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mp.c: Tighten up the `MP' and `GF' implicit conversions.
[catacomb-python] / t / t-mp.py
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ffad1322
MW		 1### -*-python-*-
2###
3### Testing multiprecision integer (and related) functionality
4###
5### (c) 2019 Straylight/Edgeware
6###
7
8###----- Licensing notice ---------------------------------------------------
9###
10### This file is part of the Python interface to Catacomb.
11###
12### Catacomb/Python is free software: you can redistribute it and/or
13### modify it under the terms of the GNU General Public License as
14### published by the Free Software Foundation; either version 2 of the
15### License, or (at your option) any later version.
16###
17### Catacomb/Python is distributed in the hope that it will be useful, but
18### WITHOUT ANY WARRANTY; without even the implied warranty of
19### MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
20### General Public License for more details.
21###
22### You should have received a copy of the GNU General Public License
23### along with Catacomb/Python. If not, write to the Free Software
24### Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307,
25### USA.
26
27###--------------------------------------------------------------------------
28### Imported modules.
29
30import catacomb as C
31import unittest as U
32import testutils as T
33
34###--------------------------------------------------------------------------
35class TestMP (U.TestCase):
36
37 def test_make(me):
38 x = C.MP(5)
39 k = C.PrimeField(17)
40 kk = C.BinPolyField(C.GF(0x13))
41 E = k.ec(-3, 1)
42 me.assertEqual(x, 5)
43 me.assertTrue(C.MP(x) is x)
44 me.assertEqual(C.MP(k(8)), 8)
45 me.assertEqual(C.MP(kk(8)), 8)
46 me.assertEqual(C.MP(E(1, 4)), 1)
47 me.assertRaises(TypeError, C.MP, E())
48
49 me.assertEqual(int(x), 5)
50 big = 6556380541834372447694561492436749633
51 me.assertEqual(type(big), T.long)
52 y = C.MP(big)
53 me.assertEqual(y, big)
54 me.assertEqual(int(y), big)
55
56 me.assertEqual(C.MP(str(big)), big)
57 me.assertEqual(C.MP('0x4eeb684a0954ec4ceb255e3e9778d41'), big)
58 me.assertEqual(C.MP('4eeb684a0954ec4ceb255e3e9778d41', 16), big)
59 me.assertEqual(C.MP('0b0', 16), 176) # not 0
60
61 me.assertEqual(C.MP('047353320450112516611472622536175135706501'), big)
62 me.assertEqual(C.MP('0o47353320450112516611472622536175135706501'), big)
63 me.assertEqual(C.MP('047353320450112516611472622536175135706501', 8), big)
64 me.assertEqual(C.MP('47353320450112516611472622536175135706501', 8), big)
65
66 me.assertEqual(C.MP('0b100111011011001100000010001011'), 661438603)
67 me.assertEqual(C.MP('100111011011001100000010001011', 2), 661438603)
68
69 def test_string(me):
70 y = C.MP(6556380541834372447694561492436749633)
71 me.assertEqual(str(y), '6556380541834372447694561492436749633')
e8cd4ca5 72 me.assertEqual(repr(y), 'MP(6556380541834372447694561492436749633)')
ffad1322 73 me.assertEqual(hex(y), '0x4eeb684a0954ec4ceb255e3e9778d41')
d472b9a1
MW		 74 me.assertEqual(oct(y), T.py23('0', '0o') +
75 '47353320450112516611472622536175135706501')
8aafc119
MW		 76 try: bin
77 except NameError: pass
78 else: me.assertEqual(bin(C.MP(661438603)),
79 '0b100111011011001100000010001011')
ffad1322
MW		 80
81 def test_number(me):
