Merge tag 'efi-2020-10-rc3-2' of https://gitlab.denx.de/u-boot/custodians/u-boot-efi

Pull request for UEFI sub-system for efi-2020-10-rc3 (2)

This series includes bug fixes for:

* UEFI secure boot - images with multiple signatures
* UEFI secure boot - support for intermediate certificates
* corrections for UEFI unit tests
* missing loadaddr on MAIX board

5 files changed, 326 insertions, 24 deletions

diff --git a/test/py/tests/test_efi_secboot/conftest.py b/test/py/tests/test_efi_secboot/conftest.py
index c0943b6..69a498c 100644
--- a/test/py/tests/test_efi_secboot/conftest.py
+++ b/test/py/tests/test_efi_secboot/conftest.py
@@ -25,13 +25,8 @@ def efi_boot_env(request, u_boot_config):
     Return:
         A path to disk image to be used for testing
     """
-    global HELLO_PATH
-
     image_path = u_boot_config.persistent_data_dir
-    image_path = image_path + '/' + EFI_SECBOOT_IMAGE_NAME
-
-    if HELLO_PATH == '':
-        HELLO_PATH = u_boot_config.build_dir + '/lib/efi_loader/helloworld.efi'
+    image_path = image_path + '/test_efi_secboot.img'
 
     try:
         mnt_point = u_boot_config.build_dir + '/mnt_efisecure'
@@ -75,9 +70,6 @@ def efi_boot_env(request, u_boot_config):
         check_call('cd %s; %scert-to-efi-sig-list -g %s db1.crt db1.esl; %ssign-efi-sig-list -t "2020-04-05" -c KEK.crt -k KEK.key db db1.esl db1.auth'
                    % (mnt_point, EFITOOLS_PATH, GUID, EFITOOLS_PATH),
                    shell=True)
-        # db1-update
-        check_call('cd %s; %ssign-efi-sig-list -t "2020-04-06" -a -c KEK.crt -k KEK.key db db1.esl db1-update.auth'
-                   % (mnt_point, EFITOOLS_PATH), shell=True)
         # dbx (TEST_dbx certificate)
         check_call('cd %s; openssl req -x509 -sha256 -newkey rsa:2048 -subj /CN=TEST_dbx/ -keyout dbx.key -out dbx.crt -nodes -days 365'
                    % mnt_point, shell=True)
@@ -89,7 +81,7 @@ def efi_boot_env(request, u_boot_config):
                    % (mnt_point, EFITOOLS_PATH, GUID, EFITOOLS_PATH),
                    shell=True)
         # dbx_hash1 (digest of TEST_db1 certificate)
-        check_call('cd %s; %scert-to-efi-hash-list -g %s -t 0 -s 256 db1.crt dbx_hash1.crl; %ssign-efi-sig-list -t "2020-04-05" -c KEK.crt -k KEK.key dbx dbx_hash1.crl dbx_hash1.auth'
+        check_call('cd %s; %scert-to-efi-hash-list -g %s -t 0 -s 256 db1.crt dbx_hash1.crl; %ssign-efi-sig-list -t "2020-04-06" -c KEK.crt -k KEK.key dbx dbx_hash1.crl dbx_hash1.auth'
                    % (mnt_point, EFITOOLS_PATH, GUID, EFITOOLS_PATH),
                    shell=True)
         # dbx_db (with TEST_db certificate)
@@ -98,7 +90,8 @@ def efi_boot_env(request, u_boot_config):
                    shell=True)
 
         # Copy image
-        check_call('cp %s %s' % (HELLO_PATH, mnt_point), shell=True)
+        check_call('cp %s/lib/efi_loader/helloworld.efi %s' %
+                   (u_boot_config.build_dir, mnt_point), shell=True)
 
