9\x94\x9a\x64\xec\x90" + "\x0c\xc2\x76\xd0\xaa\xb5\x1c\x94" + "\xc8\x23\x05\x89\x05\x96\x07\xc9" + "\x10\x4f\xba\xe7\x4a\x9b\x30\xeb" + "\x2b\x88\xeb\xe5\xef\x68\xc5\x73" + "\x68\x1f\x7a\x7e\x87\xa9\x40\x35" + "\x16\xe9\xd1\x2d\xbb\x76\xa0\x73" + + "\x4a\x66\x77\x3e\x37\x47\x39\x40" + "\x3e\xee\x6c\x34\x4f\x74\xae\x55" + "\xad\xa3\x17\x5b\x1a\x96\x0a\xd5" + "\x73\x36\x21\x54\x59\x4b\x07\x13" + "\x4b\xe4\x77\xd3\x20\x62\xd3\x93" + "\xb5\x14\xff\xad\x53\x2b\x9c\x29" + "\x11\x9f\x63\xef\x4c\xd4\x24\xf4" + "\x5f\xf7\x07\x4a\x6d\x91\xc9\xa4" + + "\x4f\x3b\x17\xa0\x4e\x35\x46\x07" + "\xf7\x00\x3c\xd2\x13\x02\xd2\x2b" + "\x08\xbb\x23\x0c\xb5\xaa\x3e\xf4" + "\x03\x3e\x12\xc3\x19\x51\xba\x13" + "\x4d\x9d\x5b\x3f\x30\xd0\x47\x28" + "\xdd\x7b\xa6\x5d\xf2\xf2\x42\x67" + "\x95\x41\xc9\x77\xdc\x3b\x93\xef" + "\x67\x08\x24\x6e\x15\xd9\xed\xea" + + "\x8f\xa7\x99\x94\xd1\x4c\xf1\x27" + "\x55\x34\x9b\x6f\xc5\xb5\x2a\x46" + "\x6b\xfc\x2c\xf0\x2a\xf0\x90\x8f" + "\x0d\x23\x65\xb2\x1e\x89\x63\xb7" + "\x77\x49\x2d\x53\xa9\xa3\x9d\xf5" + "\x15\xba\x9e\xcf\x7d\x32\xe3\x21" + "\xf0\xbb\x60\xbe\x84\x7b\x3c\x12" + "\x76\xdf\x06\x77\xf2\x12\xec\x56" + + "\xe8\x20\x4e\x26\x8f\x6e\xc9\x75" + "\x41\xa8\xa7\x59\xed\xbf\xe6\xab" + "\x00\xeb\xc8\x44\x04\x9c\xc0\x2c" + "\x6b\xe1\xc4\xf0\x80\x30\x5b\xe0" + "\x14\x33\x5f\xa4\x7a\x77\xb7\x1e" + "\xe3\x45\x5d\xce\xed\x7b\xaf\x56" + "\x1a\x2f\xb1\x88\x9a\x01\x6e\x2b" + "\x9b\x5f\x83\xfd\xcd\x59\x66\x08" + + "\xc8\x1e\xc2\x9d\xd1\xdb\x18\x2c" + "\x39\x81\xcf\x0f\x8a\x86\xf9\x98" + "\x49\x0b\x25\x48\xd6\x2c\x7d\x73" + "\x8f\x42\xb3\x24\x47\xc9\x61\xcc" + "\x76\x9e\xdd\x80\x78\x40\x2b\x0c" + "\x08\xbe\x3f\x38\x91\x89\x3a\xc4" + "\xd2\xe5\x9b\x77\x65\x2d\x7d\x5f" + "\xb5\x4a\x3b\xeb\x54\x9a\x71\x78" + + "\x04\xe4\x45\x62\x0a\x26\x7d\xea" + "\xe0\xdf\x7f\x6e\x95\x07\xe4\x9d" + "\xb5\x1a\xac\x8d\x15\xa4\xf3\x1f" + "\x73\x90\x9c\x64\xf1\x90\x70\x3e" + "\x88\x4e\x94\x2b\x61\x85\x76\x1a" + "\xc8\x61\x7f\xe5\x9e\x93\x0f\x25" + "\x3d\x64\xad\x1e\x89\xaa\x0d\x0c" + "\x8e\xb8\x25\xe1\x23\x00\x93\x68" + + "\x68\x77\x69\xd2\xa7\x1a\xb7\x04" + "\x33\x5a\x34\xca\xf5\xde\xde\xab" + "\x5e\x38\x37\xee\x9d\xd2\x09\x24" + "\x56\xe1\x83\xcb\x77\xdf\xe1\x4e" + "\x43\x5b\xbb\x1c\xd9\x12\xac\x0c" + "\x37\x56\x89\xca\xf6\xd2\x0e\x17" + "\x66\x6d\xde\x8a\xfa\x8c\x22\x28" + "\xca\x8a\x23\x53\x95\x7c\xf5\x7f" + + "\x09\xd7\x2e\x4b\x63\x25\xc4\xcc" + "\x0d\xd3\x6f\x85\x69\x67\x35\x0e" + "\x11\x98\x9e\x55\x3f\xd4\xbc\xbc" + "\x59\xb7\x95\x53\xac\x77\x84\x73" + "\x7f\xe1\x0e\xc0\x90\x2b\x75\x35" + "\xe3\xd2\x2e\x74\x90\x83\x74\x68" + "\xc1\x5b\x1f\xbd\x22\x64\xd0\x7c" + "\x97\xb7\xe7\xc9\x69\x87\xc0\xfb" + + "\x4a\x66\xcf\xb0\x5b\xa3\x42\xa2" + "\xe3\x07\x97\x7f\xf7\x48\x6e\x12" + "\x60\x26\x83\xc6\x54\xbf\x17\x17" + "\x2e\xc7\x12\xfd\x32\x73\xae\xfa" + "\x6b\x58\x5d\x99\xb7\x2d\xb5\x27" + "\xc2\x37\x22\x83\x9e\x56\x29\xbe" + "\xdb\xe7\x65\x2a\x3e\x19\xe4\xe8" + "\xbb\x1b\xaa\x2e\xdc\x06\x27\x15" + + "\x5b\x05\x60\xbc\xb7\xd8\xbc\x72" + "\x4b\x7e\xe2\x56\xee\x23\xcc\x03" + "\x70\x93\x81\xe4\x24\x74\x33\xee" + "\x09\xda\xd3\x0a\x43\x0e\xaa\xe2" + "\x5d\xc4\x83\x63\x4f\x52\xb8\x40" + "\x25\x1b\xa4\x42\x54\x35\x66\xd7" + "\x97\x47\x8a\x77\xde\xa6\xef\x64" + "\xf4\xad\x79\x70\x0a\x17\x42\x20" + + "\x80\xfb\xc6\x0b\x