Ejemplo n.º 1
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 def test_lengths(self):
     default = NIST192p
     priv = SigningKey.generate()
     pub = priv.get_verifying_key()
     self.assertEqual(len(pub.to_string()), default.verifying_key_length)
     sig = priv.sign(b("data"))
     self.assertEqual(len(sig), default.signature_length)
     if BENCH:
         print_()
     for curve in (NIST192p, NIST224p, NIST256p, NIST384p, NIST521p):
         start = time.time()
         priv = SigningKey.generate(curve=curve)
         pub1 = priv.get_verifying_key()
         keygen_time = time.time() - start
         pub2 = VerifyingKey.from_string(pub1.to_string(), curve)
         self.assertEqual(pub1.to_string(), pub2.to_string())
         self.assertEqual(len(pub1.to_string()), curve.verifying_key_length)
         start = time.time()
         sig = priv.sign(b("data"))
         sign_time = time.time() - start
         self.assertEqual(len(sig), curve.signature_length)
         if BENCH:
             start = time.time()
             pub1.verify(sig, b("data"))
             verify_time = time.time() - start
             print_("%s: siglen=%d, keygen=%0.3fs, sign=%0.3f, verify=%0.3f" \
                    % (curve.name, curve.signature_length,
                       keygen_time, sign_time, verify_time))
Ejemplo n.º 2
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    def test_privkey_creation(self):
        s = "all the entropy in the entire world, compressed into one line"

        def not_much_entropy(numbytes):
            return s[:numbytes]

        priv1 = SigningKey.generate()
        self.failUnlessEqual(priv1.baselen, NIST192p.baselen)

        priv1 = SigningKey.generate(curve=NIST224p)
        self.failUnlessEqual(priv1.baselen, NIST224p.baselen)

        priv1 = SigningKey.generate(entropy=not_much_entropy)
        self.failUnlessEqual(priv1.baselen, NIST192p.baselen)
        priv2 = SigningKey.generate(entropy=not_much_entropy)
        self.failUnlessEqual(priv2.baselen, NIST192p.baselen)
        self.failUnlessPrivkeysEqual(priv1, priv2)

        priv1 = SigningKey.from_secret_exponent(secexp=3)
        self.failUnlessEqual(priv1.baselen, NIST192p.baselen)
        priv2 = SigningKey.from_secret_exponent(secexp=3)
        self.failUnlessPrivkeysEqual(priv1, priv2)

        priv1 = SigningKey.from_secret_exponent(secexp=4, curve=NIST224p)
        self.failUnlessEqual(priv1.baselen, NIST224p.baselen)
Ejemplo n.º 3
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    def test_privkey_creation(self):
        s = b("all the entropy in the entire world, compressed into one line")

        def not_much_entropy(numbytes):
            return s[:numbytes]

        priv1 = SigningKey.generate()
        self.assertEqual(priv1.baselen, NIST192p.baselen)

        priv1 = SigningKey.generate(curve=NIST224p)
        self.assertEqual(priv1.baselen, NIST224p.baselen)

        priv1 = SigningKey.generate(entropy=not_much_entropy)
        self.assertEqual(priv1.baselen, NIST192p.baselen)
        priv2 = SigningKey.generate(entropy=not_much_entropy)
        self.assertEqual(priv2.baselen, NIST192p.baselen)
        self.assertTruePrivkeysEqual(priv1, priv2)

        priv1 = SigningKey.from_secret_exponent(secexp=3)
        self.assertEqual(priv1.baselen, NIST192p.baselen)
        priv2 = SigningKey.from_secret_exponent(secexp=3)
        self.assertTruePrivkeysEqual(priv1, priv2)

        priv1 = SigningKey.from_secret_exponent(secexp=4, curve=NIST224p)
        self.assertEqual(priv1.baselen, NIST224p.baselen)
Ejemplo n.º 4
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    def test_privkey_strings(self):
        priv1 = SigningKey.generate()
        s1 = priv1.to_string()
        self.assertEqual(type(s1), binary_type)
        self.assertEqual(len(s1), NIST192p.baselen)
        priv2 = SigningKey.from_string(s1)
        self.assertTruePrivkeysEqual(priv1, priv2)