         # Sign image
         check_call('cd %s; sbsign --key db.key --cert db.crt helloworld.efi'
@@ -128,3 +121,119 @@ def efi_boot_env(request, u_boot_config):
         yield image_path
     finally:
         call('rm -f %s' % image_path, shell=True)
+
+#
+# Fixture for UEFI secure boot test of intermediate certificates
+#
+
+
+@pytest.fixture(scope='session')
+def efi_boot_env_intca(request, u_boot_config):
+    """Set up a file system to be used in UEFI secure boot test
+    of intermediate certificates.
+
+    Args:
+        request: Pytest request object.
+        u_boot_config: U-boot configuration.
+
+    Return:
+        A path to disk image to be used for testing
+    """
+    image_path = u_boot_config.persistent_data_dir
+    image_path = image_path + '/test_efi_secboot_intca.img'
+
+    try:
+        mnt_point = u_boot_config.persistent_data_dir + '/mnt_efi_secboot_intca'
+        check_call('rm -rf {}'.format(mnt_point), shell=True)
+        check_call('mkdir -p {}'.format(mnt_point), shell=True)
+
+        # Create signature database
+        # PK
+        check_call('cd %s; openssl req -x509 -sha256 -newkey rsa:2048 -subj /CN=TEST_PK/ -keyout PK.key -out PK.crt -nodes -days 365'
+                   % mnt_point, shell=True)
+        check_call('cd %s; %scert-to-efi-sig-list -g %s PK.crt PK.esl; %ssign-efi-sig-list -c PK.crt -k PK.key PK PK.esl PK.auth'
+                   % (mnt_point, EFITOOLS_PATH, GUID, EFITOOLS_PATH),
+                   shell=True)
+        # KEK
+        check_call('cd %s; openssl req -x509 -sha256 -newkey rsa:2048 -subj /CN=TEST_KEK/ -keyout KEK.key -out KEK.crt -nodes -days 365'
+                   % mnt_point, shell=True)
+        check_call('cd %s; %scert-to-efi-sig-list -g %s KEK.crt KEK.esl; %ssign-efi-sig-list -c PK.crt -k PK.key KEK KEK.esl KEK.auth'
+                   % (mnt_point, EFITOOLS_PATH, GUID, EFITOOLS_PATH),
+                   shell=True)
+
+        # We will have three-tier hierarchy of certificates:
+        #   TestRoot: Root CA (self-signed)
+        #   TestSub: Intermediate CA (signed by Root CA)
+        #   TestCert: User certificate (signed by Intermediate CA, and used
+        #             for signing an image)
+        #
+        # NOTE:
+        # I consulted the following EDK2 document for certificate options:
+        #     BaseTools/Source/Python/Pkcs7Sign/Readme.md
+        # Please not use them as they are in product system. They are
+        # for test purpose only.
+
+        # TestRoot
+        check_call('cp %s/test/py/tests/test_efi_secboot/openssl.cnf %s'
+                   % (u_boot_config.source_dir, mnt_point), shell=True)
+        check_call('cd %s; export OPENSSL_CONF=./openssl.cnf; openssl genrsa -out TestRoot.key 2048; openssl req -extensions v3_ca -new -x509 -days 365 -key TestRoot.key -out TestRoot.crt -subj "/CN=TEST_root/"; touch index.txt; touch index.txt.attr'
+                   % mnt_point, shell=True)
+        # TestSub
+        check_call('cd %s; touch serial.new; export OPENSSL_CONF=./openssl.cnf; openssl genrsa -out TestSub.key 2048; openssl req -new -key TestSub.key -out TestSub.csr -subj "/CN=TEST_sub/"; openssl ca -in TestSub.csr -out TestSub.crt -extensions v3_int_ca -days 365 -batch -rand_serial -cert TestRoot.crt -keyfile TestRoot.key'
+                   % mnt_point, shell=True)
+        # TestCert
+        check_call('cd %s; touch serial.new; export OPENSSL_CONF=./openssl.cnf; openssl genrsa -out TestCert.key 2048; openssl req -new -key TestCert.key -out TestCert.csr -subj "/CN=TEST_cert/"; openssl ca -in TestCert.csr -out TestCert.crt -extensions usr_cert -days 365 -batch -rand_serial -cert TestSub.crt -keyfile TestSub.key'