65\x0b\x8b\x80" + "\x6b\x2e\xfe\x3f\x75\xe0\x82\x58" + "\x49\xf5\x83\x2c\x7c\x2f\xef\xd5" + "\x23\xb7\x03\x91\x80\x3c\xd6\x54" + "\x9b\x3f\xa2\x52\xd6\x1b\xf1\xf2" + "\x87\x65\x0b\x4b\x19\xc3\x70\x36" + "\x9e\x0e\x58\xb1\x3b\x62\xc4\x55" + "\x20\xe2\xef\x01\xb2\xf7\xed\x64" + + "\x9d\x5c\x3c\xd5\xcb\x1d\x09\x97" + "\x7b\x17\x0a\xac\xb6\x24\x76\xf1" + "\xff\x2d\xfe\x2c\x75\x39\xf1\xb0" + "\x4e\x57\x7a\x6c\x0a\x5c\xa3\xc1" + "\x87\x99\xe7\x93\x46\x31\x7d\x22" + "\x0e\xb8\x9c\xe8\x30\xbf\x75\x05" + "\xbb\x83\x18\x0d\x7f\x24\x4e\x2f" + "\xd0\xc3\x74\x32\x26\x12\xd5\xeb" + + "\x7a\xa9\xad\x56\xc8\x51\x3e\x5f" + "\x3e\x40\x8b\x8f\x4d\x96\xfc\x4a" + "\x79\x29\x2e\x41\xab\x47\xf2\xa6" + "\xda\xeb\x80\x6f\x1b\xbd\x5a\x67" + "\x1d\x5a\x48\x5e\x72\xbd\xa2\x66" + "\x3c\x0b\x4f\x8f\xaf\x5c\x2a\x4b" + "\xba\x7b\x84\x1b\x7f\x92\x26\x26" + "\x4d\x39\x02\x05\xd9\xc7\x6f\x6c" + + "\xe8\x9a\x65\xa5\xba\x12\xa9\xfe" + "\x6e\xa1\xe1\x25\xba\x3a\x36\x68" + "\xac\x41\x2c\x75\x77\x22\x84\xb8" + "\xfc\xc3\x97\x28\x28\x5c\x54\xfe" + "\x6b\x69\x4c\xdc\xe7\xe9\x36\x2d" + "\xc5\x77\xa9\xfb\x4a\x24\x06\x58" + "\xc1\x08\x95\xe3\x9b\x5e\x66\x85" + "\x7b\x59\x12\x6d\x25\xee\x20\xf7" + + "\x31\x7a\x33\xd2\x29\x91\x97\x8a" + "\xdc\x2b\x86\x0f\x8f\x86\x16\x59" + "\xba\x83\xd2\x5d\xd9\x99\x80\x04" + "\x4e\xfb\x5b\xfe\xb6\xee\xd1\xe2" + "\x5d\x00\x84\x78\x41\x1c\xef\x82" + "\xae\xcb\xff\xff\x17\xec\xd4\xa2" + "\x66\x5e\xa9\x8a\x3f\xc5\x61\x91" + "\xd0\xe0\xfe\xc5\xe1\x04\xe1\x5e" + + "\x08\xb2\x35\xc1\xec\x4c\x2e\x56" + "\x7d\xf4\x83\x47\x65\xb2\xe1\x74" + "\x30\x3b\x3f\x5a\x6c\x50\x2a\x6d" + "\xfc\x62\x67\xc1\xf4\xd9\xea\xec" + "\xb9\xe5\x86\xe2\xb2\xd4\x9d\xf2" + "\x61\x3c\xbb\x83\xc0\xad\x0f\x1b" + "\xa4\x29\xac\x7f\x3e\x02\x75\x7a" + "\xa3\x7f\x47\xc9\xf1\xd5\x86\xc0" + + 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index f91108b..544362a 100644 --- a/libgo/go/crypto/elliptic/p256_asm_table_test.go +++ b/libgo/go/crypto/elliptic/p256_asm_table_test.go @@ -2,12 +2,12 @@ // Use of this source code is governed by a BSD-style // license that can be found in the LICENSE file. -//go:build ignore -// +build ignore +//go:build ignore && (amd64 || arm64) package elliptic import ( + "encoding/binary" "reflect" "testing" ) @@ -45,7 +45,12 @@ func TestP256PrecomputedTable(t *testing.T) { copy(t1[8:12], basePoint[8:12]) - if got, want := p256Precomputed[i][j*8:(j*8)+8], t1[:8]; !reflect.DeepEqual(got, want) { + buf := make([]byte, 8*8) + for i, u := range t1[:8] { + binary.LittleEndian.PutUint64(buf[i*8:i*8+8], u) + } + start := i*32*8*8 + j*8*8 + if got, want := p256Precomputed[start:start+64], string(buf); !reflect.DeepEqual(got, want) { t.Fatalf("Unexpected table entry at [%d][%d:%d]: got %v, want %v", i, j*8, (j*8)+8, got, want) } } diff --git a/libgo/go/crypto/elliptic/p256_generic.go b/libgo/go/crypto/elliptic/p256_generic.go index 48793f0..a92b9ca 100644 --- a/libgo/go/crypto/elliptic/p256_generic.go +++ b/libgo/go/crypto/elliptic/p256_generic.go @@ -3,7 +3,6 @@ // license that can be found in the LICENSE file. //-go:build !amd64 && !s390x && !arm64 && !ppc64le -// -build !amd64,!s390x,!arm64,!ppc64le package elliptic diff --git a/libgo/go/crypto/elliptic/p256_ppc64le.go b/libgo/go/crypto/elliptic/p256_ppc64le.go index 