        s1 = priv1.to_pem()
        self.assertEqual(type(s1), binary_type)
        self.assertTrue(s1.startswith(b("-----BEGIN EC PRIVATE KEY-----")))
        self.assertTrue(s1.strip().endswith(b("-----END EC PRIVATE KEY-----")))
        priv2 = SigningKey.from_pem(s1)
        self.assertTruePrivkeysEqual(priv1, priv2)

        s1 = priv1.to_der()
        self.assertEqual(type(s1), binary_type)
        priv2 = SigningKey.from_der(s1)
        self.assertTruePrivkeysEqual(priv1, priv2)

        priv1 = SigningKey.generate(curve=NIST256p)
        s1 = priv1.to_pem()
        self.assertEqual(type(s1), binary_type)
        self.assertTrue(s1.startswith(b("-----BEGIN EC PRIVATE KEY-----")))
        self.assertTrue(s1.strip().endswith(b("-----END EC PRIVATE KEY-----")))
        priv2 = SigningKey.from_pem(s1)
        self.assertTruePrivkeysEqual(priv1, priv2)

        s1 = priv1.to_der()
        self.assertEqual(type(s1), binary_type)
        priv2 = SigningKey.from_der(s1)
        self.assertTruePrivkeysEqual(priv1, priv2)
Ejemplo n.º 5
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 def test_lengths(self):
     default = NIST192p
     priv = SigningKey.generate()
     pub = priv.get_verifying_key()
     self.failUnlessEqual(len(pub.to_string()), default.verifying_key_length)
     sig = priv.sign("data")
     self.failUnlessEqual(len(sig), default.signature_length)
     if BENCH:
         print
     for curve in (NIST192p, NIST224p, NIST256p, NIST384p, NIST521p):
         start = time.time()
         priv = SigningKey.generate(curve=curve)
         pub1 = priv.get_verifying_key()
         keygen_time = time.time() - start
         pub2 = VerifyingKey.from_string(pub1.to_string(), curve)
         self.failUnlessEqual(pub1.to_string(), pub2.to_string())
         self.failUnlessEqual(len(pub1.to_string()),
                              curve.verifying_key_length)
         start = time.time()
         sig = priv.sign("data")
         sign_time = time.time() - start
         self.failUnlessEqual(len(sig), curve.signature_length)
         if BENCH:
             start = time.time()
             pub1.verify(sig, "data")
             verify_time = time.time() - start
             print "%s: siglen=%d, keygen=%0.3fs, sign=%0.3f, verify=%0.3f" \
                   % (curve.name, curve.signature_length,
                      keygen_time, sign_time, verify_time)
Ejemplo n.º 6
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    def test_privkey_strings(self):
        priv1 = SigningKey.generate()
        s1 = priv1.to_string()
        self.failUnlessEqual(type(s1), str)
        self.failUnlessEqual(len(s1), NIST192p.baselen)
        priv2 = SigningKey.from_string(s1)
        self.failUnlessPrivkeysEqual(priv1, priv2)

        s1 = priv1.to_pem()
        self.failUnlessEqual(type(s1), str)
        self.failUnless(s1.startswith("-----BEGIN EC PRIVATE KEY-----"))
        self.failUnless(s1.strip().endswith("-----END EC PRIVATE KEY-----"))
        priv2 = SigningKey.from_pem(s1)
        self.failUnlessPrivkeysEqual(priv1, priv2)

        s1 = priv1.to_der()
        self.failUnlessEqual(type(s1), str)
        priv2 = SigningKey.from_der(s1)
        self.failUnlessPrivkeysEqual(priv1, priv2)

        priv1 = SigningKey.generate(curve=NIST256p)
        s1 = priv1.to_pem()
        self.failUnlessEqual(type(s1), str)
        self.failUnless(s1.startswith("-----BEGIN EC PRIVATE KEY-----"))
        self.failUnless(s1.strip().endswith("-----END EC PRIVATE KEY-----"))
        priv2 = SigningKey.from_pem(s1)
        self.failUnlessPrivkeysEqual(priv1, priv2)