+                   % mnt_point, shell=True)
+        # db
+        #  for TestCert
+        check_call('cd %s; %scert-to-efi-sig-list -g %s TestCert.crt TestCert.esl; %ssign-efi-sig-list -c KEK.crt -k KEK.key db TestCert.esl db_a.auth'
+                   % (mnt_point, EFITOOLS_PATH, GUID, EFITOOLS_PATH),
+                   shell=True)
+        #  for TestSub
+        check_call('cd %s; %scert-to-efi-sig-list -g %s TestSub.crt TestSub.esl; %ssign-efi-sig-list -t "2020-07-16" -c KEK.crt -k KEK.key db TestSub.esl db_b.auth'
+                   % (mnt_point, EFITOOLS_PATH, GUID, EFITOOLS_PATH),
+                   shell=True)
+        #  for TestRoot
+        check_call('cd %s; %scert-to-efi-sig-list -g %s TestRoot.crt TestRoot.esl; %ssign-efi-sig-list -t "2020-07-17" -c KEK.crt -k KEK.key db TestRoot.esl db_c.auth'
+                   % (mnt_point, EFITOOLS_PATH, GUID, EFITOOLS_PATH),
+                   shell=True)
+        ## dbx (hash of certificate with revocation time)
+        #  for TestCert
+        check_call('cd %s; %scert-to-efi-hash-list -g %s -t "2020-07-20" -s 256 TestCert.crt TestCert.crl; %ssign-efi-sig-list -c KEK.crt -k KEK.key dbx TestCert.crl dbx_a.auth'
+                   % (mnt_point, EFITOOLS_PATH, GUID, EFITOOLS_PATH),
+                   shell=True)
+        #  for TestSub
+        check_call('cd %s; %scert-to-efi-hash-list -g %s -t "2020-07-21" -s 256 TestSub.crt TestSub.crl; %ssign-efi-sig-list -t "2020-07-18" -c KEK.crt -k KEK.key dbx TestSub.crl dbx_b.auth'
+                   % (mnt_point, EFITOOLS_PATH, GUID, EFITOOLS_PATH),
+                   shell=True)
+        #  for TestRoot
+        check_call('cd %s; %scert-to-efi-hash-list -g %s -t "2020-07-22" -s 256 TestRoot.crt TestRoot.crl; %ssign-efi-sig-list -t "2020-07-19" -c KEK.crt -k KEK.key dbx TestRoot.crl dbx_c.auth'
+                   % (mnt_point, EFITOOLS_PATH, GUID, EFITOOLS_PATH),
+                   shell=True)
+
+        # Sign image
+        # additional intermediate certificates may be included
+        # in SignedData
+
+        check_call('cp %s/lib/efi_loader/helloworld.efi %s' %
+                   (u_boot_config.build_dir, mnt_point), shell=True)
+        # signed by TestCert
+        check_call('cd %s; %ssbsign --key TestCert.key --cert TestCert.crt --out helloworld.efi.signed_a helloworld.efi'
+                   % (mnt_point, SBSIGN_PATH), shell=True)
+        # signed by TestCert with TestSub in signature
+        check_call('cd %s; %ssbsign --key TestCert.key --cert TestCert.crt --addcert TestSub.crt --out helloworld.efi.signed_ab helloworld.efi'
+                   % (mnt_point, SBSIGN_PATH), shell=True)
+        # signed by TestCert with TestSub and TestRoot in signature
+        check_call('cd %s; cat TestSub.crt TestRoot.crt > TestSubRoot.crt; %ssbsign --key TestCert.key --cert TestCert.crt --addcert TestSubRoot.crt --out helloworld.efi.signed_abc helloworld.efi'
+                   % (mnt_point, SBSIGN_PATH), shell=True)
+
+        check_call('virt-make-fs --partition=gpt --size=+1M --type=vfat {} {}'.format(mnt_point, image_path), shell=True)
+        check_call('rm -rf {}'.format(mnt_point), shell=True)
+
+    except CalledProcessError as e:
+        pytest.skip('Setup failed: %s' % e.cmd)
+        return
+    else:
+        yield image_path
+    finally:
+        call('rm -f %s' % image_path, shell=True)
diff --git a/test/py/tests/test_efi_secboot/defs.py b/test/py/tests/test_efi_secboot/defs.py
index ba6b9f3..b7a2a11 100644
--- a/test/py/tests/test_efi_secboot/defs.py
+++ b/test/py/tests/test_efi_secboot/defs.py
@@ -1,14 +1,14 @@
 # SPDX-License-Identifier:      GPL-2.0+
 
