Binary field arithmetic contributed by Sun Microsystems.

The 'OPENSSL_NO_SUN_DIV' default is still subject to change,
so I didn't bother to finish the CHANGES entry yet.

Submitted by: Douglas Stebila <douglas.stebila@sun.com>, Sheueling Chang <sheueling.chang@sun.com>
(CHANGES entry by Bodo Moeller)

5 files changed, 1716 insertions, 3 deletions

diff --git a/crypto/bn/Makefile.ssl b/crypto/bn/Makefile.ssl
index 46663d3..c8bfa7f 100644
--- a/crypto/bn/Makefile.ssl
+++ b/crypto/bn/Makefile.ssl
@@ -39,12 +39,12 @@ LIB=$(TOP)/libcrypto.a
 LIBSRC=	bn_add.c bn_div.c bn_exp.c bn_lib.c bn_ctx.c bn_mul.c bn_mod.c \
 	bn_print.c bn_rand.c bn_shift.c bn_word.c bn_blind.c \
 	bn_kron.c bn_sqrt.c bn_gcd.c bn_prime.c bn_err.c bn_sqr.c bn_asm.c \
-	bn_recp.c bn_mont.c bn_mpi.c bn_exp2.c
+	bn_recp.c bn_mont.c bn_mpi.c bn_exp2.c bn_gf2m.c
 
 LIBOBJ=	bn_add.o bn_div.o bn_exp.o bn_lib.o bn_ctx.o bn_mul.o bn_mod.o \
 	bn_print.o bn_rand.o bn_shift.o bn_word.o bn_blind.o \
 	bn_kron.o bn_sqrt.o bn_gcd.o bn_prime.o bn_err.o bn_sqr.o $(BN_ASM) \
-	bn_recp.o bn_mont.o bn_mpi.o bn_exp2.o
+	bn_recp.o bn_mont.o bn_mpi.o bn_exp2.o bn_gf2m.o
 
 SRC= $(LIBSRC)
 
@@ -194,6 +194,13 @@ bn_asm.o: ../../include/openssl/lhash.h ../../include/openssl/opensslconf.h
 bn_asm.o: ../../include/openssl/opensslv.h ../../include/openssl/safestack.h
 bn_asm.o: ../../include/openssl/stack.h ../../include/openssl/symhacks.h
 bn_asm.o: ../cryptlib.h bn_asm.c bn_lcl.h
+bn_gf2m.o: ../../e_os.h ../../include/openssl/bio.h ../../include/openssl/bn.h
+bn_gf2m.o: ../../include/openssl/buffer.h ../../include/openssl/crypto.h
+bn_gf2m.o: ../../include/openssl/e_os2.h ../../include/openssl/err.h
+bn_gf2m.o: ../../include/openssl/lhash.h ../../include/openssl/opensslconf.h
+bn_gf2m.o: ../../include/openssl/opensslv.h ../../include/openssl/safestack.h
+bn_gf2m.o: ../../include/openssl/stack.h ../../include/openssl/symhacks.h
+bn_gf2m.o: ../cryptlib.h bn_gf2m.c bn_lcl.h
 bn_blind.o: ../../e_os.h ../../include/openssl/bio.h ../../include/openssl/bn.h
 bn_blind.o: ../../include/openssl/buffer.h ../../include/openssl/crypto.h
 bn_blind.o: ../../include/openssl/e_os2.h ../../include/openssl/err.h
diff --git a/crypto/bn/bn.h b/crypto/bn/bn.h
index 1eaf879..ce2e746 100644
--- a/crypto/bn/bn.h
+++ b/crypto/bn/bn.h
@@ -55,6 +55,32 @@
  * copied and put under another distribution licence
  * [including the GNU Public Licence.]
  */
+/* ====================================================================
+ * Copyright 2002 Sun Microsystems, Inc. ALL RIGHTS RESERVED.
+ *
+ * Portions of the attached software ("Contribution") are developed by 
+ * SUN MICROSYSTEMS, INC., and are contributed to the OpenSSL project.
+ *
+ * The Contribution is licensed pursuant to the Eric Young open source
+ * license provided above.
+ *
+ * In addition, Sun covenants to all licensees who provide a reciprocal
+ * covenant with respect to their own patents if any, not to sue under
+ * current and future patent claims necessarily infringed by the making,
+ * using, practicing, selling, offering for sale and/or otherwise
+ * disposing of the Contribution as delivered hereunder 
+ * (or portions thereof), provided that such covenant shall not apply:
+ *  1) for code that a licensee deletes from the Contribution;
+ *  2) separates from the Contribution; or
+ *  3) for infringements caused by:
+ *       i) the modification of the Contribution or
+ *      ii) the combination of the  Contribution with other software or
+ *          devices where such combination causes the infringement.
+ *
+ * The binary polynomial arithmetic software is originally written by 
+ * Sheueling Chang Shantz and Douglas Stebila of Sun Microsystems Laboratories.
+ *
+ */
 
 #ifndef HEADER_BN_H
 #define HEADER_BN_H
@@ -453,6 +479,40 @@ int	BN_mod_exp_recp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
 int	BN_div_recp(BIGNUM *dv, BIGNUM *rem, const BIGNUM *m,
 	BN_RECP_CTX *recp, BN_CTX *ctx);
 
+/* Functions for arithmetic over binary polynomials represented by BIGNUMs. 
+ *
+ * The BIGNUM::neg property of BIGNUMs representing binary polynomials is ignored.
+ *
+ * Note that input arguments are not const so that their bit arrays can
+ * be expanded to the appropriate size if needed.
+ */
+int	BN_GF2m_add(BIGNUM *r, const BIGNUM *a, const BIGNUM *b); /* r = a + b */
+#define BN_GF2m_sub(r, a, b) BN_GF2m_add(r, a, b)
+int	BN_GF2m_mod(BIGNUM *r, const BIGNUM *a, const BIGNUM *p); /* r = a mod p */
+int	BN_GF2m_mod_mul(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, const BIGNUM *p, BN_CTX *ctx); /* r = (a * b) mod p */
+int	BN_GF2m_mod_sqr(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx); /* r = (a * a) mod p */
+int BN_GF2m_mod_inv(BIGNUM *r, const BIGNUM *b, const BIGNUM *p, BN_CTX *ctx); /* r = (1 / b) mod p */
+int BN_GF2m_mod_div(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, const BIGNUM *p, BN_CTX *ctx); /* r = (a / b) mod p */
+int BN_GF2m_mod_exp(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, const BIGNUM *p, BN_CTX *ctx); /* r = (a ^ b) mod p */
+int BN_GF2m_mod_sqrt(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx); /* r = sqrt(a) mod p */
+int BN_GF2m_mod_solve_quad(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx); /* r^2 + r = a mod p */
+#define BN_GF2m_cmp(a, b) BN_ucmp((a), (b))
+/* Some functions allow for representation of the irreducible polynomials
+ * as an unsigned int[], say p.  The irreducible f(t) is then of the form:
+ *     t^p[0] + t^p[1] + ... + t^p[k]
+ * where m = p[0] > p[1] > ... > p[k] = 0.
+ */
+int	BN_GF2m_mod_arr(BIGNUM *r, const BIGNUM *a, const unsigned int p[]); /* r = a mod p */
+int	BN_GF2m_mod_mul_arr(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, const unsigned int p[], BN_CTX *ctx); /* r = (a * b) mod p */
+int	BN_GF2m_mod_sqr_arr(BIGNUM *r, const BIGNUM *a, const unsigned int p[], BN_CTX *ctx); /* r = (a * a) mod p */
+int BN_GF2m_mod_inv_arr(BIGNUM *r, const BIGNUM *b, const unsigned int p[], BN_CTX *ctx); /* r = (1 / b) mod p */
+int BN_GF2m_mod_div_arr(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, const unsigned int p[], BN_CTX *ctx); /* r = (a / b) mod p */
+int BN_GF2m_mod_exp_arr(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, const unsigned int p[], BN_CTX *ctx); /* r = (a ^ b) mod p */
+int BN_GF2m_mod_sqrt_arr(BIGNUM *r, const BIGNUM *a, const unsigned int p[], BN_CTX *ctx); /* r = sqrt(a) mod p */
+int BN_GF2m_mod_solve_quad_arr(BIGNUM *r, const BIGNUM *a, const unsigned int p[], BN_CTX *ctx); /* r^2 + r = a mod p */
+int BN_GF2m_poly2arr(const BIGNUM *a, unsigned int p[], int max);
+int BN_GF2m_arr2poly(const unsigned int p[], BIGNUM *a);
+
 /* library internal functions */
 
 #define bn_expand(a,bits) ((((((bits+BN_BITS2-1))/BN_BITS2)) <= (a)->dmax)?\
@@ -510,6 +570,13 @@ void ERR_load_BN_strings(void);
 #define BN_F_BN_DIV					 107
 #define BN_F_BN_EXPAND2					 108
 #define BN_F_BN_EXPAND_INTERNAL				 120
+#define BN_F_BN_GF2M_MOD				 126
+#define BN_F_BN_GF2M_MOD_DIV				 123
+#define BN_F_BN_GF2M_MOD_EXP				 127
+#define BN_F_BN_GF2M_MOD_MUL				 124
+#define BN_F_BN_GF2M_MOD_SOLVE_QUAD			 128
+#define BN_F_BN_GF2M_MOD_SOLVE_QUAD_ARR			 129
+#define BN_F_BN_GF2M_MOD_SQR				 125
 #define BN_F_BN_MOD_EXP2_MONT				 118
 #define BN_F_BN_MOD_EXP_MONT				 109
 #define BN_F_BN_MOD_EXP_MONT_WORD			 117
@@ -535,6 +602,7 @@ void ERR_load_BN_strings(void);
 #define BN_R_INVALID_LENGTH				 106
 #define BN_R_INVALID_RANGE				 115
 #define BN_R_NOT_A_SQUARE				 111
+#define BN_R_NOT_IMPLEMENTED				 116
 #define BN_R_NOT_INITIALIZED				 107
 #define BN_R_NO_INVERSE					 108
 #define BN_R_P_IS_NOT_PRIME				 112
diff --git a/crypto/bn/bn_err.c b/crypto/bn/bn_err.c
index fb84ee9..bcc7ff9 100644
--- a/crypto/bn/bn_err.c
+++ b/crypto/bn/bn_err.c
@@ -1,6 +1,6 @@
 /* crypto/bn/bn_err.c */
 /* ====================================================================
- * Copyright (c) 1999 The OpenSSL Project.  All rights reserved.