        s1 = priv1.to_der()
        self.failUnlessEqual(type(s1), str)
        priv2 = SigningKey.from_der(s1)
        self.failUnlessPrivkeysEqual(priv1, priv2)
Ejemplo n.º 7
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    def do_test_to_openssl(self, curve, curvename):
        # Python: create sk, vk, sign.
        # OpenSSL: read vk(4), checksig(6), read sk(2), sign, check
        if os.path.isdir("t"):
            shutil.rmtree("t")
        os.mkdir("t")
        sk = SigningKey.generate(curve=curve)
        vk = sk.get_verifying_key()
        data = "data"
        open("t/pubkey.der", "wb").write(vk.to_der())  # 4
        open("t/pubkey.pem", "wb").write(vk.to_pem())  # 4
        sig_der = sk.sign(data, hashfunc=sha1, sigencode=sigencode_der)
        open("t/data.sig", "wb").write(sig_der)  # 6
        open("t/data.txt", "wb").write(data)
        open("t/baddata.txt", "wb").write(data + "corrupt")

        self.failUnlessRaises(
            SubprocessError, run,
            "openssl dgst -ecdsa-with-SHA1 -verify t/pubkey.der -keyform DER -signature t/data.sig t/baddata.txt"
        )
        run("openssl dgst -ecdsa-with-SHA1 -verify t/pubkey.der -keyform DER -signature t/data.sig t/data.txt"
            )

        open("t/privkey.pem", "wb").write(sk.to_pem())  # 2
        run("openssl dgst -ecdsa-with-SHA1 -sign t/privkey.pem -out t/data.sig2 t/data.txt"
            )
        run("openssl dgst -ecdsa-with-SHA1 -verify t/pubkey.pem -signature t/data.sig2 t/data.txt"
            )
Ejemplo n.º 8
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    def do_test_to_openssl(self, curve, curvename):
        # Python: create sk, vk, sign.
        # OpenSSL: read vk(4), checksig(6), read sk(2), sign, check
        mdarg = self.get_openssl_messagedigest_arg()
        if os.path.isdir("t"):
            shutil.rmtree("t")
        os.mkdir("t")
        sk = SigningKey.generate(curve=curve)
        vk = sk.get_verifying_key()
        data = "data"
        open("t/pubkey.der", "wb").write(vk.to_der())  # 4
        open("t/pubkey.pem", "wb").write(vk.to_pem())  # 4
        sig_der = sk.sign(data, hashfunc=sha1, sigencode=sigencode_der)
        open("t/data.sig", "wb").write(sig_der)  # 6
        open("t/data.txt", "wb").write(data)
        open("t/baddata.txt", "wb").write(data + "corrupt")

        self.failUnlessRaises(
            SubprocessError,
            run_openssl,
            "dgst %s -verify t/pubkey.der -keyform DER -signature t/data.sig t/baddata.txt" % mdarg,
        )
        run_openssl("dgst %s -verify t/pubkey.der -keyform DER -signature t/data.sig t/data.txt" % mdarg)

        open("t/privkey.pem", "wb").write(sk.to_pem())  # 2
        run_openssl("dgst %s -sign t/privkey.pem -out t/data.sig2 t/data.txt" % mdarg)
        run_openssl("dgst %s -verify t/pubkey.pem -signature t/data.sig2 t/data.txt" % mdarg)
Ejemplo n.º 9
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 def test_nonrandom(self):
     s = "all the entropy in the entire world, compressed into one line"
     def not_much_entropy(numbytes):
         return s[:numbytes]
     # we control the entropy source, these two keys should be identical:
     priv1 = SigningKey.generate(entropy=not_much_entropy)
     priv2 = SigningKey.generate(entropy=not_much_entropy)
     self.failUnlessEqual(hexlify(priv1.get_verifying_key().to_string()),
                          hexlify(priv2.get_verifying_key().to_string()))
     # likewise, signatures should be identical. Obviously you'd never
     # want to do this with keys you care about, because the secrecy of
     # the private key depends upon using different random numbers for
     # each signature
     sig1 = priv1.sign("data", entropy=not_much_entropy)
     sig2 = priv2.sign("data", entropy=not_much_entropy)
     self.failUnlessEqual(hexlify(sig1), hexlify(sig2))
Ejemplo n.º 10
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    def test_hashfunc(self):
        sk = SigningKey.generate(curve=NIST256p, hashfunc=sha256)
        data = "security level is 128 bits"
        sig = sk.sign(data)
        vk = VerifyingKey.from_string(sk.get_verifying_key().to_string(),
                                      curve=NIST256p, hashfunc=sha256)
        self.failUnless(vk.verify(sig, data))

