1 files changed, 448 insertions, 0 deletions
diff --git a/third_party/python/ecdsa/ecdsa/test_ecdsa.py b/third_party/python/ecdsa/ecdsa/test_ecdsa.py
new file mode 100644
index 0000000000..71c68913ac
--- /dev/null
+++ b/third_party/python/ecdsa/ecdsa/test_ecdsa.py
@@ -0,0 +1,448 @@
+from __future__ import print_function
+import sys
+import hypothesis.strategies as st
+from hypothesis import given, settings, note, example
+try:
+    import unittest2 as unittest
+except ImportError:
+    import unittest
+import pytest
+from .ecdsa import Private_key, Public_key, Signature, \
+    generator_192, digest_integer, ellipticcurve, point_is_valid, \
+    generator_224, generator_256, generator_384, generator_521, \
+    generator_secp256k1
+
+
+HYP_SETTINGS = {}
+# old hypothesis doesn't have the "deadline" setting
+if sys.version_info > (2, 7):  # pragma: no branch
+    # SEC521p is slow, allow long execution for it
+    HYP_SETTINGS["deadline"] = 5000
+
+
+class TestP192FromX9_62(unittest.TestCase):
+    """Check test vectors from X9.62"""
+    @classmethod
+    def setUpClass(cls):
+        cls.d = 651056770906015076056810763456358567190100156695615665659
+        cls.Q = cls.d * generator_192
+        cls.k = 6140507067065001063065065565667405560006161556565665656654
+        cls.R = cls.k * generator_192
+
+        cls.msg = 968236873715988614170569073515315707566766479517
+        cls.pubk = Public_key(generator_192, generator_192 * cls.d)
+        cls.privk = Private_key(cls.pubk, cls.d)
+        cls.sig = cls.privk.sign(cls.msg, cls.k)
+
+    def test_point_multiplication(self):
+        assert self.Q.x() == 0x62B12D60690CDCF330BABAB6E69763B471F994DD702D16A5
+
+    def test_point_multiplication_2(self):
+        assert self.R.x() == 0x885052380FF147B734C330C43D39B2C4A89F29B0F749FEAD
+        assert self.R.y() == 0x9CF9FA1CBEFEFB917747A3BB29C072B9289C2547884FD835
+
+    def test_mult_and_addition(self):
+        u1 = 2563697409189434185194736134579731015366492496392189760599
+        u2 = 6266643813348617967186477710235785849136406323338782220568
+        temp = u1 * generator_192 + u2 * self.Q
+        assert temp.x() == 0x885052380FF147B734C330C43D39B2C4A89F29B0F749FEAD
+        assert temp.y() == 0x9CF9FA1CBEFEFB917747A3BB29C072B9289C2547884FD835
+
+    def test_signature(self):
+        r, s = self.sig.r, self.sig.s
+        assert r == 3342403536405981729393488334694600415596881826869351677613
+        assert s == 5735822328888155254683894997897571951568553642892029982342
+
+    def test_verification(self):
+        assert self.pubk.verifies(self.msg, self.sig)
+
+    def test_rejection(self):
+        assert not self.pubk.verifies(self.msg - 1, self.sig)
+
+
+class TestPublicKey(unittest.TestCase):
+       
+    def test_equality_public_keys(self):
+        gen = generator_192
+        x = 0xc58d61f88d905293bcd4cd0080bcb1b7f811f2ffa41979f6
+        y = 0x8804dc7a7c4c7f8b5d437f5156f3312ca7d6de8a0e11867f        
+        point = ellipticcurve.Point(gen.curve(), x, y)
+        pub_key1 = Public_key(gen, point)
+        pub_key2 = Public_key(gen, point)
+        self.assertEqual(pub_key1, pub_key2)
+        
+    def test_inequality_public_key(self):
+        gen = generator_192
+        x1 = 0xc58d61f88d905293bcd4cd0080bcb1b7f811f2ffa41979f6
+        y1 = 0x8804dc7a7c4c7f8b5d437f5156f3312ca7d6de8a0e11867f  
+        point1 = ellipticcurve.Point(gen.curve(), x1, y1)
+                
+        x2 = 0x6a223d00bd22c52833409a163e057e5b5da1def2a197dd15
+        y2 = 0x7b482604199367f1f303f9ef627f922f97023e90eae08abf
+        point2 = ellipticcurve.Point(gen.curve(), x2, y2)