+ * Copyright (c) 1999-2002 The OpenSSL Project.  All rights reserved.
  *
  * Redistribution and use in source and binary forms, with or without
  * modification, are permitted provided that the following conditions
@@ -77,6 +77,13 @@ static ERR_STRING_DATA BN_str_functs[]=
 {ERR_PACK(0,BN_F_BN_DIV,0),	"BN_div"},
 {ERR_PACK(0,BN_F_BN_EXPAND2,0),	"bn_expand2"},
 {ERR_PACK(0,BN_F_BN_EXPAND_INTERNAL,0),	"BN_EXPAND_INTERNAL"},
+{ERR_PACK(0,BN_F_BN_GF2M_MOD,0),	"BN_GF2m_mod"},
+{ERR_PACK(0,BN_F_BN_GF2M_MOD_DIV,0),	"BN_GF2m_mod_div"},
+{ERR_PACK(0,BN_F_BN_GF2M_MOD_EXP,0),	"BN_GF2m_mod_exp"},
+{ERR_PACK(0,BN_F_BN_GF2M_MOD_MUL,0),	"BN_GF2m_mod_mul"},
+{ERR_PACK(0,BN_F_BN_GF2M_MOD_SOLVE_QUAD,0),	"BN_GF2m_mod_solve_quad"},
+{ERR_PACK(0,BN_F_BN_GF2M_MOD_SOLVE_QUAD_ARR,0),	"BN_GF2m_mod_solve_quad_arr"},
+{ERR_PACK(0,BN_F_BN_GF2M_MOD_SQR,0),	"BN_GF2m_mod_sqr"},
 {ERR_PACK(0,BN_F_BN_MOD_EXP2_MONT,0),	"BN_mod_exp2_mont"},
 {ERR_PACK(0,BN_F_BN_MOD_EXP_MONT,0),	"BN_mod_exp_mont"},
 {ERR_PACK(0,BN_F_BN_MOD_EXP_MONT_WORD,0),	"BN_mod_exp_mont_word"},
@@ -105,6 +112,7 @@ static ERR_STRING_DATA BN_str_reasons[]=
 {BN_R_INVALID_LENGTH                     ,"invalid length"},
 {BN_R_INVALID_RANGE                      ,"invalid range"},
 {BN_R_NOT_A_SQUARE                       ,"not a square"},
+{BN_R_NOT_IMPLEMENTED                    ,"not implemented"},
 {BN_R_NOT_INITIALIZED                    ,"not initialized"},
 {BN_R_NO_INVERSE                         ,"no inverse"},
 {BN_R_P_IS_NOT_PRIME                     ,"p is not prime"},
diff --git a/crypto/bn/bn_gf2m.c b/crypto/bn/bn_gf2m.c
new file mode 100644
index 0000000..ed8e704
--- /dev/null
+++ b/crypto/bn/bn_gf2m.c
@@ -0,0 +1,984 @@
+/* crypto/bn/bn_gf2m.c */
+/* ====================================================================
+ * Copyright 2002 Sun Microsystems, Inc. ALL RIGHTS RESERVED.
+ *
+ * The Elliptic Curve Public-Key Crypto Library (ECC Code) included
+ * herein is developed by SUN MICROSYSTEMS, INC., and is contributed
+ * to the OpenSSL project.
+ *
+ * The ECC Code is licensed pursuant to the OpenSSL open source
+ * license provided below.
+ *
+ * In addition, Sun covenants to all licensees who provide a reciprocal
+ * covenant with respect to their own patents if any, not to sue under
+ * current and future patent claims necessarily infringed by the making,
+ * using, practicing, selling, offering for sale and/or otherwise
+ * disposing of the ECC Code as delivered hereunder (or portions thereof),
+ * provided that such covenant shall not apply:
+ *  1) for code that a licensee deletes from the ECC Code;
+ *  2) separates from the ECC Code; or
+ *  3) for infringements caused by:
+ *       i) the modification of the ECC Code or
+ *      ii) the combination of the ECC Code with other software or
+ *          devices where such combination causes the infringement.
+ *
+ * The software is originally written by Sheueling Chang Shantz and
+ * Douglas Stebila of Sun Microsystems Laboratories.
+ *
+ */
+
+/* ====================================================================
+ * Copyright (c) 1998-2002 The OpenSSL Project.  All rights reserved.
+ *
+ * Redistribution and use in source and binary forms, with or without
+ * modification, are permitted provided that the following conditions
+ * are met:
+ *
+ * 1. Redistributions of source code must retain the above copyright
+ *    notice, this list of conditions and the following disclaimer. 
+ *
+ * 2. Redistributions in binary form must reproduce the above copyright
+ *    notice, this list of conditions and the following disclaimer in
+ *    the documentation and/or other materials provided with the
+ *    distribution.
+ *
+ * 3. All advertising materials mentioning features or use of this
+ *    software must display the following acknowledgment:
+ *    "This product includes software developed by the OpenSSL Project
+ *    for use in the OpenSSL Toolkit. (http://www.openssl.org/)"
+ *
+ * 4. The names "OpenSSL Toolkit" and "OpenSSL Project" must not be used to
+ *    endorse or promote products derived from this software without
+ *    prior written permission. For written permission, please contact
+ *    openssl-core@openssl.org.
+ *
+ * 5. Products derived from this software may not be called "OpenSSL"
+ *    nor may "OpenSSL" appear in their names without prior written
+ *    permission of the OpenSSL Project.
+ *
+ * 6. Redistributions of any form whatsoever must retain the following
+ *    acknowledgment:
+ *    "This product includes software developed by the OpenSSL Project
+ *    for use in the OpenSSL Toolkit (http://www.openssl.org/)"
+ *
+ * THIS SOFTWARE IS PROVIDED BY THE OpenSSL PROJECT ``AS IS'' AND ANY
+ * EXPRESSED OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
+ * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
+ * PURPOSE ARE DISCLAIMED.  IN NO EVENT SHALL THE OpenSSL PROJECT OR
+ * ITS CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
+ * SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
+ * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
+ * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
+ * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT,
+ * STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
+ * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED
+ * OF THE POSSIBILITY OF SUCH DAMAGE.
+ * ====================================================================
+ *
+ * This product includes cryptographic software written by Eric Young
+ * (eay@cryptsoft.com).  This product includes software written by Tim
+ * Hudson (tjh@cryptsoft.com).
+ *
+ */
+
+#include <assert.h>
+#include <limits.h>
+#include <stdio.h>
+#include "cryptlib.h"
+#include "bn_lcl.h"
+
+/* Maximum number of iterations before BN_GF2m_mod_solve_quad_arr should fail. */
+#define MAX_ITERATIONS 50
+
+static const BN_ULONG SQR_tb[16] =
+  {     0,     1,     4,     5,    16,    17,    20,    21,
+       64,    65,    68,    69,    80,    81,    84,    85 };
+/* Platform-specific macros to accelerate squaring. */
+#if defined(SIXTY_FOUR_BIT) || defined(SIXTY_FOUR_BIT_LONG)
+#define SQR1(w) \
+    SQR_tb[(w) >> 60 & 0xF] << 56 | SQR_tb[(w) >> 56 & 0xF] << 48 | \
+    SQR_tb[(w) >> 52 & 0xF] << 40 | SQR_tb[(w) >> 48 & 0xF] << 32 | \
+    SQR_tb[(w) >> 44 & 0xF] << 24 | SQR_tb[(w) >> 40 & 0xF] << 16 | \
+    SQR_tb[(w) >> 36 & 0xF] <<  8 | SQR_tb[(w) >> 32 & 0xF]
+#define SQR0(w) \
+    SQR_tb[(w) >> 28 & 0xF] << 56 | SQR_tb[(w) >> 24 & 0xF] << 48 | \
+    SQR_tb[(w) >> 20 & 0xF] << 40 | SQR_tb[(w) >> 16 & 0xF] << 32 | \
+    SQR_tb[(w) >> 12 & 0xF] << 24 | SQR_tb[(w) >>  8 & 0xF] << 16 | \
+    SQR_tb[(w) >>  4 & 0xF] <<  8 | SQR_tb[(w)       & 0xF]
+#endif
+#ifdef THIRTY_TWO_BIT
+#define SQR1(w) \
+    SQR_tb[(w) >> 28 & 0xF] << 24 | SQR_tb[(w) >> 24 & 0xF] << 16 | \
+    SQR_tb[(w) >> 20 & 0xF] <<  8 | SQR_tb[(w) >> 16 & 0xF]
+#define SQR0(w) \
+    SQR_tb[(w) >> 12 & 0xF] << 24 | SQR_tb[(w) >>  8 & 0xF] << 16 | \
+    SQR_tb[(w) >>  4 & 0xF] <<  8 | SQR_tb[(w)       & 0xF]
+#endif
+#ifdef SIXTEEN_BIT
+#define SQR1(w) \
+    SQR_tb[(w) >> 12 & 0xF] <<  8 | SQR_tb[(w) >>  8 & 0xF]
+#define SQR0(w) \
+    SQR_tb[(w) >>  4 & 0xF] <<  8 | SQR_tb[(w)       & 0xF]
+#endif
+#ifdef EIGHT_BIT
+#define SQR1(w) \
+    SQR_tb[(w) >>  4 & 0xF]
+#define SQR0(w) \
+    SQR_tb[(w)       & 15]
+#endif
+
+/* Product of two polynomials a, b each with degree < BN_BITS2 - 1,
+ * result is a polynomial r with degree < 2 * BN_BITS - 1
+ * The caller MUST ensure that the variables have the right amount
+ * of space allocated.