-# Disk image name
-EFI_SECBOOT_IMAGE_NAME = 'test_efi_secboot.img'
-
 # Owner guid
 GUID = '11111111-2222-3333-4444-123456789abc'
 
 # v1.5.1 or earlier of efitools has a bug in sha256 calculation, and
 # you need build a newer version on your own.
+# The path must terminate with '/'.
 EFITOOLS_PATH = ''
 
-# Hello World application for sandbox
-HELLO_PATH = ''
+# "--addcert" option of sbsign must be available, otherwise
+# you need build a newer version on your own.
+# The path must terminate with '/'.
+SBSIGN_PATH = ''
diff --git a/test/py/tests/test_efi_secboot/openssl.cnf b/test/py/tests/test_efi_secboot/openssl.cnf
new file mode 100644
index 0000000..f684f1d
--- /dev/null
+++ b/test/py/tests/test_efi_secboot/openssl.cnf
@@ -0,0 +1,48 @@
+[ ca ]
+default_ca = CA_default
+
+[ CA_default ]
+new_certs_dir = .
+database = ./index.txt
+serial = ./serial
+default_md = sha256
+policy = policy_min
+
+[ req ]
+distinguished_name = def_distinguished_name
+
+[def_distinguished_name]
+
+# Extensions
+#   -addext " ... = ..."
+#
+[ v3_ca ]
+   # Extensions for a typical Root CA.
+   basicConstraints = critical,CA:TRUE
+   keyUsage = critical, digitalSignature, cRLSign, keyCertSign
+   subjectKeyIdentifier = hash
+   authorityKeyIdentifier = keyid:always,issuer
+
+[ v3_int_ca ]
+   # Extensions for a typical intermediate CA.
+   basicConstraints = critical, CA:TRUE
+   keyUsage = critical, digitalSignature, cRLSign, keyCertSign
+   subjectKeyIdentifier = hash
+   authorityKeyIdentifier = keyid:always,issuer
+
+[ usr_cert ]
+   # Extensions for user end certificates.
+   basicConstraints = CA:FALSE
+   keyUsage = critical, nonRepudiation, digitalSignature, keyEncipherment
+   extendedKeyUsage = clientAuth, emailProtection
+   subjectKeyIdentifier = hash
+   authorityKeyIdentifier = keyid,issuer
+
+[ policy_min ]
+   countryName		= optional
+   stateOrProvinceName	= optional
+   localityName		= optional
+   organizationName	= optional
+   organizationalUnitName = optional
+   commonName		= supplied
+   emailAddress		= optional
diff --git a/test/py/tests/test_efi_secboot/test_signed.py b/test/py/tests/test_efi_secboot/test_signed.py
index 7531bba..1443ba7 100644
--- a/test/py/tests/test_efi_secboot/test_signed.py
+++ b/test/py/tests/test_efi_secboot/test_signed.py
@@ -157,7 +157,8 @@ class TestEfiSignedImage(object):
         u_boot_console.restart_uboot()
         disk_img = efi_boot_env
         with u_boot_console.log.section('Test Case 5a'):
-            # Test Case 5a, rejected if any of signatures is not verified
+            # Test Case 5a, authenticated even if only one of signatures
+            # is verified
             output = u_boot_console.run_command_list([
                 'host bind 0 %s' % disk_img,
                 'fatload host 0:1 4000000 db.auth',
@@ -171,8 +172,7 @@ class TestEfiSignedImage(object):
                 'efidebug boot add 1 HELLO host 0:1 /helloworld.efi.signed_2sigs ""',
                 'efidebug boot next 1',
                 'efidebug test bootmgr'])
-            assert '\'HELLO\' failed' in ''.join(output)
-            assert 'efi_start_image() returned: 26' in ''.join(output)
+            assert 'Hello, world!' in ''.join(output)
 
         with u_boot_console.log.section('Test Case 5b'):
             # Test Case 5b, authenticated if both signatures are verified
@@ -181,19 +181,29 @@ class TestEfiSignedImage(object):
                 'setenv -e -nv -bs -rt -at -a -i 4000000,$filesize db'])
             assert 'Failed to set EFI variable' not in ''.join(output)
             output = u_boot_console.run_command_list([
-                'efidebug boot add 1 HELLO host 0:1 /helloworld.efi.signed_2sigs ""',
                 'efidebug boot next 1',
-                'bootefi bootmgr'])
+                'efidebug test bootmgr'])
             assert 'Hello, world!' in ''.join(output)
 