+        
+        pub_key1 = Public_key(gen, point1)
+        pub_key2 = Public_key(gen, point2)
+        self.assertNotEqual(pub_key1, pub_key2)
+        
+    def test_inequality_public_key_not_implemented(self):
+        gen = generator_192
+        x = 0xc58d61f88d905293bcd4cd0080bcb1b7f811f2ffa41979f6
+        y = 0x8804dc7a7c4c7f8b5d437f5156f3312ca7d6de8a0e11867f        
+        point = ellipticcurve.Point(gen.curve(), x, y)
+        pub_key = Public_key(gen, point)
+        self.assertNotEqual(pub_key, None)
+
+
+class TestPrivateKey(unittest.TestCase):
+
+    @classmethod
+    def setUpClass(cls):
+        gen = generator_192
+        x = 0xc58d61f88d905293bcd4cd0080bcb1b7f811f2ffa41979f6
+        y = 0x8804dc7a7c4c7f8b5d437f5156f3312ca7d6de8a0e11867f        
+        point = ellipticcurve.Point(gen.curve(), x, y)
+        cls.pub_key = Public_key(gen, point)
+        
+    def test_equality_private_keys(self):
+        pr_key1 = Private_key(self.pub_key, 100)
+        pr_key2 = Private_key(self.pub_key, 100)
+        self.assertEqual(pr_key1, pr_key2)
+        
+    def test_inequality_private_keys(self):
+        pr_key1 = Private_key(self.pub_key, 100)
+        pr_key2 = Private_key(self.pub_key, 200)
+        self.assertNotEqual(pr_key1, pr_key2)
+        
+    def test_inequality_private_keys_not_implemented(self):
+        pr_key = Private_key(self.pub_key, 100)
+        self.assertNotEqual(pr_key, None)
+        
+
+# Testing point validity, as per ECDSAVS.pdf B.2.2:
+P192_POINTS = [
+    (generator_192,
+     0xcd6d0f029a023e9aaca429615b8f577abee685d8257cc83a,
+     0x00019c410987680e9fb6c0b6ecc01d9a2647c8bae27721bacdfc,
+     False),
+
+    (generator_192,
+     0x00017f2fce203639e9eaf9fb50b81fc32776b30e3b02af16c73b,
+     0x95da95c5e72dd48e229d4748d4eee658a9a54111b23b2adb,
+     False),
+
+    (generator_192,
+     0x4f77f8bc7fccbadd5760f4938746d5f253ee2168c1cf2792,
+     0x000147156ff824d131629739817edb197717c41aab5c2a70f0f6,
+     False),
+
+    (generator_192,
+     0xc58d61f88d905293bcd4cd0080bcb1b7f811f2ffa41979f6,
+     0x8804dc7a7c4c7f8b5d437f5156f3312ca7d6de8a0e11867f,
+     True),
+
+    (generator_192,
+     0xcdf56c1aa3d8afc53c521adf3ffb96734a6a630a4a5b5a70,
+     0x97c1c44a5fb229007b5ec5d25f7413d170068ffd023caa4e,
+     True),
+
+    (generator_192,
+     0x89009c0dc361c81e99280c8e91df578df88cdf4b0cdedced,
+     0x27be44a529b7513e727251f128b34262a0fd4d8ec82377b9,
+     True),
+
+    (generator_192,
+     0x6a223d00bd22c52833409a163e057e5b5da1def2a197dd15,
+     0x7b482604199367f1f303f9ef627f922f97023e90eae08abf,
+     True),
+
+    (generator_192,
+     0x6dccbde75c0948c98dab32ea0bc59fe125cf0fb1a3798eda,
+     0x0001171a3e0fa60cf3096f4e116b556198de430e1fbd330c8835,
+     False),
+
+    (generator_192,
+     0xd266b39e1f491fc4acbbbc7d098430931cfa66d55015af12,
+     0x193782eb909e391a3148b7764e6b234aa94e48d30a16dbb2,
+     False),
+
+    (generator_192,
+     0x9d6ddbcd439baa0c6b80a654091680e462a7d1d3f1ffeb43,
+     0x6ad8efc4d133ccf167c44eb4691c80abffb9f82b932b8caa,
+     False),
+
+    (generator_192,
+     0x146479d944e6bda87e5b35818aa666a4c998a71f4e95edbc,
+     0xa86d6fe62bc8fbd88139693f842635f687f132255858e7f6,
+     False),
+
+    (generator_192,
+     0xe594d4a598046f3598243f50fd2c7bd7d380edb055802253,
+     0x509014c0c4d6b536e3ca750ec09066af39b4c8616a53a923,
+     False)]
+
+
+@pytest.mark.parametrize("generator,x,y,expected", P192_POINTS)
+def test_point_validity(generator, x, y, expected):
+    """
+    `generator` defines the curve; is `(x, y)` a point on
+    this curve? `expected` is True if the right answer is Yes.