+ */
+#ifdef EIGHT_BIT
+static void bn_GF2m_mul_1x1(BN_ULONG *r1, BN_ULONG *r0, const BN_ULONG a, const BN_ULONG b)
+	{
+	register BN_ULONG h, l, s;
+	BN_ULONG tab[4], top1b = a >> 7;
+	register BN_ULONG a1, a2;
+
+	a1 = a & (0x7F); a2 = a1 << 1;
+
+	tab[0] = 0; tab[1] = a1; tab[2] = a2; tab[3] = a1^a2;
+
+	s = tab[b      & 0x3]; l  = s;
+	s = tab[b >> 2 & 0x3]; l ^= s << 2; h  = s >> 6;
+	s = tab[b >> 4 & 0x3]; l ^= s << 4; h ^= s >> 4;
+	s = tab[b >> 6      ]; l ^= s << 6; h ^= s >> 2;
+	
+	/* compensate for the top bit of a */
+
+	if (top1b & 01) { l ^= b << 7; h ^= b >> 1; } 
+
+	*r1 = h; *r0 = l;
+	} 
+#endif
+#ifdef SIXTEEN_BIT
+static void bn_GF2m_mul_1x1(BN_ULONG *r1, BN_ULONG *r0, const BN_ULONG a, const BN_ULONG b)
+	{
+	register BN_ULONG h, l, s;
+	BN_ULONG tab[4], top1b = a >> 15; 
+	register BN_ULONG a1, a2;
+
+	a1 = a & (0x7FFF); a2 = a1 << 1;
+
+	tab[0] = 0; tab[1] = a1; tab[2] = a2; tab[3] = a1^a2;
+
+	s = tab[b      & 0x3]; l  = s;
+	s = tab[b >> 2 & 0x3]; l ^= s <<  2; h  = s >> 14;
+	s = tab[b >> 4 & 0x3]; l ^= s <<  4; h ^= s >> 12;
+	s = tab[b >> 6 & 0x3]; l ^= s <<  6; h ^= s >> 10;
+	s = tab[b >> 8 & 0x3]; l ^= s <<  8; h ^= s >>  8;
+	s = tab[b >>10 & 0x3]; l ^= s << 10; h ^= s >>  6;
+	s = tab[b >>12 & 0x3]; l ^= s << 12; h ^= s >>  4;
+	s = tab[b >>14      ]; l ^= s << 14; h ^= s >>  2;
+
+	/* compensate for the top bit of a */
+
+	if (top1b & 01) { l ^= b << 15; h ^= b >> 1; } 
+
+	*r1 = h; *r0 = l;
+	} 
+#endif
+#ifdef THIRTY_TWO_BIT
+static void bn_GF2m_mul_1x1(BN_ULONG *r1, BN_ULONG *r0, const BN_ULONG a, const BN_ULONG b)
+	{
+	register BN_ULONG h, l, s;
+	BN_ULONG tab[8], top2b = a >> 30; 
+	register BN_ULONG a1, a2, a4;
+
+	a1 = a & (0x3FFFFFFF); a2 = a1 << 1; a4 = a2 << 1;
+
+	tab[0] =  0; tab[1] = a1;    tab[2] = a2;    tab[3] = a1^a2;
+	tab[4] = a4; tab[5] = a1^a4; tab[6] = a2^a4; tab[7] = a1^a2^a4;
+
+	s = tab[b       & 0x7]; l  = s;
+	s = tab[b >>  3 & 0x7]; l ^= s <<  3; h  = s >> 29;
+	s = tab[b >>  6 & 0x7]; l ^= s <<  6; h ^= s >> 26;
+	s = tab[b >>  9 & 0x7]; l ^= s <<  9; h ^= s >> 23;
+	s = tab[b >> 12 & 0x7]; l ^= s << 12; h ^= s >> 20;
+	s = tab[b >> 15 & 0x7]; l ^= s << 15; h ^= s >> 17;
+	s = tab[b >> 18 & 0x7]; l ^= s << 18; h ^= s >> 14;
+	s = tab[b >> 21 & 0x7]; l ^= s << 21; h ^= s >> 11;
+	s = tab[b >> 24 & 0x7]; l ^= s << 24; h ^= s >>  8;
+	s = tab[b >> 27 & 0x7]; l ^= s << 27; h ^= s >>  5;
+	s = tab[b >> 30      ]; l ^= s << 30; h ^= s >>  2;
+
+	/* compensate for the top two bits of a */
+
+	if (top2b & 01) { l ^= b << 30; h ^= b >> 2; } 
+	if (top2b & 02) { l ^= b << 31; h ^= b >> 1; } 
+
+	*r1 = h; *r0 = l;
+	} 
+#endif
+#if defined(SIXTY_FOUR_BIT) || defined(SIXTY_FOUR_BIT_LONG)
+static void bn_GF2m_mul_1x1(BN_ULONG *r1, BN_ULONG *r0, const BN_ULONG a, const BN_ULONG b)
+	{
+	register BN_ULONG h, l, s;
+	BN_ULONG tab[16], top3b = a >> 61;
+	register BN_ULONG a1, a2, a4, a8;
+
+	a1 = a & (0x1FFFFFFFFFFFFFFF); a2 = a1 << 1; a4 = a2 << 1; a8 = a4 << 1;
+
+	tab[ 0] = 0;     tab[ 1] = a1;       tab[ 2] = a2;       tab[ 3] = a1^a2;
+	tab[ 4] = a4;    tab[ 5] = a1^a4;    tab[ 6] = a2^a4;    tab[ 7] = a1^a2^a4;
+	tab[ 8] = a8;    tab[ 9] = a1^a8;    tab[10] = a2^a8;    tab[11] = a1^a2^a8;
+	tab[12] = a4^a8; tab[13] = a1^a4^a8; tab[14] = a2^a4^a8; tab[15] = a1^a2^a4^a8;
+
+	s = tab[b       & 0xF]; l  = s;
+	s = tab[b >>  4 & 0xF]; l ^= s <<  4; h  = s >> 60;
+	s = tab[b >>  8 & 0xF]; l ^= s <<  8; h ^= s >> 56;
+	s = tab[b >> 12 & 0xF]; l ^= s << 12; h ^= s >> 52;
+	s = tab[b >> 16 & 0xF]; l ^= s << 16; h ^= s >> 48;
+	s = tab[b >> 20 & 0xF]; l ^= s << 20; h ^= s >> 44;
+	s = tab[b >> 24 & 0xF]; l ^= s << 24; h ^= s >> 40;
+	s = tab[b >> 28 & 0xF]; l ^= s << 28; h ^= s >> 36;
+	s = tab[b >> 32 & 0xF]; l ^= s << 32; h ^= s >> 32;
+	s = tab[b >> 36 & 0xF]; l ^= s << 36; h ^= s >> 28;
+	s = tab[b >> 40 & 0xF]; l ^= s << 40; h ^= s >> 24;
+	s = tab[b >> 44 & 0xF]; l ^= s << 44; h ^= s >> 20;
+	s = tab[b >> 48 & 0xF]; l ^= s << 48; h ^= s >> 16;
+	s = tab[b >> 52 & 0xF]; l ^= s << 52; h ^= s >> 12;
+	s = tab[b >> 56 & 0xF]; l ^= s << 56; h ^= s >>  8;
+	s = tab[b >> 60      ]; l ^= s << 60; h ^= s >>  4;
+
+	/* compensate for the top three bits of a */
+
+	if (top3b & 01) { l ^= b << 61; h ^= b >> 3; } 
+	if (top3b & 02) { l ^= b << 62; h ^= b >> 2; } 
+	if (top3b & 04) { l ^= b << 63; h ^= b >> 1; } 
+
+	*r1 = h; *r0 = l;
+	} 
+#endif
+
+/* Product of two polynomials a, b each with degree < 2 * BN_BITS2 - 1,
+ * result is a polynomial r with degree < 4 * BN_BITS2 - 1
+ * The caller MUST ensure that the variables have the right amount
+ * of space allocated.
+ */
+static void bn_GF2m_mul_2x2(BN_ULONG *r, const BN_ULONG a1, const BN_ULONG a0, const BN_ULONG b1, const BN_ULONG b0)
+	{
+	BN_ULONG m1, m0;
+	/* r[3] = h1, r[2] = h0; r[1] = l1; r[0] = l0 */
+	bn_GF2m_mul_1x1(r+3, r+2, a1, b1);
+	bn_GF2m_mul_1x1(r+1, r, a0, b0);
+	bn_GF2m_mul_1x1(&m1, &m0, a0 ^ a1, b0 ^ b1);
+	/* Correction on m1 ^= l1 ^ h1; m0 ^= l0 ^ h0; */
+	r[2] ^= m1 ^ r[1] ^ r[3];  /* h0 ^= m1 ^ l1 ^ h1; */
+	r[1] = r[3] ^ r[2] ^ r[0] ^ m1 ^ m0;  /* l1 ^= l0 ^ h0 ^ m0; */
+	}
+
+
+/* Add polynomials a and b and store result in r; r could be a or b, a and b 
+ * could be equal; r is the bitwise XOR of a and b.