         with u_boot_console.log.section('Test Case 5c'):
-            # Test Case 5c, rejected if any of signatures is revoked
+            # Test Case 5c, not rejected if one of signatures (digest of
+            # certificate) is revoked
             output = u_boot_console.run_command_list([
-                'fatload host 0:1 4000000 dbx_hash1.auth',
+                'fatload host 0:1 4000000 dbx_hash.auth',
                 'setenv -e -nv -bs -rt -at -i 4000000,$filesize dbx'])
             assert 'Failed to set EFI variable' not in ''.join(output)
             output = u_boot_console.run_command_list([
-                'efidebug boot add 1 HELLO host 0:1 /helloworld.efi.signed_2sigs ""',
+                'efidebug boot next 1',
+                'efidebug test bootmgr'])
+            assert 'Hello, world!' in ''.join(output)
+
+        with u_boot_console.log.section('Test Case 5d'):
+            # Test Case 5d, rejected if both of signatures are revoked
+            output = u_boot_console.run_command_list([
+                'fatload host 0:1 4000000 dbx_hash1.auth',
+                'setenv -e -nv -bs -rt -at -a -i 4000000,$filesize dbx'])
+            assert 'Failed to set EFI variable' not in ''.join(output)
+            output = u_boot_console.run_command_list([
                 'efidebug boot next 1',
                 'efidebug test bootmgr'])
             assert '\'HELLO\' failed' in ''.join(output)
diff --git a/test/py/tests/test_efi_secboot/test_signed_intca.py b/test/py/tests/test_efi_secboot/test_signed_intca.py
new file mode 100644
index 0000000..1e5f4d0
--- /dev/null
+++ b/test/py/tests/test_efi_secboot/test_signed_intca.py
@@ -0,0 +1,135 @@
+# SPDX-License-Identifier:      GPL-2.0+
+# Copyright (c) 2020, Linaro Limited
+# Author: AKASHI Takahiro <takahiro.akashi@linaro.org>
+#
+# U-Boot UEFI: Image Authentication Test (signature with certificates chain)
+
+"""
+This test verifies image authentication for a signed image which is signed
+by user certificate and contains additional intermediate certificates in its
+signature.
+"""
+
+import pytest
+
+
+@pytest.mark.boardspec('sandbox')
+@pytest.mark.buildconfigspec('efi_secure_boot')
+@pytest.mark.buildconfigspec('cmd_efidebug')
+@pytest.mark.buildconfigspec('cmd_fat')
+@pytest.mark.buildconfigspec('cmd_nvedit_efi')
+@pytest.mark.slow
+class TestEfiSignedImageIntca(object):
+    def test_efi_signed_image_intca1(self, u_boot_console, efi_boot_env_intca):
+        """
+        Test Case 1 - authenticated by root CA in db
+        """
+        u_boot_console.restart_uboot()
+        disk_img = efi_boot_env_intca
+        with u_boot_console.log.section('Test Case 1a'):
+            # Test Case 1a, with no Int CA and not authenticated by root CA
+            output = u_boot_console.run_command_list([
+                'host bind 0 %s' % disk_img,
+                'fatload host 0:1 4000000 db_c.auth',
+                'setenv -e -nv -bs -rt -at -i 4000000,$filesize db',
+                'fatload host 0:1 4000000 KEK.auth',
+                'setenv -e -nv -bs -rt -at -i 4000000,$filesize KEK',
+                'fatload host 0:1 4000000 PK.auth',
+                'setenv -e -nv -bs -rt -at -i 4000000,$filesize PK'])
+            assert 'Failed to set EFI variable' not in ''.join(output)
+
+            output = u_boot_console.run_command_list([
+                'efidebug boot add 1 HELLO_a host 0:1 /helloworld.efi.signed_a ""',
+                'efidebug boot next 1',
+                'efidebug test bootmgr'])
+            assert '\'HELLO_a\' failed' in ''.join(output)
+            assert 'efi_start_image() returned: 26' in ''.join(output)
+
+        with u_boot_console.log.section('Test Case 1b'):
+            # Test Case 1b, signed and authenticated by root CA
+            output = u_boot_console.run_command_list([
+                'efidebug boot add 2 HELLO_ab host 0:1 /helloworld.efi.signed_ab ""',
+                'efidebug boot next 2',
+                'bootefi bootmgr'])
+            assert 'Hello, world!' in ''.join(output)
+