2af9d75..05e11fd 100644 --- a/libgo/go/crypto/elliptic/p256_ppc64le.go +++ b/libgo/go/crypto/elliptic/p256_ppc64le.go @@ -2,8 +2,7 @@ // Use of this source code is governed by a BSD-style // license that can be found in the LICENSE file. -//go:build ignore -// +build ignore +//go:build ignore && ppc64le package elliptic diff --git a/libgo/go/crypto/elliptic/p256_s390x.go b/libgo/go/crypto/elliptic/p256_s390x.go index 3b9a767..1220d68 100644 --- a/libgo/go/crypto/elliptic/p256_s390x.go +++ b/libgo/go/crypto/elliptic/p256_s390x.go @@ -2,8 +2,7 @@ // Use of this source code is governed by a BSD-style // license that can be found in the LICENSE file. -//go:build ignore -// +build ignore +//go:build ignore && s390x package elliptic diff --git a/libgo/go/crypto/elliptic/p256_test.go b/libgo/go/crypto/elliptic/p256_test.go index 1435f5e..c6862d9 100644 --- a/libgo/go/crypto/elliptic/p256_test.go +++ b/libgo/go/crypto/elliptic/p256_test.go @@ -34,7 +34,7 @@ var p256MultTests = []scalarMultTest{ func TestP256BaseMult(t *testing.T) { p256 := P256() - p256Generic := p256.Params() + p256Generic := genericParamsForCurve(p256) scalars := make([]*big.Int, 0, len(p224BaseMultTests)+1) for _, e := range p224BaseMultTests { @@ -60,23 +60,6 @@ func TestP256BaseMult(t *testing.T) { func TestP256Mult(t *testing.T) { p256 := P256() - p256Generic := p256.Params() - - for i, e := range p224BaseMultTests { - x, _ := new(big.Int).SetString(e.x, 16) - y, _ := new(big.Int).SetString(e.y, 16) - k, _ := new(big.Int).SetString(e.k, 10) - - xx, yy := p256.ScalarMult(x, y, k.Bytes()) - xx2, yy2 := p256Generic.ScalarMult(x, y, k.Bytes()) - if xx.Cmp(xx2) != 0 || yy.Cmp(yy2) != 0 { - t.Errorf("#%d: got (%x, %x), want (%x, %x)", i, xx, yy, xx2, yy2) - } - if testing.Short() && i > 5 { - break - } - } - for i, e := range p256MultTests { x, _ := new(big.Int).SetString(e.xIn, 16) y, _ := new(big.Int).SetString(e.yIn, 16) diff --git a/libgo/go/crypto/elliptic/p384.go b/libgo/go/crypto/elliptic/p384.go new file mode 100644 index 0000000..0fb7471 --- /dev/null +++ b/libgo/go/crypto/elliptic/p384.go @@ -0,0 +1,141 @@ +// Copyright 2013 The Go Authors. All rights reserved. +// Use of this source code is governed by a BSD-style +// license that can be found in the LICENSE file. + +package elliptic + +import ( + "crypto/elliptic/internal/nistec" + "crypto/rand" + "math/big" +) + +// p384Curve is a Curve implementation based on nistec.P384Point. +// +// It's a wrapper that exposes the big.Int-based Curve interface and encodes the +// legacy idiosyncrasies it requires, such as invalid and infinity point +// handling. +// +// To interact with the nistec package, points are encoded into and decoded from +// properly formatted byte slices. All big.Int use is limited to this package. +// Encoding and decoding is 1/1000th of the runtime of a scalar multiplication, +// so the overhead is acceptable. +type p384Curve struct { + params *CurveParams +} + +var p384 p384Curve +var _ Curve = p384 + +func initP384() { + p384.params = &CurveParams{ + Name: "P-384", + BitSize: 384, + // FIPS 186-4, section D.1.2.4 + P: bigFromDecimal("394020061963944792122790401001436138050797392704654" + + "46667948293404245721771496870329047266088258938001861606973112319"), + N: bigFromDecimal("394020061963944792122790401001436138050797392704654" + + "46667946905279627659399113263569398956308152294913554433653942643"), + B: bigFromHex("b3312fa7e23ee7e4988e056be3f82d19181d9c6efe8141120314088" + + "f5013875ac656398d8a2ed19d2a85c8edd3ec2aef"), + Gx: bigFromHex("aa87ca22be8b05378eb1c71ef320ad746e1d3b628ba79b9859f741" + + "e082542a385502f25dbf55296c3a545e3872760ab7"), + Gy: bigFromHex("3617de4a96262c6f5d9e98bf9292dc29f8f41dbd289a147ce9da31" + + "13b5f0b8c00a60b1ce1d7e819d7a431d7c90ea0e5f"), + } +} + +func (curve p384Curve) Params() *CurveParams { + return curve.params +} + +func (curve p384Curve) IsOnCurve(x, y *big.Int) bool { + // IsOnCurve is documented to reject (0, 0), the conventional point at + // infinity, which however is accepted by p384PointFromAffine. + if x.Sign() == 0 && y.Sign() == 0 { + return false + } + _, ok := p384PointFromAffine(x, y) + return ok +} + +func p384PointFromAffine(x, y *big.Int) (p *nistec.P384Point, ok bool) { + // (0, 0) is by convention the point at infinity, which can't be represented + // in affine coordinates. Marshal incorrectly encodes it as an uncompressed + // point, which SetBytes would correctly reject. See Issue 37294. + if x.Sign() == 0 && y.Sign() == 0 { + return nistec.NewP384Point(), true + } + if x.BitLen() > 384 || y.BitLen() > 384 { + return nil, false + } + p, err := nistec.NewP384Point().SetBytes(Marshal(P384(), x, y)) + if err != nil { + return nil, false + } + return p, true +} + +func p384PointToAffine(p *nistec.P384Point) (x, y *big.Int) { + out := p.Bytes() + if len(out) == 1 && out[0] == 0 { + // This is the correct encoding of the point at infinity, which + // Unmarshal does not support. See Issue 37294. + return new(big.Int), new(big.Int) + } + x, y = Unmarshal(P384(), out) + if x == nil { + panic("crypto/elliptic: internal error: Unmarshal rejected a valid point encoding") + } + return x, y +} + +// p384RandomPoint returns a random point on the curve. It's used when Add, +// Double, or ScalarMult are fed a point not on the curve, which is undefined +// behavior. Originally, we used to do the math on it anyway (which allows +// invalid curve attacks) and relied on the caller and Unmarshal to avoid this +// happening in the first place. Now, we just can't construct a nistec.P384Point +// for an invalid pair of coordinates, because that API is safer. If we panic, +// we risk introducing a DoS. If we return nil, we risk a panic. If we return +// the input, ecdsa.Verify might fail open. The safest course seems to be to +// return a valid, random point, which hopefully won't help the attacker. +func p384RandomPoint() (x, y *big.Int) { + _, x, y, err := GenerateKey(P384(), rand.Reader) + if err != nil { + panic("crypto/elliptic: failed to generate random point") + } + return x, y +} + +func (p384Curve) Add(x1, y1, x2, y2 *big.Int) (*big.Int, *big.Int) { + p1, ok := p384PointFromAffine(x1, y1) + if !ok { + return p384RandomPoint() + } + p2, ok := p384PointFromAffine(x2, y2) + if !ok { + return p384RandomPoint() + } + return p384PointToAffine(p1.Add(p1, p2)) +} + +func (p384Curve) Double(x1, y1 *big.Int) (*big.Int, *big.Int) { + p, ok := p384PointFromAffine(x1, y1) + if !ok { + return p384RandomPoint() + } + return