82 x, y, m, zero = C.MP(169), C.MP(24), C.MP(205), C.MP(0)
83
84 me.assertEqual(-x, -169)
85 me.assertEqual(~x, -170)
86 me.assertEqual(abs(x), 169)
87 me.assertEqual(abs(-x), 169)
88
89 me.assertEqual(x + y, 193)
90 me.assertEqual(x - y, 145)
91 me.assertEqual(x*y, 4056)
92 me.assertEqual(x&y, 8)
93 me.assertEqual(x&-y, 168)
94 me.assertEqual(x | y, 185)
95 me.assertEqual(x | -y, -23)
96 me.assertEqual(x ^ y, 177)
97 me.assertEqual(x ^ -y, -191)
98
99 me.assertEqual(x << 3, 1352)
100 me.assertEqual(x << -2, 42)
101 me.assertEqual(x >> 2, 42)
102 me.assertEqual(x >> -3, 1352)
103 me.assertEqual(-x << 3, -1352)
104 me.assertEqual(-x >> 2, -43)
105
106 u = x/y; me.assertEqual((u.numer, u.denom), (169, 24))
107 me.assertEqual(x//y, 7)
108 me.assertEqual(x%y, 1)
109 me.assertEqual(divmod(x, y), (7, 1))
110 me.assertRaises(ZeroDivisionError, lambda: x/zero)
111 me.assertRaises(ZeroDivisionError, lambda: x//zero)
112 me.assertRaises(ZeroDivisionError, lambda: x%zero)
113 me.assertRaises(ZeroDivisionError, divmod, x, zero)
114
115 me.assertEqual(pow(x, y), 294632676319010105335586872991323185304149065116720321)
116 me.assertEqual(pow(x, y, m), 51)
117 me.assertRaises(ValueError, pow, x, -y)
118 me.assertEqual(pow(x, -y, m), 201)
119 me.assertRaises(ZeroDivisionError, pow, x, -y, 208)
120
121 me.assertTrue(x)
122 me.assertFalse(zero)
123
124 def test_order(me):
125 x, y = C.MP(169), C.MP(24)
126 me.assertTrue(x == x)
127 me.assertFalse(x != x)
128 me.assertFalse(x == y)
129 me.assertTrue(x != y)
130 me.assertTrue(x > y)
131 me.assertFalse(y > x)
132 me.assertFalse(x > x)
133 me.assertTrue(x >= y)
134 me.assertFalse(y >= x)
135 me.assertTrue(x >= x)
136 me.assertFalse(x <= y)
137 me.assertTrue(y <= x)
138 me.assertTrue(x <= x)
139 me.assertFalse(x < y)
140 me.assertTrue(y < x)
141 me.assertFalse(x < x)
142
1810cc51
MW		 143 def test_float(me):
144 x, y = C.MP(169), 24.0
145 for fn in [T.add, T.sub, T.mul, T.div]:
146 me.assertEqual(type(fn(x, y)), float)
147 me.assertEqual(type(fn(y, x)), float)
148 me.assertEqual(x, 169.0)
149 me.assertNotEqual(x, 169.1)
150 me.assertNotEqual(x, 168.9)
151 me.assertTrue(x > 168.9)
152 me.assertTrue(x < 169.1)
153 z = 1.0
154 while z == z + 1: z *= 2.0
155 me.assertNotEqual(C.MP(int(z)) + 1, z)
156
7032ee7c
MW		 157 def test_strconv(me):
158 x, y = C.MP(169), "24"
159 for fn in [T.add, T.sub]:
160 me.assertRaises(TypeError, fn, x, y)
161 me.assertRaises(TypeError, fn, y, x)
162 me.assertEqual(x*y, 169*"24")
163 me.assertEqual(y*x, 169*"24")
164
ffad1322
MW		 165 def test_bits(me):
166 x, y, zero = C.MP(169), C.MP(-24), C.MP(0)
167 me.assertTrue(x.testbit(0))
168 me.assertFalse(x.testbit(1))
169 me.assertFalse(x.testbit(1000))
170 me.assertFalse(y.testbit(0))
171 me.assertTrue(y.testbit(3))
172 me.assertTrue(y.testbit(1000))
173
174 me.assertEqual(x.setbit(0), x)
175 me.assertEqual(x.clearbit(0), 168)
176 me.assertEqual(x.setbit(1), 171)
177 me.assertEqual(x.clearbit(1), x)
178 me.assertEqual(y.setbit(0), -23)
179 me.assertEqual(y.clearbit(0), y)
180 me.assertEqual(y.setbit(3), y)
181 me.assertEqual(y.clearbit(3), -32)
182 me.assertEqual(y.setbit(1000), y)
183
184 me.assertEqual(x.nbits, 8)
185 me.assertEqual(y.nbits, 5)
186 me.assertEqual(zero.nbits, 0)
187
188 def test_loadstore(me):
189 x = C.MP(0x0123456789ab)
190 y = -x