+ */
+int	BN_GF2m_add(BIGNUM *r, const BIGNUM *a, const BIGNUM *b)
+	{
+	int i;
+	const BIGNUM *at, *bt;
+
+	if (a->top < b->top) { at = b; bt = a; }
+	else { at = a; bt = b; }
+
+	bn_expand2(r, at->top);
+
+	for (i = 0; i < bt->top; i++)
+		{
+		r->d[i] = at->d[i] ^ bt->d[i];
+		}
+	for (; i < at->top; i++)
+		{
+		r->d[i] = at->d[i];
+		}
+	
+	r->top = at->top;
+	bn_fix_top(r);
+	
+	return 1;
+	}
+
+
+/* Some functions allow for representation of the irreducible polynomials
+ * as an int[], say p.  The irreducible f(t) is then of the form:
+ *     t^p[0] + t^p[1] + ... + t^p[k]
+ * where m = p[0] > p[1] > ... > p[k] = 0.
+ */
+
+
+/* Performs modular reduction of a and store result in r.  r could be a. */
+int BN_GF2m_mod_arr(BIGNUM *r, const BIGNUM *a, const unsigned int p[])
+	{
+	int j, k;
+	int n, dN, d0, d1;
+	BN_ULONG zz, *z;
+	
+	/* Since the algorithm does reduction in place, if a == r, copy the
+	 * contents of a into r so we can do reduction in r. 
+	 */
+	if ((a != NULL) && (a->d != r->d))
+		{
+		if (!bn_wexpand(r, a->top)) return 0;
+		for (j = 0; j < a->top; j++)
+			{
+			r->d[j] = a->d[j];
+			}
+		r->top = a->top;
+		}
+	z = r->d;
+
+	/* start reduction */
+	dN = p[0] / BN_BITS2;  
+	for (j = r->top - 1; j > dN;)
+		{
+		zz = z[j];
+		if (z[j] == 0) { j--; continue; }
+		z[j] = 0;
+
+		for (k = 1; p[k] > 0; k++)
+			{
+			/* reducing component t^p[k] */
+			n = p[0] - p[k];
+			d0 = n % BN_BITS2;  d1 = BN_BITS2 - d0;
+			n /= BN_BITS2; 
+			z[j-n] ^= (zz>>d0);
+			if (d0) z[j-n-1] ^= (zz<<d1);
+			}
+
+		/* reducing component t^0 */
+		n = dN;  
+		d0 = p[0] % BN_BITS2;
+		d1 = BN_BITS2 - d0;
+		z[j-n] ^= (zz >> d0);
+		if (d0) z[j-n-1] ^= (zz << d1);
+		}
+
+	/* final round of reduction */
+	while (j == dN)
+		{
+
+		d0 = p[0] % BN_BITS2;
+		zz = z[dN] >> d0;
+		if (zz == 0) break;
+		d1 = BN_BITS2 - d0;
+		
+		if (d0) z[dN] = (z[dN] << d1) >> d1; /* clear up the top d1 bits */
+		z[0] ^= zz; /* reduction t^0 component */
+
+		for (k = 1; p[k] > 0; k++)
+			{
+			/* reducing component t^p[k]*/
+			n = p[k] / BN_BITS2;   
+			d0 = p[k] % BN_BITS2;
+			d1 = BN_BITS2 - d0;
+			z[n] ^= (zz << d0);
+			if (d0) z[n+1] ^= (zz >> d1);
+			}
+
+		
+		}
+
+	bn_fix_top(r);
+	
+	return 1;
+	}
+
+/* Performs modular reduction of a by p and store result in r.  r could be a.
+ *
+ * This function calls down to the BN_GF2m_mod_arr implementation; this wrapper
+ * function is only provided for convenience; for best performance, use the 
+ * BN_GF2m_mod_arr function.
+ */
+int	BN_GF2m_mod(BIGNUM *r, const BIGNUM *a, const BIGNUM *p)
+	{
+	const int max = BN_num_bits(p);
+	unsigned int *arr=NULL, ret = 0;
+	if ((arr = (unsigned int *)OPENSSL_malloc(sizeof(unsigned int) * max)) == NULL) goto err;
+	if (BN_GF2m_poly2arr(p, arr, max) > max)
+		{
+		BNerr(BN_F_BN_GF2M_MOD,BN_R_INVALID_LENGTH);
+		goto err;
+		}
+	ret = BN_GF2m_mod_arr(r, a, arr);
+  err:
+	if (arr) OPENSSL_free(arr);
+	return ret;
+	}
+
+
+/* Compute the product of two polynomials a and b, reduce modulo p, and store
+ * the result in r.  r could be a or b; a could be b.
+ */
+int	BN_GF2m_mod_mul_arr(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, const unsigned int p[], BN_CTX *ctx)
+	{
+	int zlen, i, j, k, ret = 0;
+	BIGNUM *s;
+	BN_ULONG x1, x0, y1, y0, zz[4];
+	
+	if (a == b)
+		{
+		return BN_GF2m_mod_sqr_arr(r, a, p, ctx);
+		}
+	
+
+	BN_CTX_start(ctx);
+	if ((s = BN_CTX_get(ctx)) == NULL) goto err;
+	
+	zlen = a->top + b->top;
+	if (!bn_wexpand(s, zlen)) goto err;
+	s->top = zlen;
+
+	for (i = 0; i < zlen; i++) s->d[i] = 0;
+
+	for (j = 0; j < b->top; j += 2)
+		{
+		y0 = b->d[j];
+		y1 = ((j+1) == b->top) ? 0 : b->d[j+1];
+		for (i = 0; i < a->top; i += 2)
+			{
+			x0 = a->d[i];
+			x1 = ((i+1) == a->top) ? 0 : a->d[i+1];
+			bn_GF2m_mul_2x2(zz, x1, x0, y1, y0);
+			for (k = 0; k < 4; k++) s->d[i+j+k] ^= zz[k];
+			}
+		}
+
+	bn_fix_top(s);
+	BN_GF2m_mod_arr(r, s, p);
+	ret = 1;
+
+  err:
+	BN_CTX_end(ctx);
+	return ret;
+	
+	}
+
+/* Compute the product of two polynomials a and b, reduce modulo p, and store
+ * the result in r.  r could be a or b; a could equal b.
+ *
+ * This function calls down to the BN_GF2m_mod_mul_arr implementation; this wrapper
+ * function is only provided for convenience; for best performance, use the 
+ * BN_GF2m_mod_mul_arr function.
+ */
+int	BN_GF2m_mod_mul(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, const BIGNUM *p, BN_CTX *ctx)
+	{
+	const int max = BN_num_bits(p);
+	unsigned int *arr=NULL, ret = 0;
+	if ((arr = (unsigned int *)OPENSSL_malloc(sizeof(unsigned int) * max)) == NULL) goto err;
+	if (BN_GF2m_poly2arr(p, arr, max) > max)
+		{
+		BNerr(BN_F_BN_GF2M_MOD_MUL,BN_R_INVALID_LENGTH);
+		goto err;
+		}
+	ret = BN_GF2m_mod_mul_arr(r, a, b, arr, ctx);
+  err:
+	if (arr) OPENSSL_free(arr);
+	return ret;
+	}
+
+
+/* Square a, reduce the result mod p, and store it in a.  r could be a. */
+int	BN_GF2m_mod_sqr_arr(BIGNUM *r, const BIGNUM *a, const unsigned int p[], BN_CTX *ctx)
+	{
+	int i, ret = 0;
+	BIGNUM *s;
+	
+	BN_CTX_start(ctx);
+	if ((s = BN_CTX_get(ctx)) == NULL) return 0;
+	if (!bn_wexpand(s, 2 * a->top)) goto err;
+
+	for (i = a->top - 1; i >= 0; i--)
+		{
+		s->d[2*i+1] = SQR1(a->d[i]);
+		s->d[2*i  ] = SQR0(a->d[i]);
+		}
+
+	s->top = 2 * a->top;
+	bn_fix_top(s);
+	if (!BN_GF2m_mod_arr(r, s, p)) goto err;
+	ret = 1;
+  err:
+	BN_CTX_end(ctx);
+	return ret;
+	}
+
+/* Square a, reduce the result mod p, and store it in a.  r could be a.
+ *
+ * This function calls down to the BN_GF2m_mod_sqr_arr implementation; this wrapper
+ * function is only provided for convenience; for best performance, use the 
+ * BN_GF2m_mod_sqr_arr function.
+ */
+int	BN_GF2m_mod_sqr(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx)
+	{
+	const int max = BN_num_bits(p);
+	unsigned int *arr=NULL, ret = 0;
+	if ((arr = (unsigned int *)OPENSSL_malloc(sizeof(unsigned int) * max)) == NULL) goto err;
+	if (BN_GF2m_poly2arr(p, arr, max) > max)
+		{
+		BNerr(BN_F_BN_GF2M_MOD_SQR,BN_R_INVALID_LENGTH);
+		goto err;
+		}
+	ret = BN_GF2m_mod_sqr_arr(r, a, arr, ctx);
+  err:
+	if (arr) OPENSSL_free(arr);
+	return ret;
+	}
+
+
+/* Invert a, reduce modulo p, and store the result in r. r could be a. 
+ * Uses Modified Almost Inverse Algorithm (Algorithm 10) from
+ *     Hankerson, D., Hernandez, J.L., and Menezes, A.  "Software Implementation
+ *     of Elliptic Curve Cryptography Over Binary Fields".
+ */
+int BN_GF2m_mod_inv(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx)
+	{
+	BIGNUM *b, *c, *u, *v, *tmp;
+	int ret = 0;
+
+	BN_CTX_start(ctx);
+	
+	b = BN_CTX_get(ctx);
+	c = BN_CTX_get(ctx);
+	u = BN_CTX_get(ctx);
+	v = BN_CTX_get(ctx);
+	if (v == NULL) goto err;
+
+	if (!BN_one(b)) goto err;
+	if (!BN_zero(c)) goto err;
+	if (!BN_GF2m_mod(u, a, p)) goto err;
+	if (!BN_copy(v, p)) goto err;
+
+	u->neg = 0; /* Need to set u->neg = 0 because BN_is_one(u) checks
+	             * the neg flag of the bignum.