p384PointToAffine(p.Double(p)) +} + +func (p384Curve) ScalarMult(Bx, By *big.Int, scalar []byte) (*big.Int, *big.Int) { + p, ok := p384PointFromAffine(Bx, By) + if !ok { + return p384RandomPoint() + } + return p384PointToAffine(p.ScalarMult(p, scalar)) +} + +func (p384Curve) ScalarBaseMult(scalar []byte) (*big.Int, *big.Int) { + p := nistec.NewP384Generator() + return p384PointToAffine(p.ScalarMult(p, scalar)) +} diff --git a/libgo/go/crypto/elliptic/p521.go b/libgo/go/crypto/elliptic/p521.go index 3d35594..6c9eed3 100644 --- a/libgo/go/crypto/elliptic/p521.go +++ b/libgo/go/crypto/elliptic/p521.go @@ -5,255 +5,158 @@ package elliptic import ( - "crypto/elliptic/internal/fiat" + "crypto/elliptic/internal/nistec" + "crypto/rand" "math/big" ) +// p521Curve is a Curve implementation based on nistec.P521Point. +// +// It's a wrapper that exposes the big.Int-based Curve interface and encodes the +// legacy idiosyncrasies it requires, such as invalid and infinity point +// handling. +// +// To interact with the nistec package, points are encoded into and decoded from +// properly formatted byte slices. All big.Int use is limited to this package. +// Encoding and decoding is 1/1000th of the runtime of a scalar multiplication, +// so the overhead is acceptable. type p521Curve struct { - *CurveParams + params *CurveParams } var p521 p521Curve -var p521Params *CurveParams +var _ Curve = p521 func initP521() { - // See FIPS 186-3, section D.2.5 - p521.CurveParams = &CurveParams{Name: "P-521"} - p521.P, _ = new(big.Int).SetString("6864797660130609714981900799081393217269435300143305409394463459185543183397656052122559640661454554977296311391480858037121987999716643812574028291115057151", 10) - p521.N, _ = new(big.Int).SetString("6864797660130609714981900799081393217269435300143305409394463459185543183397655394245057746333217197532963996371363321113864768612440380340372808892707005449", 10) - p521.B, _ = new(big.Int).SetString("051953eb9618e1c9a1f929a21a0b68540eea2da725b99b315f3b8b489918ef109e156193951ec7e937b1652c0bd3bb1bf073573df883d2c34f1ef451fd46b503f00", 16) - p521.Gx, _ = new(big.Int).SetString("c6858e06b70404e9cd9e3ecb662395b4429c648139053fb521f828af606b4d3dbaa14b5e77efe75928fe1dc127a2ffa8de3348b3c1856a429bf97e7e31c2e5bd66", 16) - p521.Gy, _ = new(big.Int).SetString("11839296a789a3bc0045c8a5fb42c7d1bd998f54449579b446817afbd17273e662c97ee72995ef42640c550b9013fad0761353c7086a272c24088be94769fd16650", 16) - p521.BitSize = 521 + p521.params = &CurveParams{ + Name: "P-521", + BitSize: 521, + // FIPS 186-4, section D.1.2.5 + P: bigFromDecimal("68647976601306097149819007990813932172694353001433" + + "0540939446345918554318339765605212255964066145455497729631139148" + + "0858037121987999716643812574028291115057151"), + N: bigFromDecimal("68647976601306097149819007990813932172694353001433" + + "0540939446345918554318339765539424505774633321719753296399637136" + + "3321113864768612440380340372808892707005449"), + B: bigFromHex("0051953eb9618e1c9a1f929a21a0b68540eea2da725b99b315f3b8" + + "b489918ef109e156193951ec7e937b1652c0bd3bb1bf073573df883d2c34f1ef" + + "451fd46b503f00"), + Gx: bigFromHex("00c6858e06b70404e9cd9e3ecb662395b4429c648139053fb521f8" + + "28af606b4d3dbaa14b5e77efe75928fe1dc127a2ffa8de3348b3c1856a429bf9" + + "7e7e31c2e5bd66"), + Gy: bigFromHex("011839296a789a3bc0045c8a5fb42c7d1bd998f54449579b446817" + + "afbd17273e662c97ee72995ef42640c550b9013fad0761353c7086a272c24088" + + "be94769fd16650"), + } } func (curve p521Curve) Params() *CurveParams { - return curve.CurveParams + return curve.params } func (curve p521Curve) IsOnCurve(x, y *big.Int) bool { - x1 := bigIntToFiatP521(x) - y1 := bigIntToFiatP521(y) - b := bigIntToFiatP521(curve.B) // TODO: precompute this value. - - // x³ - 3x + b. - x3 := new(fiat.P521Element).Square(x1) - x3.Mul(x3, x1) - - threeX := new(fiat.P521Element).Add(x1, x1) - threeX.Add(threeX, x1) - - x3.Sub(x3, threeX) - x3.Add(x3, b) - - // y² = x³ - 3x + b - y2 := new(fiat.P521Element).Square(y1) - - return x3.Equal(y2) == 1 -} - -type p521Point struct { - x, y, z *fiat.P521Element + // IsOnCurve is documented to reject (0, 0), the conventional point at + // infinity, which however is accepted by p521PointFromAffine. + if x.Sign() == 0 && y.Sign() == 0 { + return false + } + _, ok := p521PointFromAffine(x, y) + return ok } -func fiatP521ToBigInt(x *fiat.P521Element) *big.Int { - xBytes := x.Bytes() - for i := range xBytes[:len(xBytes)/2] { - xBytes[i], xBytes[len(xBytes)-i-1] = xBytes[len(xBytes)-i-1], xBytes[i] +func p521PointFromAffine(x, y *big.Int) (p *nistec.P521Point, ok bool) { + // (0, 0) is by convention the point at infinity, which can't be represented + // in affine coordinates. Marshal incorrectly encodes it as an uncompressed + // point, which SetBytes would correctly reject. See Issue 37294. + if x.Sign() == 0 && y.Sign() == 0 { + return nistec.NewP521Point(), true + } + if x.BitLen() > 521 || y.BitLen() > 521 { + return nil, false + } + p, err := nistec.NewP521Point().SetBytes(Marshal(P521(), x, y)) + if err != nil { + return nil, false } - return new(big.Int).SetBytes(xBytes) + return p, true } -// affineFromJacobian brings a point in Jacobian coordinates back to affine -// coordinates, with (0, 0) representing infinity by convention. It also goes -// back to big.Int values to match the exposed API. -func (curve p521Curve) affineFromJacobian(p *p521Point) (x, y *big.Int) { - if p.z.IsZero() == 1 { +func p521PointToAffine(p *nistec.P521Point) (x, y *big.Int) { + out := p.Bytes() + if len(out) == 1 && out[0] == 0 { + // This is the correct encoding of the point at infinity, which + // Unmarshal does not support. See Issue 37294. return new(big.Int), new(big.Int) } - - zinv := new(fiat.P521Element).Invert(p.z) - zinvsq := new(fiat.P521Element).Mul(zinv, zinv) - - xx := new(fiat.P521Element).Mul(p.x, zinvsq) - zinvsq.Mul(zinvsq, zinv) - yy := new(fiat.P521Element).Mul(p.y, zinvsq) - - return fiatP521ToBigInt(xx), fiatP521ToBigInt(yy) + x, y = Unmarshal(P521(), out) + if x == nil { + panic("crypto/elliptic: internal error: Unmarshal rejected a valid point encoding") + } + return x, y } -func bigIntToFiatP521(x *big.Int) *fiat.P521Element { - xBytes := new(big.Int).Mod(x, p521.P).FillBytes(make([]byte, 66)) - for i := range xBytes[:len(xBytes)/2] { - xBytes[i], xBytes[len(xBytes)-i-1] = xBytes[len(xBytes)-i-1], xBytes[i] - } - x1, err := new(fiat.P521Element).SetBytes(xBytes) +// p521RandomPoint returns a random point on the curve. It's