+    """
+    assert point_is_valid(generator, x, y) == expected
+
+
+# Trying signature-verification tests from ECDSAVS.pdf B.2.4:
+CURVE_192_KATS = [
+    (generator_192,
+     int("0x84ce72aa8699df436059f052ac51b6398d2511e49631bcb7e71f89c499b9ee"
+         "425dfbc13a5f6d408471b054f2655617cbbaf7937b7c80cd8865cf02c8487d30"
+         "d2b0fbd8b2c4e102e16d828374bbc47b93852f212d5043c3ea720f086178ff79"
+         "8cc4f63f787b9c2e419efa033e7644ea7936f54462dc21a6c4580725f7f0e7d1"
+         "58", 16),
+     0xd9dbfb332aa8e5ff091e8ce535857c37c73f6250ffb2e7ac,
+     0x282102e364feded3ad15ddf968f88d8321aa268dd483ebc4,
+     0x64dca58a20787c488d11d6dd96313f1b766f2d8efe122916,
+     0x1ecba28141e84ab4ecad92f56720e2cc83eb3d22dec72479,
+     True),
+
+    (generator_192,
+     int("0x94bb5bacd5f8ea765810024db87f4224ad71362a3c28284b2b9f39fab86db1"
+         "2e8beb94aae899768229be8fdb6c4f12f28912bb604703a79ccff769c1607f5a"
+         "91450f30ba0460d359d9126cbd6296be6d9c4bb96c0ee74cbb44197c207f6db3"
+         "26ab6f5a659113a9034e54be7b041ced9dcf6458d7fb9cbfb2744d999f7dfd63"
+         "f4", 16),
+     0x3e53ef8d3112af3285c0e74842090712cd324832d4277ae7,
+     0xcc75f8952d30aec2cbb719fc6aa9934590b5d0ff5a83adb7,
+     0x8285261607283ba18f335026130bab31840dcfd9c3e555af,
+     0x356d89e1b04541afc9704a45e9c535ce4a50929e33d7e06c,
+     True),
+
+    (generator_192,
+     int("0xf6227a8eeb34afed1621dcc89a91d72ea212cb2f476839d9b4243c66877911"
+         "b37b4ad6f4448792a7bbba76c63bdd63414b6facab7dc71c3396a73bd7ee14cd"
+         "d41a659c61c99b779cecf07bc51ab391aa3252386242b9853ea7da67fd768d30"
+         "3f1b9b513d401565b6f1eb722dfdb96b519fe4f9bd5de67ae131e64b40e78c42"
+         "dd", 16),
+     0x16335dbe95f8e8254a4e04575d736befb258b8657f773cb7,
+     0x421b13379c59bc9dce38a1099ca79bbd06d647c7f6242336,
+     0x4141bd5d64ea36c5b0bd21ef28c02da216ed9d04522b1e91,
+     0x159a6aa852bcc579e821b7bb0994c0861fb08280c38daa09,
+     False),
+
+    (generator_192,
+     int("0x16b5f93afd0d02246f662761ed8e0dd9504681ed02a253006eb36736b56309"
+         "7ba39f81c8e1bce7a16c1339e345efabbc6baa3efb0612948ae51103382a8ee8"
+         "bc448e3ef71e9f6f7a9676694831d7f5dd0db5446f179bcb737d4a526367a447"
+         "bfe2c857521c7f40b6d7d7e01a180d92431fb0bbd29c04a0c420a57b3ed26ccd"
+         "8a", 16),
+     0xfd14cdf1607f5efb7b1793037b15bdf4baa6f7c16341ab0b,
+     0x83fa0795cc6c4795b9016dac928fd6bac32f3229a96312c4,
+     0x8dfdb832951e0167c5d762a473c0416c5c15bc1195667dc1,
+     0x1720288a2dc13fa1ec78f763f8fe2ff7354a7e6fdde44520,
+     False),
+
+    (generator_192,
+     int("0x08a2024b61b79d260e3bb43ef15659aec89e5b560199bc82cf7c65c77d3919"
+         "2e03b9a895d766655105edd9188242b91fbde4167f7862d4ddd61e5d4ab55196"
+         "683d4f13ceb90d87aea6e07eb50a874e33086c4a7cb0273a8e1c4408f4b846bc"
+         "eae1ebaac1b2b2ea851a9b09de322efe34cebe601653efd6ddc876ce8c2f2072"
+         "fb", 16),
+     0x674f941dc1a1f8b763c9334d726172d527b90ca324db8828,