+	             */
+
+	if (BN_is_zero(u)) goto err;
+
+	while (1)
+		{
+		while (!BN_is_odd(u))
+			{
+			if (!BN_rshift1(u, u)) goto err;
+			if (BN_is_odd(b))
+				{
+				if (!BN_GF2m_add(b, b, p)) goto err;
+				}
+			if (!BN_rshift1(b, b)) goto err;
+			}
+
+		if (BN_is_one(u)) break;
+
+		if (BN_num_bits(u) < BN_num_bits(v))
+			{
+			tmp = u; u = v; v = tmp;
+			tmp = b; b = c; c = tmp;
+			}
+		
+		if (!BN_GF2m_add(u, u, v)) goto err;
+		if (!BN_GF2m_add(b, b, c)) goto err;
+		}
+
+
+	if (!BN_copy(r, b)) goto err;
+	ret = 1;
+
+  err:
+  	BN_CTX_end(ctx);
+	return ret;
+	}
+
+/* Invert xx, reduce modulo p, and store the result in r. r could be xx. 
+ *
+ * This function calls down to the BN_GF2m_mod_inv implementation; this wrapper
+ * function is only provided for convenience; for best performance, use the 
+ * BN_GF2m_mod_inv function.
+ */
+int BN_GF2m_mod_inv_arr(BIGNUM *r, const BIGNUM *xx, const unsigned int p[], BN_CTX *ctx)
+	{
+	BIGNUM *field;
+	int ret = 0;
+
+	BN_CTX_start(ctx);
+	if ((field = BN_CTX_get(ctx)) == NULL) goto err;
+	if (!BN_GF2m_arr2poly(p, field)) goto err;
+	
+	ret = BN_GF2m_mod_inv(r, xx, field, ctx);
+
+  err:
+	BN_CTX_end(ctx);
+	return ret;
+	}
+
+
+#ifdef OPENSSL_NO_SUN_DIV
+/* Divide y by x, reduce modulo p, and store the result in r. r could be x 
+ * or y, x could equal y.
+ */
+int BN_GF2m_mod_div(BIGNUM *r, const BIGNUM *y, const BIGNUM *x, const BIGNUM *p, BN_CTX *ctx)
+	{
+	BIGNUM *xinv = NULL;
+	int ret = 0;
+	
+	BN_CTX_start(ctx);
+	xinv = BN_CTX_get(ctx);
+	if (xinv == NULL) goto err;
+	
+	if (!BN_GF2m_mod_inv(xinv, x, p, ctx)) goto err;
+	if (!BN_GF2m_mod_mul(r, y, xinv, p, ctx)) goto err;
+	ret = 1;
+
+  err:
+	BN_CTX_end(ctx);
+	return ret;
+	}
+#else
+/* Divide y by x, reduce modulo p, and store the result in r. r could be x 
+ * or y, x could equal y.
+ * Uses algorithm Modular_Division_GF(2^m) from 
+ *     Chang-Shantz, S.  "From Euclid's GCD to Montgomery Multiplication to 
+ *     the Great Divide".
+ */
+int BN_GF2m_mod_div(BIGNUM *r, const BIGNUM *y, const BIGNUM *x, const BIGNUM *p, BN_CTX *ctx)
+	{
+	BIGNUM *a, *b, *u, *v;
+	int ret = 0;
+
+	BN_CTX_start(ctx);
+	
+	a = BN_CTX_get(ctx);
+	b = BN_CTX_get(ctx);
+	u = BN_CTX_get(ctx);
+	v = BN_CTX_get(ctx);
+	if (v == NULL) goto err;
+
+	/* reduce x and y mod p */
+	if (!BN_GF2m_mod(u, y, p)) goto err;
+	if (!BN_GF2m_mod(a, x, p)) goto err;
+	if (!BN_copy(b, p)) goto err;
+	if (!BN_zero(v)) goto err;
+	
+	a->neg = 0; /* Need to set a->neg = 0 because BN_is_one(a) checks
+	             * the neg flag of the bignum.
+	             */
+
+	while (!BN_is_odd(a))
+		{
+		if (!BN_rshift1(a, a)) goto err;
+		if (BN_is_odd(u)) if (!BN_GF2m_add(u, u, p)) goto err;
+		if (!BN_rshift1(u, u)) goto err;
+		}
+
+	do
+		{
+		if (BN_GF2m_cmp(b, a) > 0)
+			{
+			if (!BN_GF2m_add(b, b, a)) goto err;
+			if (!BN_GF2m_add(v, v, u)) goto err;
+			do
+				{
+				if (!BN_rshift1(b, b)) goto err;
+				if (BN_is_odd(v)) if (!BN_GF2m_add(v, v, p)) goto err;
+				if (!BN_rshift1(v, v)) goto err;
+				} while (!BN_is_odd(b));
+			}
+		else if (BN_is_one(a))
+			break;
+		else
+			{
+			if (!BN_GF2m_add(a, a, b)) goto err;
+			if (!BN_GF2m_add(u, u, v)) goto err;
+			do
+				{
+				if (!BN_rshift1(a, a)) goto err;
+				if (BN_is_odd(u)) if (!BN_GF2m_add(u, u, p)) goto err;
+				if (!BN_rshift1(u, u)) goto err;
+				} while (!BN_is_odd(a));
+			}
+		} while (1);
+
+	if (!BN_copy(r, u)) goto err;
+	ret = 1;
+
+  err:
+  	BN_CTX_end(ctx);
+	return ret;
+	}
+#endif
+
+/* Divide yy by xx, reduce modulo p, and store the result in r. r could be xx 
+ * or yy, xx could equal yy.
+ *
+ * This function calls down to the BN_GF2m_mod_div implementation; this wrapper
+ * function is only provided for convenience; for best performance, use the 
+ * BN_GF2m_mod_div function.
+ */
+int BN_GF2m_mod_div_arr(BIGNUM *r, const BIGNUM *yy, const BIGNUM *xx, const unsigned int p[], BN_CTX *ctx)
+	{
+	BIGNUM *field;
+	int ret = 0;
+
+	BN_CTX_start(ctx);
+	if ((field = BN_CTX_get(ctx)) == NULL) goto err;
+	if (!BN_GF2m_arr2poly(p, field)) goto err;
+	
+	ret = BN_GF2m_mod_div(r, yy, xx, field, ctx);
+
+  err:
+	BN_CTX_end(ctx);
+	return ret;
+	}
+
+
+/* Compute the bth power of a, reduce modulo p, and store
+ * the result in r.  r could be a.
+ * Uses simple square-and-multiply algorithm A.5.1 from IEEE P1363.
+ */
+int	BN_GF2m_mod_exp_arr(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, const unsigned int p[], BN_CTX *ctx)
+	{
+	int ret = 0, i, n;
+	BIGNUM *u;
+	
+	if (BN_is_zero(b))
+		{
+		return(BN_one(r));
+		}
+	
+
+	BN_CTX_start(ctx);
+	if ((u = BN_CTX_get(ctx)) == NULL) goto err;
+	
+	if (!BN_GF2m_mod_arr(u, a, p)) goto err;
+	
+	n = BN_num_bits(b) - 1;
+	for (i = n - 1; i >= 0; i--)
+		{
+		if (!BN_GF2m_mod_sqr_arr(u, u, p, ctx)) goto err;
+		if (BN_is_bit_set(b, i))
+			{
+			if (!BN_GF2m_mod_mul_arr(u, u, a, p, ctx)) goto err;
+			}
+		}
+	if (!BN_copy(r, u)) goto err;
+
+	ret = 1;
+
+  err:
+	BN_CTX_end(ctx);
+	return ret;
+	}
+
+/* Compute the bth power of a, reduce modulo p, and store
+ * the result in r.  r could be a.
+ *
+ * This function calls down to the BN_GF2m_mod_exp_arr implementation; this wrapper
+ * function is only provided for convenience; for best performance, use the 
+ * BN_GF2m_mod_exp_arr function.
+ */
+int BN_GF2m_mod_exp(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, const BIGNUM *p, BN_CTX *ctx)
+	{
+	const int max = BN_num_bits(p);
+	unsigned int *arr=NULL, ret = 0;
+	if ((arr = (unsigned int *)OPENSSL_malloc(sizeof(unsigned int) * max)) == NULL) goto err;
+	if (BN_GF2m_poly2arr(p, arr, max) > max)
+		{
+		BNerr(BN_F_BN_GF2M_MOD_EXP,BN_R_INVALID_LENGTH);
+		goto err;
+		}
+	ret = BN_GF2m_mod_exp_arr(r, a, b, arr, ctx);
+  err:
+	if (arr) OPENSSL_free(arr);
+	return ret;
+	}
+
+/* Compute the square root of a, reduce modulo p, and store
+ * the result in r.  r could be a.
+ * Uses exponentiation as in algorithm A.4.1 from IEEE P1363.
+ */
+int	BN_GF2m_mod_sqrt_arr(BIGNUM *r, const BIGNUM *a, const unsigned int p[], BN_CTX *ctx)
+	{
+	int ret = 0;
+	BIGNUM *u;
+	
+	BN_CTX_start(ctx);
+	if ((u = BN_CTX_get(ctx)) == NULL) goto err;
+	
+	if (!BN_zero(u)) goto err;
+	if (!BN_set_bit(u, p[0] - 1)) goto err;
+	ret = BN_GF2m_mod_exp_arr(r, a, u, p, ctx);
+
+  err:
+	BN_CTX_end(ctx);
+	return ret;
+	}
+
+/* Compute the square root of a, reduce modulo p, and store
+ * the result in r.  r could be a.
+ *
+ * This function calls down to the BN_GF2m_mod_sqrt_arr implementation; this wrapper
+ * function is only provided for convenience; for best performance, use the 
+ * BN_GF2m_mod_sqrt_arr function.