used when Add, +// Double, or ScalarMult are fed a point not on the curve, which is undefined +// behavior. Originally, we used to do the math on it anyway (which allows +// invalid curve attacks) and relied on the caller and Unmarshal to avoid this +// happening in the first place. Now, we just can't construct a nistec.P521Point +// for an invalid pair of coordinates, because that API is safer. If we panic, +// we risk introducing a DoS. If we return nil, we risk a panic. If we return +// the input, ecdsa.Verify might fail open. The safest course seems to be to +// return a valid, random point, which hopefully won't help the attacker. +func p521RandomPoint() (x, y *big.Int) { + _, x, y, err := GenerateKey(P521(), rand.Reader) if err != nil { - // The input is reduced modulo P and encoded in a fixed size bytes - // slice, this should be impossible. - panic("internal error: bigIntToFiatP521") + panic("crypto/elliptic: failed to generate random point") } - return x1 + return x, y } -// jacobianFromAffine converts (x, y) affine coordinates into (x, y, z) Jacobian -// coordinates. It also converts from big.Int to fiat, which is necessarily a -// messy and variable-time operation, which we can't avoid due to the exposed API. -func (curve p521Curve) jacobianFromAffine(x, y *big.Int) *p521Point { - // (0, 0) is by convention the point at infinity, which can't be represented - // in affine coordinates, but is (0, 0, 0) in Jacobian. - if x.Sign() == 0 && y.Sign() == 0 { - return &p521Point{ - x: new(fiat.P521Element), - y: new(fiat.P521Element), - z: new(fiat.P521Element), - } +func (p521Curve) Add(x1, y1, x2, y2 *big.Int) (*big.Int, *big.Int) { + p1, ok := p521PointFromAffine(x1, y1) + if !ok { + return p521RandomPoint() } - return &p521Point{ - x: bigIntToFiatP521(x), - y: bigIntToFiatP521(y), - z: new(fiat.P521Element).One(), + p2, ok := p521PointFromAffine(x2, y2) + if !ok { + return p521RandomPoint() } + return p521PointToAffine(p1.Add(p1, p2)) } -func (curve p521Curve) Add(x1, y1, x2, y2 *big.Int) (*big.Int, *big.Int) { - p1 := curve.jacobianFromAffine(x1, y1) - p2 := curve.jacobianFromAffine(x2, y2) - return curve.affineFromJacobian(p1.addJacobian(p1, p2)) -} - -// addJacobian sets q = p1 + p2, and returns q. The points may overlap. -func (q *p521Point) addJacobian(p1, p2 *p521Point) *p521Point { - // https://hyperelliptic.org/EFD/g1p/auto-shortw-jacobian-3.html#addition-add-2007-bl - z1IsZero := p1.z.IsZero() - z2IsZero := p2.z.IsZero() - - z1z1 := new(fiat.P521Element).Square(p1.z) - z2z2 := new(fiat.P521Element).Square(p2.z) - - u1 := new(fiat.P521Element).Mul(p1.x, z2z2) - u2 := new(fiat.P521Element).Mul(p2.x, z1z1) - h := new(fiat.P521Element).Sub(u2, u1) - xEqual := h.IsZero() == 1 - i := new(fiat.P521Element).Add(h, h) - i.Square(i) - j := new(fiat.P521Element).Mul(h, i) - - s1 := new(fiat.P521Element).Mul(p1.y, p2.z) - s1.Mul(s1, z2z2) - s2 := new(fiat.P521Element).Mul(p2.y, p1.z) - s2.Mul(s2, z1z1) - r := new(fiat.P521Element).Sub(s2, s1) - yEqual := r.IsZero() == 1 - if xEqual && yEqual && z1IsZero == 0 && z2IsZero == 0 { - return q.doubleJacobian(p1) +func (p521Curve) Double(x1, y1 *big.Int) (*big.Int, *big.Int) { + p, ok := p521PointFromAffine(x1, y1) + if !ok { + return