191 u = C.MP(0xfedcba9876)
192
193 me.assertEqual(x.noctets, 6)
194 me.assertEqual(x.noctets2c, 6)
195 me.assertEqual(y.noctets, 6)
196 me.assertEqual(y.noctets2c, 6)
197 me.assertEqual(u.noctets, 5)
198 me.assertEqual(u.noctets2c, 6)
199
200 me.assertEqual(x, C.MP.loadb(C.bytes("0123456789ab")))
201 me.assertEqual(x, C.MP.loadb2c(C.bytes("0123456789ab")))
202 me.assertEqual(y, C.MP.loadb2c(C.bytes("fedcba987655")))
203
204 me.assertEqual(x.storeb(), C.bytes("0123456789ab"))
205 me.assertEqual(x.storeb(3), C.bytes("6789ab"))
206 me.assertEqual(x.storeb(8), C.bytes("00000123456789ab"))
207 me.assertEqual(x.storeb2c(), C.bytes("0123456789ab"))
208 me.assertEqual(x.storeb2c(3), C.bytes("6789ab"))
209 me.assertEqual(x.storeb2c(8), C.bytes("00000123456789ab"))
210 me.assertEqual(u.storeb2c(), C.bytes("00fedcba9876"))
211 me.assertEqual(y.storeb2c(), C.bytes("fedcba987655"))
212 me.assertEqual(y.storeb2c(3), C.bytes("987655"))
213 me.assertEqual(y.storeb2c(8), C.bytes("fffffedcba987655"))
214
215 me.assertEqual(x, C.MP.loadl(C.bytes("ab8967452301")))
216 me.assertEqual(x, C.MP.loadl2c(C.bytes("ab8967452301")))
217 me.assertEqual(y, C.MP.loadl2c(C.bytes("557698badcfe")))
218
219 me.assertEqual(x.storel(), C.bytes("ab8967452301"))
220 me.assertEqual(x.storel(3), C.bytes("ab8967"))
221 me.assertEqual(x.storel(8), C.bytes("ab89674523010000"))
222 me.assertEqual(x.storel2c(), C.bytes("ab8967452301"))
223 me.assertEqual(x.storel2c(3), C.bytes("ab8967"))
224 me.assertEqual(x.storel2c(8), C.bytes("ab89674523010000"))
225 me.assertEqual(u.storel2c(), C.bytes("7698badcfe00"))
226 me.assertEqual(y.storel2c(), C.bytes("557698badcfe"))
227 me.assertEqual(y.storel2c(3), C.bytes("557698"))
228 me.assertEqual(y.storel2c(8), C.bytes("557698badcfeffff"))
229
230 me.assertEqual(x.tobuf(), C.bytes("00060123456789ab"))
231 me.assertEqual((x, T.bin("abcd")),
232 C.MP.frombuf(C.bytes("00060123456789ab61626364")))
233
234 def test_numbertheory(me):
235 p, x, y, z = C.MP(173), C.MP(169), C.MP(24), C.MP(20)
236
237 me.assertEqual(x.odd(), (0, x))
238 me.assertEqual(y.odd(), (3, 3))
239
240 me.assertEqual(x.sqr(), 28561)
241 me.assertEqual(x.sqrt(), 13)
242 me.assertEqual(y.sqrt(), 4)
243
244 me.assertEqual(x.gcd(y), 1)
245 me.assertEqual(x.gcdx(y), (1, -23, 162))
246 me.assertEqual(y.gcdx(x), (1, -7, 1))
247 me.assertEqual(x.modinv(y), 162)
248 me.assertEqual(y.modinv(x), 1)
249
250 me.assertEqual(x.jacobi(y), 1)
251 me.assertEqual(x.jacobi(13), 0)
252 me.assertEqual(y.jacobi(x), 1)
253 me.assertEqual(p.jacobi(y), 1)
254 me.assertEqual(p.jacobi(z), -1)
255 me.assertEqual(p.modsqrt(y), 71)
256 me.assertRaises(ValueError, p.modsqrt, z)
257
258 me.assertEqual(y.leastcongruent(x, 32), 184)
259
260 me.assertTrue(p.primep())
261 me.assertFalse(x.primep())
262
263 def test_bang(me):
264 me.assertEqual(C.MP.factorial(0), 1)
265 me.assertEqual \
266 (C.MP.factorial(50),
267 30414093201713378043612608166064768844377641568960512000000000000)
268 me.assertRaises((ValueError, OverflowError), C.MP.factorial, -1)
269
270 def test_fib(me):
271 me.assertEqual(C.MP.fibonacci(-2), -1)
272 me.assertEqual(C.MP.fibonacci(-1), +1)
273 me.assertEqual(C.MP.fibonacci( 0), 0)
274 me.assertEqual(C.MP.fibonacci(+1), +1)
275 me.assertEqual(C.MP.fibonacci(+2), +1)
276 me.assertEqual(C.MP.fibonacci(50), 12586269025)