+     0x65adfa32e8b236cb33a3e84cf59bfb9417ae7e8ede57a7ff,
+     0x9508b9fdd7daf0d8126f9e2bc5a35e4c6d800b5b804d7796,
+     0x36f2bf6b21b987c77b53bb801b3435a577e3d493744bfab0,
+     False),
+
+    (generator_192,
+     int("0x1843aba74b0789d4ac6b0b8923848023a644a7b70afa23b1191829bbe4397c"
+         "e15b629bf21a8838298653ed0c19222b95fa4f7390d1b4c844d96e645537e0aa"
+         "e98afb5c0ac3bd0e4c37f8daaff25556c64e98c319c52687c904c4de7240a1cc"
+         "55cd9756b7edaef184e6e23b385726e9ffcba8001b8f574987c1a3fedaaa83ca"
+         "6d", 16),
+     0x10ecca1aad7220b56a62008b35170bfd5e35885c4014a19f,
+     0x04eb61984c6c12ade3bc47f3c629ece7aa0a033b9948d686,
+     0x82bfa4e82c0dfe9274169b86694e76ce993fd83b5c60f325,
+     0xa97685676c59a65dbde002fe9d613431fb183e8006d05633,
+     False),
+
+    (generator_192,
+     int("0x5a478f4084ddd1a7fea038aa9732a822106385797d02311aeef4d0264f824f"
+         "698df7a48cfb6b578cf3da416bc0799425bb491be5b5ecc37995b85b03420a98"
+         "f2c4dc5c31a69a379e9e322fbe706bbcaf0f77175e05cbb4fa162e0da82010a2"
+         "78461e3e974d137bc746d1880d6eb02aa95216014b37480d84b87f717bb13f76"
+         "e1", 16),
+     0x6636653cb5b894ca65c448277b29da3ad101c4c2300f7c04,
+     0xfdf1cbb3fc3fd6a4f890b59e554544175fa77dbdbeb656c1,
+     0xeac2ddecddfb79931a9c3d49c08de0645c783a24cb365e1c,
+     0x3549fee3cfa7e5f93bc47d92d8ba100e881a2a93c22f8d50,
+     False),
+
+    (generator_192,
+     int("0xc598774259a058fa65212ac57eaa4f52240e629ef4c310722088292d1d4af6"
+         "c39b49ce06ba77e4247b20637174d0bd67c9723feb57b5ead232b47ea452d5d7"
+         "a089f17c00b8b6767e434a5e16c231ba0efa718a340bf41d67ea2d295812ff1b"
+         "9277daacb8bc27b50ea5e6443bcf95ef4e9f5468fe78485236313d53d1c68f6b"
+         "a2", 16),
+     0xa82bd718d01d354001148cd5f69b9ebf38ff6f21898f8aaa,
+     0xe67ceede07fc2ebfafd62462a51e4b6c6b3d5b537b7caf3e,
+     0x4d292486c620c3de20856e57d3bb72fcde4a73ad26376955,
+     0xa85289591a6081d5728825520e62ff1c64f94235c04c7f95,
+     False),
+
+    (generator_192,
+     int("0xca98ed9db081a07b7557f24ced6c7b9891269a95d2026747add9e9eb80638a"
+         "961cf9c71a1b9f2c29744180bd4c3d3db60f2243c5c0b7cc8a8d40a3f9a7fc91"
+         "0250f2187136ee6413ffc67f1a25e1c4c204fa9635312252ac0e0481d89b6d53"
+         "808f0c496ba87631803f6c572c1f61fa049737fdacce4adff757afed4f05beb6"
+         "58", 16),
+     0x7d3b016b57758b160c4fca73d48df07ae3b6b30225126c2f,
+     0x4af3790d9775742bde46f8da876711be1b65244b2b39e7ec,
+     0x95f778f5f656511a5ab49a5d69ddd0929563c29cbc3a9e62,
+     0x75c87fc358c251b4c83d2dd979faad496b539f9f2ee7a289,
+     False),
+
+    (generator_192,
+     int("0x31dd9a54c8338bea06b87eca813d555ad1850fac9742ef0bbe40dad400e102"
+         "88acc9c11ea7dac79eb16378ebea9490e09536099f1b993e2653cd50240014c9"
+         "0a9c987f64545abc6a536b9bd2435eb5e911fdfde2f13be96ea36ad38df4ae9e"
+         "a387b29cced599af777338af2794820c9cce43b51d2112380a35802ab7e396c9"
+         "7a", 16),