p521RandomPoint() } - r.Add(r, r) - v := new(fiat.P521Element).Mul(u1, i) - - x := new(fiat.P521Element).Set(r) - x.Square(x) - x.Sub(x, j) - x.Sub(x, v) - x.Sub(x, v) - - y := new(fiat.P521Element).Set(r) - v.Sub(v, x) - y.Mul(y, v) - s1.Mul(s1, j) - s1.Add(s1, s1) - y.Sub(y, s1) - - z := new(fiat.P521Element).Add(p1.z, p2.z) - z.Square(z) - z.Sub(z, z1z1) - z.Sub(z, z2z2) - z.Mul(z, h) - - x.Select(p2.x, x, z1IsZero) - x.Select(p1.x, x, z2IsZero) - y.Select(p2.y, y, z1IsZero) - y.Select(p1.y, y, z2IsZero) - z.Select(p2.z, z, z1IsZero) - z.Select(p1.z, z, z2IsZero) - - q.x.Set(x) - q.y.Set(y) - q.z.Set(z) - return q + return p521PointToAffine(p.Double(p)) } -func (curve p521Curve) Double(x1, y1 *big.Int) (*big.Int, *big.Int) { - p := curve.jacobianFromAffine(x1, y1) - return curve.affineFromJacobian(p.doubleJacobian(p)) +func (p521Curve) ScalarMult(Bx, By *big.Int, scalar []byte) (*big.Int, *big.Int) { + p, ok := p521PointFromAffine(Bx, By) + if !ok { + return p521RandomPoint() + } + return p521PointToAffine(p.ScalarMult(p, scalar)) } -// doubleJacobian sets q = p + p, and returns q. The points may overlap. -func (q *p521Point) doubleJacobian(p *p521Point) *p521Point { - // https://hyperelliptic.org/EFD/g1p/auto-shortw-jacobian-3.html#doubling-dbl-2001-b - delta := new(fiat.P521Element).Square(p.z) - gamma := new(fiat.P521Element).Square(p.y) - alpha := new(fiat.P521Element).Sub(p.x, delta) - alpha2 := new(fiat.P521Element).Add(p.x, delta) - alpha.Mul(alpha, alpha2) - alpha2.Set(alpha) - alpha.Add(alpha, alpha) - alpha.Add(alpha, alpha2) - - beta := alpha2.Mul(p.x, gamma) - - q.x.Square(alpha) - beta8 := new(fiat.P521Element).Add(beta, beta) - beta8.Add(beta8, beta8) - beta8.Add(beta8, beta8) - q.x.Sub(q.x, beta8) - - q.z.Add(p.y, p.z) - q.z.Square(q.z) - q.z.Sub(q.z, gamma) - q.z.Sub(q.z, delta) - - beta.Add(beta, beta) - beta.Add(beta, beta) - beta.Sub(beta, q.x) - q.y.Mul(alpha, beta) - - gamma.Square(gamma) - gamma.Add(gamma, gamma) - gamma.Add(gamma, gamma) - gamma.Add(gamma, gamma) - - q.y.Sub(q.y, gamma) - - return q +func (p521Curve) ScalarBaseMult(scalar []byte) (*big.Int, *big.Int) { + p := nistec.NewP521Generator() + return p521PointToAffine(p.ScalarMult(p, scalar)) } -func (curve p521Curve) ScalarMult(Bx, By *big.Int, scalar []byte) (*big.Int, *big.Int) { - B := curve.jacobianFromAffine(Bx, By) - p, t := &p521Point{ - x: new(fiat.P521Element), - y: new(fiat.P521Element), - z: new(fiat.P521Element), - }, &p521Point{ - x: new(fiat.P521Element), - y: new(fiat.P521Element), - z: new(fiat.P521Element), - } - - for _, byte := range scalar { - for bitNum := 0; bitNum < 8; bitNum++ { - p.doubleJacobian(p) - bit := (byte >> (7 - bitNum)) & 1 - t.addJacobian(p, B) - p.x.Select(t.x, p.x, int(bit)) - p.y.Select(t.y, p.y, int(bit)) - p.z.Select(t.z, p.z, int(bit)) - } +func bigFromDecimal(s string) *big.Int { + b, ok := new(big.Int).SetString(s, 10) + if !ok { + panic("invalid encoding") } - - return curve.affineFromJacobian(p) + return b } -func (curve p521Curve) ScalarBaseMult(k []byte) (*big.Int, *big.Int) { - return curve.ScalarMult(curve.Gx, curve.Gy, k) +func bigFromHex(s string) *big.Int { + b, ok := new(big.Int).SetString(s, 16) + if !ok { + panic("invalid encoding") + } + return b } |