+ */
+int BN_GF2m_mod_sqrt(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx)
+	{
+	const int max = BN_num_bits(p);
+	unsigned int *arr=NULL, ret = 0;
+	if ((arr = (unsigned int *)OPENSSL_malloc(sizeof(unsigned int) * max)) == NULL) goto err;
+	if (BN_GF2m_poly2arr(p, arr, max) > max)
+		{
+		BNerr(BN_F_BN_GF2M_MOD_EXP,BN_R_INVALID_LENGTH);
+		goto err;
+		}
+	ret = BN_GF2m_mod_sqrt_arr(r, a, arr, ctx);
+  err:
+	if (arr) OPENSSL_free(arr);
+	return ret;
+	}
+
+/* Find r such that r^2 + r = a mod p.  r could be a. If no r exists returns 0.
+ * Uses algorithms A.4.7 and A.4.6 from IEEE P1363.
+ */
+int BN_GF2m_mod_solve_quad_arr(BIGNUM *r, const BIGNUM *a_, const unsigned int p[], BN_CTX *ctx)
+	{
+	int ret = 0, i, count = 0;
+	BIGNUM *a, *z, *rho, *w, *w2, *tmp;
+	
+	BN_CTX_start(ctx);
+	a = BN_CTX_get(ctx);
+	z = BN_CTX_get(ctx);
+	w = BN_CTX_get(ctx);
+	if (w == NULL) goto err;
+
+	if (!BN_GF2m_mod_arr(a, a_, p)) goto err;
+	
+	if (BN_is_zero(a))
+		{
+		ret = BN_zero(r);
+		goto err;
+		}
+
+	if (p[0] & 0x1) /* m is odd */
+		{
+		/* compute half-trace of a */
+		if (!BN_copy(z, a)) goto err;
+		for (i = 1; i <= (p[0] - 1) / 2; i++)
+			{
+			if (!BN_GF2m_mod_sqr_arr(z, z, p, ctx)) goto err;
+			if (!BN_GF2m_mod_sqr_arr(z, z, p, ctx)) goto err;
+			if (!BN_GF2m_add(z, z, a)) goto err;
+			}
+		
+		}
+	else /* m is even */
+		{
+		rho = BN_CTX_get(ctx);
+		w2 = BN_CTX_get(ctx);
+		tmp = BN_CTX_get(ctx);
+		if (tmp == NULL) goto err;
+		do
+			{
+			if (!BN_rand(rho, p[0], 0, 0)) goto err;
+			if (!BN_GF2m_mod_arr(rho, rho, p)) goto err;
+			if (!BN_zero(z)) goto err;
+			if (!BN_copy(w, rho)) goto err;
+			for (i = 1; i <= p[0] - 1; i++)
+				{
+				if (!BN_GF2m_mod_sqr_arr(z, z, p, ctx)) goto err;
+				if (!BN_GF2m_mod_sqr_arr(w2, w, p, ctx)) goto err;
+				if (!BN_GF2m_mod_mul_arr(tmp, w2, a, p, ctx)) goto err;
+				if (!BN_GF2m_add(z, z, tmp)) goto err;
+				if (!BN_GF2m_add(w, w2, rho)) goto err;
+				}
+			count++;
+			} while (BN_is_zero(w) && (count < MAX_ITERATIONS));
+		if (BN_is_zero(w))
+			{
+			BNerr(BN_F_BN_GF2M_MOD_SOLVE_QUAD_ARR,BN_R_TOO_MANY_ITERATIONS);
+			goto err;
+			}
+		}
+	
+	if (!BN_GF2m_mod_sqr_arr(w, z, p, ctx)) goto err;
+	if (!BN_GF2m_add(w, z, w)) goto err;
+	if (BN_GF2m_cmp(w, a)) goto err;
+
+	if (!BN_copy(r, z)) goto err;
+
+	ret = 1;
+
+  err:
+	BN_CTX_end(ctx);
+	return ret;
+	}
+
+/* Find r such that r^2 + r = a mod p.  r could be a. If no r exists returns 0.
+ *
+ * This function calls down to the BN_GF2m_mod_solve_quad_arr implementation; this wrapper
+ * function is only provided for convenience; for best performance, use the 
+ * BN_GF2m_mod_solve_quad_arr function.
+ */
+int BN_GF2m_mod_solve_quad(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx)
+	{
+	const int max = BN_num_bits(p);
+	unsigned int *arr=NULL, ret = 0;
+	if ((arr = (unsigned int *)OPENSSL_malloc(sizeof(unsigned int) * max)) == NULL) goto err;
+	if (BN_GF2m_poly2arr(p, arr, max) > max)
+		{
+		BNerr(BN_F_BN_GF2M_MOD_SOLVE_QUAD,BN_R_INVALID_LENGTH);
+		goto err;
+		}
+	ret = BN_GF2m_mod_solve_quad_arr(r, a, arr, ctx);
+  err:
+	if (arr) OPENSSL_free(arr);
+	return ret;
+	}
+
+/* Convert the bit-string representation of a polynomial a into an array
+ * of integers corresponding to the bits with non-zero coefficient.
+ * Up to max elements of the array will be filled.  Return value is total
+ * number of coefficients that would be extracted if array was large enough.
+ */
+int BN_GF2m_poly2arr(const BIGNUM *a, unsigned int p[], int max)
+	{
+	int i, j, k;
+	BN_ULONG mask;
+
+	for (k = 0; k < max; k++) p[k] = 0;
+	k = 0;
+
+	for (i = a->top - 1; i >= 0; i--)
+		{
+		mask = BN_TBIT;
+		for (j = BN_BITS2 - 1; j >= 0; j--)
+			{
+			if (a->d[i] & mask) 
+				{
+				if (k < max) p[k] = BN_BITS2 * i + j;
+				k++;
+				}
+			mask >>= 1;
+			}
+		}
+
+	return k;
+	}
+
+/* Convert the coefficient array representation of a polynomial to a 
+ * bit-string.  The array must be terminated by 0.
+ */
+int BN_GF2m_arr2poly(const unsigned int p[], BIGNUM *a)
+	{
+	int i;
+
+	BN_zero(a);
+	for (i = 0; p[i] > 0; i++)
+		{
+		BN_set_bit(a, p[i]);
+		}
+	BN_set_bit(a, 0);
+	
+	return 1;
+	}
+
diff --git a/crypto/bn/bntest.c b/crypto/bn/bntest.c
index 8158a67..377b5ba 100644
--- a/crypto/bn/bntest.c
+++ b/crypto/bn/bntest.c
@@ -55,6 +55,32 @@
  * copied and put under another distribution licence
  * [including the GNU Public Licence.]
  */
+/* ====================================================================
+ * Copyright 2002 Sun Microsystems, Inc. ALL RIGHTS RESERVED.
+ *
+ * Portions of the attached software ("Contribution") are developed by 
+ * SUN MICROSYSTEMS, INC., and are contributed to the OpenSSL project.
+ *
+ * The Contribution is licensed pursuant to the Eric Young open source
+ * license provided above.
+ *
+ * In addition, Sun covenants to all licensees who provide a reciprocal
+ * covenant with respect to their own patents if any, not to sue under
+ * current and future patent claims necessarily infringed by the making,
+ * using, practicing, selling, offering for sale and/or otherwise
+ * disposing of the Contribution as delivered hereunder 
+ * (or portions thereof), provided that such covenant shall not apply:
+ *  1) for code that a licensee deletes from the Contribution;
+ *  2) separates from the Contribution; or
+ *  3) for infringements caused by:
+ *       i) the modification of the Contribution or
+ *      ii) the combination of the Contribution with other software or
+ *          devices where such combination causes the infringement.
+ *
+ * The binary polynomial arithmetic software is originally written by 
+ * Sheueling Chang Shantz and Douglas Stebila of Sun Microsystems Laboratories.
