aboutsummaryrefslogtreecommitdiff
path: root/freezed_deps/ecdsa/test_ecdsa.py
blob: 71c68913ac70039f3e2aa0c267b37e673804f661 (plain) (blame)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
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)