        sk2 = SigningKey.generate(curve=NIST256p)
        sig2 = sk2.sign(data, hashfunc=sha256)
        vk2 = VerifyingKey.from_string(sk2.get_verifying_key().to_string(),
                                       curve=NIST256p, hashfunc=sha256)
        self.failUnless(vk2.verify(sig2, data))

        vk3 = VerifyingKey.from_string(sk.get_verifying_key().to_string(),
                                       curve=NIST256p)
        self.failUnless(vk3.verify(sig, data, hashfunc=sha256))
Ejemplo n.º 11
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    def test_nonrandom(self):
        s = b("all the entropy in the entire world, compressed into one line")

        def not_much_entropy(numbytes):
            return s[:numbytes]

        # we control the entropy source, these two keys should be identical:
        priv1 = SigningKey.generate(entropy=not_much_entropy)
        priv2 = SigningKey.generate(entropy=not_much_entropy)
        self.assertEqual(hexlify(priv1.get_verifying_key().to_string()),
                         hexlify(priv2.get_verifying_key().to_string()))
        # likewise, signatures should be identical. Obviously you'd never
        # want to do this with keys you care about, because the secrecy of
        # the private key depends upon using different random numbers for
        # each signature
        sig1 = priv1.sign(b("data"), entropy=not_much_entropy)
        sig2 = priv2.sign(b("data"), entropy=not_much_entropy)
        self.assertEqual(hexlify(sig1), hexlify(sig2))
Ejemplo n.º 12
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    def test_hashfunc(self):
        sk = SigningKey.generate(curve=NIST256p, hashfunc=sha256)
        data = b("security level is 128 bits")
        sig = sk.sign(data)
        vk = VerifyingKey.from_string(sk.get_verifying_key().to_string(),
                                      curve=NIST256p,
                                      hashfunc=sha256)
        self.assertTrue(vk.verify(sig, data))

        sk2 = SigningKey.generate(curve=NIST256p)
        sig2 = sk2.sign(data, hashfunc=sha256)
        vk2 = VerifyingKey.from_string(sk2.get_verifying_key().to_string(),
                                       curve=NIST256p,
                                       hashfunc=sha256)
        self.assertTrue(vk2.verify(sig2, data))

        vk3 = VerifyingKey.from_string(sk.get_verifying_key().to_string(),
                                       curve=NIST256p)
        self.assertTrue(vk3.verify(sig, data, hashfunc=sha256))
Ejemplo n.º 13
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    def test_pubkey_strings(self):
        priv1 = SigningKey.generate()
        pub1 = priv1.get_verifying_key()
        s1 = pub1.to_string()
        self.assertEqual(type(s1), binary_type)
        self.assertEqual(len(s1), NIST192p.verifying_key_length)
        pub2 = VerifyingKey.from_string(s1)
        self.assertTruePubkeysEqual(pub1, pub2)

        priv1 = SigningKey.generate(curve=NIST256p)
        pub1 = priv1.get_verifying_key()
        s1 = pub1.to_string()
        self.assertEqual(type(s1), binary_type)
        self.assertEqual(len(s1), NIST256p.verifying_key_length)
        pub2 = VerifyingKey.from_string(s1, curve=NIST256p)
        self.assertTruePubkeysEqual(pub1, pub2)

        pub1_der = pub1.to_der()
        self.assertEqual(type(pub1_der), binary_type)
        pub2 = VerifyingKey.from_der(pub1_der)
        self.assertTruePubkeysEqual(pub1, pub2)

        self.assertRaises(der.UnexpectedDER, VerifyingKey.from_der,
                          pub1_der + b("junk"))
        badpub = VerifyingKey.from_der(pub1_der)

        class FakeGenerator:
            def order(self):
                return 123456789

        badcurve = Curve("unknown", None, FakeGenerator(), (1, 2, 3, 4, 5, 6),
                         None)
        badpub.curve = badcurve
        badder = badpub.to_der()
        self.assertRaises(UnknownCurveError, VerifyingKey.from_der, badder)

        pem = pub1.to_pem()
        self.assertEqual(type(pem), binary_type)
        self.assertTrue(pem.startswith(b("-----BEGIN PUBLIC KEY-----")), pem)
        self.assertTrue(pem.strip().endswith(b("-----END PUBLIC KEY-----")),
                        pem)
        pub2 = VerifyingKey.from_pem(pem)
        self.assertTruePubkeysEqual(pub1, pub2)
Ejemplo n.º 14
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    def test_basic(self):
        priv = SigningKey.generate()
        pub = priv.get_verifying_key()