+    def test_efi_signed_image_intca2(self, u_boot_console, efi_boot_env_intca):
+        """
+        Test Case 2 - authenticated by root CA in db
+        """
+        u_boot_console.restart_uboot()
+        disk_img = efi_boot_env_intca
+        with u_boot_console.log.section('Test Case 2a'):
+            # Test Case 2a, unsigned and not authenticated by root CA
+            output = u_boot_console.run_command_list([
+                'host bind 0 %s' % disk_img,
+                'fatload host 0:1 4000000 KEK.auth',
+                'setenv -e -nv -bs -rt -at -i 4000000,$filesize KEK',
+                'fatload host 0:1 4000000 PK.auth',
+                'setenv -e -nv -bs -rt -at -i 4000000,$filesize PK'])
+            assert 'Failed to set EFI variable' not in ''.join(output)
+
+            output = u_boot_console.run_command_list([
+                'efidebug boot add 1 HELLO_abc host 0:1 /helloworld.efi.signed_abc ""',
+                'efidebug boot next 1',
+                'efidebug test bootmgr'])
+            assert '\'HELLO_abc\' failed' in ''.join(output)
+            assert 'efi_start_image() returned: 26' in ''.join(output)
+
+        with u_boot_console.log.section('Test Case 2b'):
+            # Test Case 2b, signed and authenticated by root CA
+            output = u_boot_console.run_command_list([
+                'fatload host 0:1 4000000 db_b.auth',
+                'setenv -e -nv -bs -rt -at -i 4000000,$filesize db',
+                'efidebug boot next 1',
+                'efidebug test bootmgr'])
+            assert '\'HELLO_abc\' failed' in ''.join(output)
+            assert 'efi_start_image() returned: 26' in ''.join(output)
+
+        with u_boot_console.log.section('Test Case 2c'):
+            # Test Case 2c, signed and authenticated by root CA
+            output = u_boot_console.run_command_list([
+                'fatload host 0:1 4000000 db_c.auth',
+                'setenv -e -nv -bs -rt -at -i 4000000,$filesize db',
+                'efidebug boot next 1',
+                'efidebug test bootmgr'])
+            assert 'Hello, world!' in ''.join(output)
+
+    def test_efi_signed_image_intca3(self, u_boot_console, efi_boot_env_intca):
+        """
+        Test Case 3 - revoked by dbx
+        """
+        u_boot_console.restart_uboot()
+        disk_img = efi_boot_env_intca
+        with u_boot_console.log.section('Test Case 3a'):
+            # Test Case 3a, revoked by int CA in dbx
+            output = u_boot_console.run_command_list([
+                'host bind 0 %s' % disk_img,
+                'fatload host 0:1 4000000 dbx_b.auth',
+                'setenv -e -nv -bs -rt -at -i 4000000,$filesize dbx',
+                'fatload host 0:1 4000000 db_c.auth',
+                'setenv -e -nv -bs -rt -at -i 4000000,$filesize db',
+                'fatload host 0:1 4000000 KEK.auth',
+                'setenv -e -nv -bs -rt -at -i 4000000,$filesize KEK',
+                'fatload host 0:1 4000000 PK.auth',
+                'setenv -e -nv -bs -rt -at -i 4000000,$filesize PK'])
+            assert 'Failed to set EFI variable' not in ''.join(output)
+
+            output = u_boot_console.run_command_list([
+                'efidebug boot add 1 HELLO_abc host 0:1 /helloworld.efi.signed_abc ""',
+                'efidebug boot next 1',
+                'efidebug test bootmgr'])
+            assert 'Hello, world!' in ''.join(output)
+            # Or,
+            # assert '\'HELLO_abc\' failed' in ''.join(output)
+            # assert 'efi_start_image() returned: 26' in ''.join(output)
+
+        with u_boot_console.log.section('Test Case 3b'):
+            # Test Case 3b, revoked by root CA in dbx
+            output = u_boot_console.run_command_list([
+                'fatload host 0:1 4000000 dbx_c.auth',
+                'setenv -e -nv -bs -rt -at -i 4000000,$filesize dbx',
+                'efidebug boot next 1',
+                'efidebug test bootmgr'])
+            assert '\'HELLO_abc\' failed' in ''.join(output)
+            assert 'efi_start_image() returned: 26' in ''.join(output)