+ *
+ */
 
 #include <stdio.h>
 #include <stdlib.h>
@@ -91,6 +117,15 @@ int test_mod(BIO *bp,BN_CTX *ctx);
 int test_mod_mul(BIO *bp,BN_CTX *ctx);
 int test_mod_exp(BIO *bp,BN_CTX *ctx);
 int test_exp(BIO *bp,BN_CTX *ctx);
+int test_gf2m_add(BIO *bp);
+int test_gf2m_mod(BIO *bp);
+int test_gf2m_mod_mul(BIO *bp,BN_CTX *ctx);
+int test_gf2m_mod_sqr(BIO *bp,BN_CTX *ctx);
+int test_gf2m_mod_inv(BIO *bp,BN_CTX *ctx);
+int test_gf2m_mod_div(BIO *bp,BN_CTX *ctx);
+int test_gf2m_mod_exp(BIO *bp,BN_CTX *ctx);
+int test_gf2m_mod_sqrt(BIO *bp,BN_CTX *ctx);
+int test_gf2m_mod_solve_quad(BIO *bp,BN_CTX *ctx);
 int test_kron(BIO *bp,BN_CTX *ctx);
 int test_sqrt(BIO *bp,BN_CTX *ctx);
 int rand_neg(void);
@@ -226,6 +261,42 @@ int main(int argc, char *argv[])
 	if (!test_exp(out,ctx)) goto err;
 	BIO_flush(out);
 
+	message(out,"BN_GF2m_add");
+	if (!test_gf2m_add(out)) goto err;
+	BIO_flush(out);
+
+	message(out,"BN_GF2m_mod");
+	if (!test_gf2m_mod(out)) goto err;
+	BIO_flush(out);
+
+	message(out,"BN_GF2m_mod_mul");
+	if (!test_gf2m_mod_mul(out,ctx)) goto err;
+	BIO_flush(out);
+
+	message(out,"BN_GF2m_mod_sqr");
+	if (!test_gf2m_mod_sqr(out,ctx)) goto err;
+	BIO_flush(out);
+
+	message(out,"BN_GF2m_mod_inv");
+	if (!test_gf2m_mod_inv(out,ctx)) goto err;
+	BIO_flush(out);
+
+	message(out,"BN_GF2m_mod_div");
+	if (!test_gf2m_mod_div(out,ctx)) goto err;
+	BIO_flush(out);
+
+	message(out,"BN_GF2m_mod_exp");
+	if (!test_gf2m_mod_exp(out,ctx)) goto err;
+	BIO_flush(out);
+
+	message(out,"BN_GF2m_mod_sqrt");
+	if (!test_gf2m_mod_sqrt(out,ctx)) goto err;
+	BIO_flush(out);
+
+	message(out,"BN_GF2m_mod_solve_quad");
+	if (!test_gf2m_mod_solve_quad(out,ctx)) goto err;
+	BIO_flush(out);
+
 	message(out,"BN_kronecker");
 	if (!test_kron(out,ctx)) goto err;
 	BIO_flush(out);
@@ -872,6 +943,581 @@ int test_exp(BIO *bp, BN_CTX *ctx)
 	return(1);
 	}
 
+int test_gf2m_add(BIO *bp)
+	{
+	BIGNUM a,b,c;
+	int i, ret = 0;
+
+	BN_init(&a);
+	BN_init(&b);
+	BN_init(&c);
+
+	for (i=0; i<num0; i++)
+		{
+		BN_rand(&a,512,0,0);
+		BN_copy(&b, BN_value_one());
+		a.neg=rand_neg();
+		b.neg=rand_neg();
+		BN_GF2m_add(&c,&a,&b);
+#if 0 /* make test uses ouput in bc but bc can't handle GF(2^m) arithmetic */
+		if (bp != NULL)
+			{
+			if (!results)
+				{
+				BN_print(bp,&a);
+				BIO_puts(bp," ^ ");
+				BN_print(bp,&b);
+				BIO_puts(bp," = ");
+				}
+			BN_print(bp,&c);
+			BIO_puts(bp,"\n");
+			}
+#endif
+		/* Test that two added values have the correct parity. */
+		if((BN_is_odd(&a) && BN_is_odd(&c)) || (!BN_is_odd(&a) && !BN_is_odd(&c)))
+			{
+		    fprintf(stderr,"GF(2^m) addition test (a) failed!\n");
+			goto err;
+			}
+		BN_GF2m_add(&c,&c,&c);
+		/* Test that c + c = 0. */
+		if(!BN_is_zero(&c))
+		    {
+		    fprintf(stderr,"GF(2^m) addition test (b) failed!\n");
+			goto err;
+		    }
+		}
+	ret = 1;
+  err:
+	BN_free(&a);
+	BN_free(&b);
+	BN_free(&c);
+	return ret;
+	}
+
+int test_gf2m_mod(BIO *bp)
+	{
+	BIGNUM *a,*b[2],*c,*d,*e;
+	int i, j, ret = 0;
+	unsigned int p0[] = {163,7,6,3,0};
+	unsigned int p1[] = {193,15,0};
+
+	a=BN_new();
+	b[0]=BN_new();
+	b[1]=BN_new();
+	c=BN_new();
+	d=BN_new();
+	e=BN_new();
+
+	BN_GF2m_arr2poly(p0, b[0]);
+	BN_GF2m_arr2poly(p1, b[1]);
+
+	for (i=0; i<num0; i++)
+		{
+		BN_bntest_rand(a, 1024, 0, 0);
+		for (j=0; j < 2; j++)
+			{
+			BN_GF2m_mod(c, a, b[j]);
+#if 0 /* make test uses ouput in bc but bc can't handle GF(2^m) arithmetic */
+			if (bp != NULL)
+				{
+				if (!results)
+					{
+					BN_print(bp,a);
+					BIO_puts(bp," % ");
+					BN_print(bp,b[j]);
+					BIO_puts(bp," - ");
+					BN_print(bp,c);
+					BIO_puts(bp,"\n");
+					}
+				}
+#endif
+			BN_GF2m_add(d, a, c);
+			BN_GF2m_mod(e, d, b[j]);
+			/* Test that a + (a mod p) mod p == 0. */
+			if(!BN_is_zero(e))
+				{
+				fprintf(stderr,"GF(2^m) modulo test failed!\n");
+				goto err;
+				}
+			}
+		}
+	ret = 1;
+  err:
+	BN_free(a);
+	BN_free(b[0]);
+	BN_free(b[1]);
+	BN_free(c);
+	BN_free(d);
+	BN_free(e);
+	return ret;
+	}
+
+int test_gf2m_mod_mul(BIO *bp,BN_CTX *ctx)
+	{
+	BIGNUM *a,*b[2],*c,*d,*e,*f,*g,*h;
+	int i, j, ret = 0;
+	unsigned int p0[] = {163,7,6,3,0};
+	unsigned int p1[] = {193,15,0};
+
+	a=BN_new();
+	b[0]=BN_new();
+	b[1]=BN_new();
+	c=BN_new();
+	d=BN_new();
+	e=BN_new();
+	f=BN_new();
+	g=BN_new();
+	h=BN_new();
+
+	BN_GF2m_arr2poly(p0, b[0]);
+	BN_GF2m_arr2poly(p1, b[1]);
+
+	for (i=0; i<num0; i++)
+		{
+		BN_bntest_rand(a, 1024, 0, 0);
+		BN_bntest_rand(c, 1024, 0, 0);
+		BN_bntest_rand(d, 1024, 0, 0);
+		for (j=0; j < 2; j++)
+			{
+			BN_GF2m_mod_mul(e, a, c, b[j], ctx);
+#if 0 /* make test uses ouput in bc but bc can't handle GF(2^m) arithmetic */
+			if (bp != NULL)
+				{
+				if (!results)
+					{
+					BN_print(bp,a);
+					BIO_puts(bp," * ");
+					BN_print(bp,c);
+					BIO_puts(bp," % ");
+					BN_print(bp,b[j]);
+					BIO_puts(bp," - ");
+					BN_print(bp,e);
+					BIO_puts(bp,"\n");
+					}
+				}
+#endif
+			BN_GF2m_add(f, a, d);
+			BN_GF2m_mod_mul(g, f, c, b[j], ctx);
+			BN_GF2m_mod_mul(h, d, c, b[j], ctx);
+			BN_GF2m_add(f, e, g);
+			BN_GF2m_add(f, f, h);
+			/* Test that (a+d)*c = a*c + d*c. */
+			if(!BN_is_zero(f))
+				{
+				fprintf(stderr,"GF(2^m) modular multiplication test failed!\n");
+				goto err;
+				}
+			}
+		}
+	ret = 1;
+  err:
+	BN_free(a);
+	BN_free(b[0]);
+	BN_free(b[1]);
+	BN_free(c);
+	BN_free(d);
+	BN_free(e);
+	BN_free(f);
+	BN_free(g);
+	BN_free(h);
+	return ret;
+	}
+
+int test_gf2m_mod_sqr(BIO *bp,BN_CTX *ctx)
+	{
+	BIGNUM *a,*b[2],*c,*d;
+	int i, j, ret = 0;
+	unsigned int p0[] = {163,7,6,3,0};
+	unsigned int p1[] = {193,15,0};
+
+	a=BN_new();
+	b[0]=BN_new();
+	b[1]=BN_new();
+	c=BN_new();
+	d=BN_new();
+
+	BN_GF2m_arr2poly(p0, b[0]);
+	BN_GF2m_arr2poly(p1, b[1]);
+
+	for (i=0; i<num0; i++)
+		{
+		BN_bntest_rand(a, 1024, 0, 0);
+		for (j=0; j < 2; j++)
+			{
+			BN_GF2m_mod_sqr(c, a, b[j], ctx);
+			BN_copy(d, a);
+			BN_GF2m_mod_mul(d, a, d, b[j], ctx);
+#if 0 /* make test uses ouput in bc but bc can't handle GF(2^m) arithmetic */
+			if (bp != NULL)
+				{
+				if (!results)
+					{
+					BN_print(bp,a);
+					BIO_puts(bp," ^ 2 % ");
+					BN_print(bp,b[j]);
+					BIO_puts(bp, " = ");
+					BN_print(bp,c);
+					BIO_puts(bp,"; a * a = ");
+					BN_print(bp,d);
+					BIO_puts(bp,"\n");
+					}
+				}
+#endif
+			BN_GF2m_add(d, c, d);
+			/* Test that a*a = a^2. */
+			if(!BN_is_zero(d))
+				{
+				fprintf(stderr,"GF(2^m) modular squaring test failed!\n");
+				goto err;
+				}
+			}
+		}
+	ret = 1;
+  err:
+	BN_free(a);
+	BN_free(b[0]);
+	BN_free(b[1]);
+	BN_free(c);
+	BN_free(d);
+	return ret;
+	}
+
+int test_gf2m_mod_inv(BIO *bp,BN_CTX *ctx)
+	{
+	BIGNUM *a,*b[2],*c,*d;
+	int i, j, ret = 0;
+	unsigned int p0[] = {163,7,6,3,0};
+	unsigned int p1[] = {193,15,0};