        data = "blahblah"
        sig = priv.sign(data)

        self.failUnless(pub.verify(sig, data))
        self.failUnlessRaises(BadSignatureError, pub.verify, sig, data + "bad")

        pub2 = VerifyingKey.from_string(pub.to_string())
        self.failUnless(pub2.verify(sig, data))
Ejemplo n.º 15
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    def test_basic(self):
        priv = SigningKey.generate()
        pub = priv.get_verifying_key()

        data = b("blahblah")
        sig = priv.sign(data)

        self.assertTrue(pub.verify(sig, data))
        self.assertRaises(BadSignatureError, pub.verify, sig, data + b("bad"))

        pub2 = VerifyingKey.from_string(pub.to_string())
        self.assertTrue(pub2.verify(sig, data))
Ejemplo n.º 16
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    def test_basic(self):
        priv = SigningKey.generate()
        pub = priv.get_verifying_key()

        data = "blahblah"
        sig = priv.sign(data)

        self.failUnless(pub.verify(sig, data))
        self.failUnlessRaises(BadSignatureError, pub.verify, sig, data+"bad")

        pub2 = VerifyingKey.from_string(pub.to_string())
        self.failUnless(pub2.verify(sig, data))
Ejemplo n.º 17
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    def test_pubkey_strings(self):
        priv1 = SigningKey.generate()
        pub1 = priv1.get_verifying_key()
        s1 = pub1.to_string()
        self.failUnlessEqual(type(s1), str)
        self.failUnlessEqual(len(s1), NIST192p.verifying_key_length)
        pub2 = VerifyingKey.from_string(s1)
        self.failUnlessPubkeysEqual(pub1, pub2)

        priv1 = SigningKey.generate(curve=NIST256p)
        pub1 = priv1.get_verifying_key()
        s1 = pub1.to_string()
        self.failUnlessEqual(type(s1), str)
        self.failUnlessEqual(len(s1), NIST256p.verifying_key_length)
        pub2 = VerifyingKey.from_string(s1, curve=NIST256p)
        self.failUnlessPubkeysEqual(pub1, pub2)

        pub1_der = pub1.to_der()
        self.failUnlessEqual(type(pub1_der), str)
        pub2 = VerifyingKey.from_der(pub1_der)
        self.failUnlessPubkeysEqual(pub1, pub2)

        self.failUnlessRaises(der.UnexpectedDER, VerifyingKey.from_der, pub1_der + "junk")
        badpub = VerifyingKey.from_der(pub1_der)

        class FakeGenerator:
            def order(self):
                return 123456789

        badcurve = Curve("unknown", None, FakeGenerator(), (1, 2, 3, 4, 5, 6))
        badpub.curve = badcurve
        badder = badpub.to_der()
        self.failUnlessRaises(UnknownCurveError, VerifyingKey.from_der, badder)

        pem = pub1.to_pem()
        self.failUnlessEqual(type(pem), str)
        self.failUnless(pem.startswith("-----BEGIN PUBLIC KEY-----"), pem)
        self.failUnless(pem.strip().endswith("-----END PUBLIC KEY-----"), pem)
        pub2 = VerifyingKey.from_pem(pem)
        self.failUnlessPubkeysEqual(pub1, pub2)
Ejemplo n.º 18
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    def do_test_to_openssl(self, curve):
        curvename = curve.openssl_name
        assert curvename
        # Python: create sk, vk, sign.
        # OpenSSL: read vk(4), checksig(6), read sk(2), sign, check
        mdarg = self.get_openssl_messagedigest_arg()
        if os.path.isdir("t"):
            shutil.rmtree("t")
        os.mkdir("t")
        sk = SigningKey.generate(curve=curve)
        vk = sk.get_verifying_key()
        data = b("data")
        with open("t/pubkey.der", "wb") as e:
            e.write(vk.to_der())  # 4
        with open("t/pubkey.pem", "wb") as e:
            e.write(vk.to_pem())  # 4
        sig_der = sk.sign(data, hashfunc=sha1, sigencode=sigencode_der)