+     0x9362f28c4ef96453d8a2f849f21e881cd7566887da8beb4a,
+     0xe64d26d8d74c48a024ae85d982ee74cd16046f4ee5333905,
+     0xf3923476a296c88287e8de914b0b324ad5a963319a4fe73b,
+     0xf0baeed7624ed00d15244d8ba2aede085517dbdec8ac65f5,
+     True),
+
+    (generator_192,
+     int("0xb2b94e4432267c92f9fdb9dc6040c95ffa477652761290d3c7de312283f645"
+         "0d89cc4aabe748554dfb6056b2d8e99c7aeaad9cdddebdee9dbc099839562d90"
+         "64e68e7bb5f3a6bba0749ca9a538181fc785553a4000785d73cc207922f63e8c"
+         "e1112768cb1de7b673aed83a1e4a74592f1268d8e2a4e9e63d414b5d442bd045"
+         "6d", 16),
+     0xcc6fc032a846aaac25533eb033522824f94e670fa997ecef,
+     0xe25463ef77a029eccda8b294fd63dd694e38d223d30862f1,
+     0x066b1d07f3a40e679b620eda7f550842a35c18b80c5ebe06,
+     0xa0b0fb201e8f2df65e2c4508ef303bdc90d934016f16b2dc,
+     False),
+
+    (generator_192,
+     int("0x4366fcadf10d30d086911de30143da6f579527036937007b337f7282460eae"
+         "5678b15cccda853193ea5fc4bc0a6b9d7a31128f27e1214988592827520b214e"
+         "ed5052f7775b750b0c6b15f145453ba3fee24a085d65287e10509eb5d5f602c4"
+         "40341376b95c24e5c4727d4b859bfe1483d20538acdd92c7997fa9c614f0f839"
+         "d7", 16),
+     0x955c908fe900a996f7e2089bee2f6376830f76a19135e753,
+     0xba0c42a91d3847de4a592a46dc3fdaf45a7cc709b90de520,
+     0x1f58ad77fc04c782815a1405b0925e72095d906cbf52a668,
+     0xf2e93758b3af75edf784f05a6761c9b9a6043c66b845b599,
+     False),
+
+    (generator_192,
+     int("0x543f8af57d750e33aa8565e0cae92bfa7a1ff78833093421c2942cadf99866"
+         "70a5ff3244c02a8225e790fbf30ea84c74720abf99cfd10d02d34377c3d3b412"
+         "69bea763384f372bb786b5846f58932defa68023136cd571863b304886e95e52"
+         "e7877f445b9364b3f06f3c28da12707673fecb4b8071de06b6e0a3c87da160ce"
+         "f3", 16),
+     0x31f7fa05576d78a949b24812d4383107a9a45bb5fccdd835,
+     0x8dc0eb65994a90f02b5e19bd18b32d61150746c09107e76b,
+     0xbe26d59e4e883dde7c286614a767b31e49ad88789d3a78ff,
+     0x8762ca831c1ce42df77893c9b03119428e7a9b819b619068,
+     False),
+
+    (generator_192,
+     int("0xd2e8454143ce281e609a9d748014dcebb9d0bc53adb02443a6aac2ffe6cb009f"
+         "387c346ecb051791404f79e902ee333ad65e5c8cb38dc0d1d39a8dc90add502357"
+         "2720e5b94b190d43dd0d7873397504c0c7aef2727e628eb6a74411f2e400c65670"
+         "716cb4a815dc91cbbfeb7cfe8c929e93184c938af2c078584da045e8f8d1", 16),
+     0x66aa8edbbdb5cf8e28ceb51b5bda891cae2df84819fe25c0,
+     0x0c6bc2f69030a7ce58d4a00e3b3349844784a13b8936f8da,
+     0xa4661e69b1734f4a71b788410a464b71e7ffe42334484f23,
+     0x738421cf5e049159d69c57a915143e226cac8355e149afe9,
+     False),
+
+    (generator_192,
+     int("0x6660717144040f3e2f95a4e25b08a7079c702a8b29babad5a19a87654bc5c5af"
+         "a261512a11b998a4fb36b5d8fe8bd942792ff0324b108120de86d63f65855e5461"
+         "184fc96a0a8ffd2ce6d5dfb0230cbbdd98f8543e361b3205f5da3d500fdc8bac6d"
+         "b377d75ebef3cb8f4d1ff738071ad0938917889250b41dd1d98896ca06fb", 16),