+
+	a=BN_new();
+	b[0]=BN_new();
+	b[1]=BN_new();
+	c=BN_new();
+	d=BN_new();
+
+	BN_GF2m_arr2poly(p0, b[0]);
+	BN_GF2m_arr2poly(p1, b[1]);
+
+	for (i=0; i<num0; i++)
+		{
+		BN_bntest_rand(a, 512, 0, 0); 
+		for (j=0; j < 2; j++)
+			{
+			BN_GF2m_mod_inv(c, a, b[j], ctx);
+			BN_GF2m_mod_mul(d, a, c, b[j], ctx);
+#if 0 /* make test uses ouput in bc but bc can't handle GF(2^m) arithmetic */
+			if (bp != NULL)
+				{
+				if (!results)
+					{
+					BN_print(bp,a);
+					BIO_puts(bp, " * ");
+					BN_print(bp,c);
+					BIO_puts(bp," - 1 % ");
+					BN_print(bp,b[j]);
+					BIO_puts(bp,"\n");
+					}
+				}
+#endif
+			/* Test that ((1/a)*a) = 1. */
+			if(!BN_is_one(d))
+				{
+				fprintf(stderr,"GF(2^m) modular inversion test failed!\n");
+				goto err;
+				}
+			}
+		}
+	ret = 1;
+  err:
+	BN_free(a);
+	BN_free(b[0]);
+	BN_free(b[1]);
+	BN_free(c);
+	BN_free(d);
+	return ret;
+	}
+
+int test_gf2m_mod_div(BIO *bp,BN_CTX *ctx)
+	{
+	BIGNUM *a,*b[2],*c,*d,*e,*f;
+	int i, j, ret = 0;
+	unsigned int p0[] = {163,7,6,3,0};
+	unsigned int p1[] = {193,15,0};
+
+	a=BN_new();
+	b[0]=BN_new();
+	b[1]=BN_new();
+	c=BN_new();
+	d=BN_new();
+	e=BN_new();
+	f=BN_new();
+
+	BN_GF2m_arr2poly(p0, b[0]);
+	BN_GF2m_arr2poly(p1, b[1]);
+
+	for (i=0; i<num0; i++)
+		{
+		BN_bntest_rand(a, 512, 0, 0); 
+		BN_bntest_rand(c, 512, 0, 0);
+		for (j=0; j < 2; j++)
+			{
+			BN_GF2m_mod_div(d, a, c, b[j], ctx);
+			BN_GF2m_mod_mul(e, d, c, b[j], ctx);
+			BN_GF2m_mod_div(f, a, e, b[j], ctx);
+#if 0 /* make test uses ouput in bc but bc can't handle GF(2^m) arithmetic */
+			if (bp != NULL)
+				{
+				if (!results)
+					{
+					BN_print(bp,a);
+					BIO_puts(bp, " = ");
+					BN_print(bp,c);
+					BIO_puts(bp," * ");
+					BN_print(bp,d);
+					BIO_puts(bp, " % ");
+					BN_print(bp,b[j]);
+					BIO_puts(bp,"\n");
+					}
+				}
+#endif
+			/* Test that ((a/c)*c)/a = 1. */
+			if(!BN_is_one(f))
+				{
+				fprintf(stderr,"GF(2^m) modular division test failed!\n");
+				goto err;
+				}
+			}
+		}
+	ret = 1;
+  err:
+	BN_free(a);
+	BN_free(b[0]);
+	BN_free(b[1]);
+	BN_free(c);
+	BN_free(d);
+	BN_free(e);
+	BN_free(f);
+	return ret;
+	}
+
+int test_gf2m_mod_exp(BIO *bp,BN_CTX *ctx)
+	{
+	BIGNUM *a,*b[2],*c,*d,*e,*f;
+	int i, j, ret = 0;
+	unsigned int p0[] = {163,7,6,3,0};
+	unsigned int p1[] = {193,15,0};
+
+	a=BN_new();
+	b[0]=BN_new();
+	b[1]=BN_new();
+	c=BN_new();
+	d=BN_new();
+	e=BN_new();
+	f=BN_new();
+
+	BN_GF2m_arr2poly(p0, b[0]);
+	BN_GF2m_arr2poly(p1, b[1]);
+
+	for (i=0; i<num0; i++)
+		{
+		BN_bntest_rand(a, 512, 0, 0);
+		BN_bntest_rand(c, 512, 0, 0);
+		BN_bntest_rand(d, 512, 0, 0);
+		for (j=0; j < 2; j++)
+			{
+			BN_GF2m_mod_exp(e, a, c, b[j], ctx);
+			BN_GF2m_mod_exp(f, a, d, b[j], ctx);
+			BN_GF2m_mod_mul(e, e, f, b[j], ctx);
+			BN_add(f, c, d);
+			BN_GF2m_mod_exp(f, a, f, b[j], ctx);
+#if 0 /* make test uses ouput in bc but bc can't handle GF(2^m) arithmetic */
+			if (bp != NULL)
+				{
+				if (!results)
+					{
+					BN_print(bp,a);
+					BIO_puts(bp, " ^ (");
+					BN_print(bp,c);
+					BIO_puts(bp," + ");
+					BN_print(bp,d);
+					BIO_puts(bp, ") = ");
+					BN_print(bp,e);
+					BIO_puts(bp, "; - ");
+					BN_print(bp,f);
+					BIO_puts(bp, " % ");
+					BN_print(bp,b[j]);
+					BIO_puts(bp,"\n");
+					}
+				}
+#endif
+			BN_GF2m_add(f, e, f);
+			/* Test that a^(c+d)=a^c*a^d. */
+			if(!BN_is_zero(f))
+				{
+				fprintf(stderr,"GF(2^m) modular exponentiation test failed!\n");
+				goto err;
+				}
+			}
+		}
+	ret = 1;
+  err:
+	BN_free(a);
+	BN_free(b[0]);
+	BN_free(b[1]);
+	BN_free(c);
+	BN_free(d);
+	BN_free(e);
+	BN_free(f);
+	return ret;
+	}
+
+int test_gf2m_mod_sqrt(BIO *bp,BN_CTX *ctx)
+	{
+	BIGNUM *a,*b[2],*c,*d,*e,*f;
+	int i, j, ret = 0;
+	unsigned int p0[] = {163,7,6,3,0};
+	unsigned int p1[] = {193,15,0};
+
+	a=BN_new();
+	b[0]=BN_new();
+	b[1]=BN_new();
+	c=BN_new();
+	d=BN_new();
+	e=BN_new();
+	f=BN_new();
+
+	BN_GF2m_arr2poly(p0, b[0]);
+	BN_GF2m_arr2poly(p1, b[1]);
+
+	for (i=0; i<num0; i++)
+		{
+		BN_bntest_rand(a, 512, 0, 0);
+		for (j=0; j < 2; j++)
+			{
+			BN_GF2m_mod(c, a, b[j]);
+			BN_GF2m_mod_sqrt(d, a, b[j], ctx);
+			BN_GF2m_mod_sqr(e, d, b[j], ctx);
+#if 0 /* make test uses ouput in bc but bc can't handle GF(2^m) arithmetic */
+			if (bp != NULL)
+				{
+				if (!results)
+					{
+					BN_print(bp,d);
+					BIO_puts(bp, " ^ 2 - ");
+					BN_print(bp,a);
+					BIO_puts(bp,"\n");
+					}
+				}
+#endif
+			BN_GF2m_add(f, c, e);
+			/* Test that d^2 = a, where d = sqrt(a). */
+			if(!BN_is_zero(f))
+				{
+				fprintf(stderr,"GF(2^m) modular square root test failed!\n");
+				goto err;
+				}
+			}
+		}
+	ret = 1;
+  err:
+	BN_free(a);
+	BN_free(b[0]);
+	BN_free(b[1]);
+	BN_free(c);
+	BN_free(d);
+	BN_free(e);
+	BN_free(f);
+	return ret;
+	}
+
+int test_gf2m_mod_solve_quad(BIO *bp,BN_CTX *ctx)
+	{
+	BIGNUM *a,*b[2],*c,*d,*e;
+	int i, j, s = 0, t, ret = 0;
+	unsigned int p0[] = {163,7,6,3,0};
+	unsigned int p1[] = {193,15,0};
+
+	a=BN_new();
+	b[0]=BN_new();
+	b[1]=BN_new();
+	c=BN_new();
+	d=BN_new();
+	e=BN_new();
+
+	BN_GF2m_arr2poly(p0, b[0]);
+	BN_GF2m_arr2poly(p1, b[1]);
+
+	for (i=0; i<num0; i++)
+		{
+		BN_bntest_rand(a, 512, 0, 0);
+		for (j=0; j < 2; j++)
+			{
+			t = BN_GF2m_mod_solve_quad(c, a, b[j], ctx);
+			if (t)
+				{
+				s++;
+				BN_GF2m_mod_sqr(d, c, b[j], ctx);
+				BN_GF2m_add(d, c, d);
+				BN_GF2m_mod(e, a, b[j]);
+#if 0 /* make test uses ouput in bc but bc can't handle GF(2^m) arithmetic */
+				if (bp != NULL)
+					{
+					if (!results)
+						{
+						BN_print(bp,c);
+						BIO_puts(bp, " is root of z^2 + z = ");
+						BN_print(bp,a);
+						BIO_puts(bp, " % ");
+						BN_print(bp,b[j]);
+						BIO_puts(bp, "\n");
+						}
+					}
+#endif
+				BN_GF2m_add(e, e, d);
+				/* Test that solution of quadratic c satisfies c^2 + c = a. */
+				if(!BN_is_zero(e))
+					{
+					fprintf(stderr,"GF(2^m) modular solve quadratic test failed!\n");
+					goto err;
+					}
+
+				}
+			else 
+				{
+#if 0 /* make test uses ouput in bc but bc can't handle GF(2^m) arithmetic */
+				if (bp != NULL)
+					{
+					if (!results)
+						{
+						BIO_puts(bp, "There are no roots of z^2 + z = ");
+						BN_print(bp,a);
+						BIO_puts(bp, " % ");
+						BN_print(bp,b[j]);
+						BIO_puts(bp, "\n");
+						}
+					}
+#endif
+				}
+			}
+		}
+	if (s == 0)
+		{	
+		fprintf(stderr,"All %i tests of GF(2^m) modular solve quadratic resulted in no roots;\n", num0);
+		fprintf(stderr,"this is very unlikely and probably indicates an error.\n");
+		goto err;
+		}
+	ret = 1;
+  err:
+	BN_free(a);
+	BN_free(b[0]);
+	BN_free(b[1]);
+	BN_free(c);
+	BN_free(d);
+	BN_free(e);
+	return ret;
+	}
+
 static void genprime_cb(int p, int n, void *arg)
 	{
 	char c='*';