        with open("t/data.sig", "wb") as e:
            e.write(sig_der)  # 6
        with open("t/data.txt", "wb") as e:
            e.write(data)
        with open("t/baddata.txt", "wb") as e:
            e.write(data + b("corrupt"))

        self.assertRaises(
            SubprocessError, run_openssl,
            "dgst %s -verify t/pubkey.der -keyform DER -signature t/data.sig t/baddata.txt"
            % mdarg)
        run_openssl(
            "dgst %s -verify t/pubkey.der -keyform DER -signature t/data.sig t/data.txt"
            % mdarg)

        with open("t/privkey.pem", "wb") as e:
            e.write(sk.to_pem())  # 2
        run_openssl("dgst %s -sign t/privkey.pem -out t/data.sig2 t/data.txt" %
                    mdarg)
        run_openssl(
            "dgst %s -verify t/pubkey.pem -signature t/data.sig2 t/data.txt" %
            mdarg)
Ejemplo n.º 19
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    def test_signature_strings(self):
        priv1 = SigningKey.generate()
        pub1 = priv1.get_verifying_key()
        data = b("data")

        sig = priv1.sign(data)
        self.assertEqual(type(sig), binary_type)
        self.assertEqual(len(sig), NIST192p.signature_length)
        self.assertTrue(pub1.verify(sig, data))

        sig = priv1.sign(data, sigencode=sigencode_strings)
        self.assertEqual(type(sig), tuple)
        self.assertEqual(len(sig), 2)
        self.assertEqual(type(sig[0]), binary_type)
        self.assertEqual(type(sig[1]), binary_type)
        self.assertEqual(len(sig[0]), NIST192p.baselen)
        self.assertEqual(len(sig[1]), NIST192p.baselen)
        self.assertTrue(pub1.verify(sig, data, sigdecode=sigdecode_strings))

        sig_der = priv1.sign(data, sigencode=sigencode_der)
        self.assertEqual(type(sig_der), binary_type)
        self.assertTrue(pub1.verify(sig_der, data, sigdecode=sigdecode_der))
Ejemplo n.º 20
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    def test_signature_strings(self):
        priv1 = SigningKey.generate()
        pub1 = priv1.get_verifying_key()
        data = "data"

        sig = priv1.sign(data)
        self.failUnlessEqual(type(sig), str)
        self.failUnlessEqual(len(sig), NIST192p.signature_length)
        self.failUnless(pub1.verify(sig, data))

        sig = priv1.sign(data, sigencode=sigencode_strings)
        self.failUnlessEqual(type(sig), tuple)
        self.failUnlessEqual(len(sig), 2)
        self.failUnlessEqual(type(sig[0]), str)
        self.failUnlessEqual(type(sig[1]), str)
        self.failUnlessEqual(len(sig[0]), NIST192p.baselen)
        self.failUnlessEqual(len(sig[1]), NIST192p.baselen)
        self.failUnless(pub1.verify(sig, data, sigdecode=sigdecode_strings))

        sig_der = priv1.sign(data, sigencode=sigencode_der)
        self.failUnlessEqual(type(sig_der), str)
        self.failUnless(pub1.verify(sig_der, data, sigdecode=sigdecode_der))
Ejemplo n.º 21
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    def test_signature_strings(self):
        priv1 = SigningKey.generate()
        pub1 = priv1.get_verifying_key()
        data = "data"

        sig = priv1.sign(data)
        self.failUnlessEqual(type(sig), str)
        self.failUnlessEqual(len(sig), NIST192p.signature_length)
        self.failUnless(pub1.verify(sig, data))

        sig = priv1.sign(data, sigencode=sigencode_strings)
        self.failUnlessEqual(type(sig), tuple)
        self.failUnlessEqual(len(sig), 2)
        self.failUnlessEqual(type(sig[0]), str)
        self.failUnlessEqual(type(sig[1]), str)
        self.failUnlessEqual(len(sig[0]), NIST192p.baselen)
        self.failUnlessEqual(len(sig[1]), NIST192p.baselen)
        self.failUnless(pub1.verify(sig, data, sigdecode=sigdecode_strings))

        sig_der = priv1.sign(data, sigencode=sigencode_der)
        self.failUnlessEqual(type(sig_der), str)
        self.failUnless(pub1.verify(sig_der, data, sigdecode=sigdecode_der))