+     0xbcfacf45139b6f5f690a4c35a5fffa498794136a2353fc77,
+     0x6f4a6c906316a6afc6d98fe1f0399d056f128fe0270b0f22,
+     0x9db679a3dafe48f7ccad122933acfe9da0970b71c94c21c1,
+     0x984c2db99827576c0a41a5da41e07d8cc768bc82f18c9da9,
+     False)
+    ]
+
+
+@pytest.mark.parametrize("gen,msg,qx,qy,r,s,expected", CURVE_192_KATS)
+def test_signature_validity(gen, msg, qx, qy, r, s, expected):
+    """
+    `msg` = message, `qx` and `qy` represent the base point on
+    elliptic curve of `gen`, `r` and `s` are the signature, and
+    `expected` is True iff the signature is expected to be valid."""
+    pubk = Public_key(gen,
+                      ellipticcurve.Point(gen.curve(), qx, qy))
+    assert expected == pubk.verifies(digest_integer(msg), Signature(r, s))
+
+
+@pytest.mark.parametrize("gen,msg,qx,qy,r,s,expected",
+                         [x for x in CURVE_192_KATS if x[6]])
+def test_pk_recovery(gen, msg, r, s, qx, qy, expected):
+    del expected
+    sign = Signature(r, s)
+    pks = sign.recover_public_keys(digest_integer(msg), gen)
+
+    assert pks
+
+    # Test if the signature is valid for all found public keys
+    for pk in pks:
+        q = pk.point
+        test_signature_validity(gen, msg, q.x(), q.y(), r, s, True)
+
+    # Test if the original public key is in the set of found keys
+    original_q = ellipticcurve.Point(gen.curve(), qx, qy)
+    points = [pk.point for pk in pks]
+    assert original_q in points
+
+
+@st.composite
+def st_random_gen_key_msg_nonce(draw):
+    """Hypothesis strategy for test_sig_verify()."""
+    name_gen = {
+        "generator_192": generator_192,
+        "generator_224": generator_224,
+        "generator_256": generator_256,
+        "generator_secp256k1": generator_secp256k1,
+        "generator_384": generator_384,
+        "generator_521": generator_521}
+    name = draw(st.sampled_from(sorted(name_gen.keys())))
+    note("Generator used: {0}".format(name))
+    generator = name_gen[name]
+    order = int(generator.order())
+
+    key = draw(st.integers(min_value=1, max_value=order))
+    msg = draw(st.integers(min_value=1, max_value=order))
+    nonce = draw(st.integers(min_value=1, max_value=order+1) |
+                 st.integers(min_value=order>>1, max_value=order))
+    return generator, key, msg, nonce
+
+
+SIG_VER_SETTINGS = dict(HYP_SETTINGS)
+SIG_VER_SETTINGS["max_examples"] = 10
+@settings(**SIG_VER_SETTINGS)
+@example((generator_224, 4, 1, 1))
+@given(st_random_gen_key_msg_nonce())
+def test_sig_verify(args):
+    """
+    Check if signing and verification works for arbitrary messages and
+    that signatures for other messages are rejected.
+    """
+    generator, sec_mult, msg, nonce = args
+
+    pubkey = Public_key(generator, generator * sec_mult)
+    privkey = Private_key(pubkey, sec_mult)
+
+    signature = privkey.sign(msg, nonce)
+
+    assert pubkey.verifies(msg, signature)
+
+    assert not pubkey.verifies(msg - 1, signature)