277
278###--------------------------------------------------------------------------
279class TestMPMul (U.TestCase):
280
281 def test(me):
282 m = C.MPMul()
283 me.assertTrue(m.livep)
284 m.factor(1, 2, 3)
285 m.factor([4, 5, 6])
286 me.assertEqual(m.done(), 720)
287 me.assertFalse(m.livep)
288
289 me.assertEqual(C.MPMul(T.range(1, 7)).done(), 720)
290 me.assertEqual(C.MP.factorial(6), 720)
291
292###--------------------------------------------------------------------------
293class TestMPMont (U.TestCase):
294
295 def test(me):
296
297 me.assertRaises(ValueError,
298 C.MPMont, 35315021952044908656941308411353985942)
299 me.assertRaises(ValueError, C.MPMont, -9)
300
301 p = C.MP(269464705320809171350781605680038324101)
302 g = C.MP(2) # lucky chance
303 x = C.MP(211184293914316080585277908844600399612)
304 y = C.MP(154454671298730680774195646814344206562)
305 xy = C.MP(209444562478584646216087606217820187655)
306 me.assertTrue(p.primep())
307 m = C.MPMont(p)
308 me.assertEqual(m.m, p)
309
310 ## The precise values of m.r and m.r2 are dependent on the internal
311 ## bignum representation. But we expect m.r to be congruent to some
312 ## power of two. (It should be 2^128.)
313 t = p.modinv(m.r)
314 for i in T.range(1025):
315 if t == 1: break
316 t *= 2
317 if t >= p: t -= p
318 else:
319 me.fail("m.r is not a small-ish power of 2")
320 me.assertEqual(m.r2, pow(2, 2*i, p))
321 me.assertEqual(m.ext(m.r), 1)
322 me.assertEqual(m.reduce(m.r), 1)
323
324 me.assertEqual(m.ext(m.int(x)), x)
325 me.assertEqual(m.int(x), m.mul(x, m.r2))
326 me.assertEqual(m.mul(m.int(x), y), xy)
327 me.assertEqual(m.ext(m.mul(m.int(x), m.int(y))), xy)
328
329 me.assertEqual(m.exp(2, p - 1), 1)
330 me.assertEqual(m.expr(m.int(2), p - 1), m.r)
331
332 q, r, s, z = 32, 128, 2048, pow(g, 156, p)
333 me.assertEqual(m.mexp([(q, 9), (r, 8), (s, 5)]), z)
334 me.assertEqual(m.mexp(q, 9, r, 8, s, 5), z)
335
336 q, r, s, z = T.imap(m.int, [32, 128, 2048, pow(g, 156, p)])
337 me.assertEqual(m.mexpr([(q, 9), (r, 8), (s, 5)]), z)
338 me.assertEqual(m.mexpr(q, 9, r, 8, s, 5), z)
339
340###--------------------------------------------------------------------------
341class TestMPBarrett (U.TestCase):
342
343 def test(me):
344
345 p = C.MP(269464705320809171350781605680038324101)
346 g = C.MP(2) # lucky chance
347 x = C.MP(211184293914316080585277908844600399612)
348 y = C.MP(154454671298730680774195646814344206562)
349 xy = C.MP(209444562478584646216087606217820187655)
350 me.assertTrue(p.primep())
351 m = C.MPBarrett(p)
352 me.assertEqual(m.m, p)
353
354 me.assertEqual(m.reduce(x*y), xy)
355
356 me.assertEqual(m.exp(2, p - 1), 1)
357
358 q, r, s, z = 32, 128, 2048, pow(g, 156, p)
359 me.assertEqual(m.mexp([(q, 9), (r, 8), (s, 5)]), z)
360 me.assertEqual(m.mexp(q, 9, r, 8, s, 5), z)
361
362###--------------------------------------------------------------------------
363class TestMPReduce (U.TestCase):
364
365 def test(me):
366
367 p = C.MP(2)**127 - 1
368 g = C.MP(2) # lucky chance
369 x = C.MP(94827182170881245766374991987593163418)
370 y = C.MP(106025009945795266831396608563402138277)
371 xy = C.MP(80027041045616838298103413933629021123)
372 me.assertTrue(p.primep())
373 m = C.MPReduce(p)
374 me.assertEqual(m.m, p)
375
376 me.assertEqual(m.reduce(x*y), xy)
377
378 me.assertEqual(m.exp(2, 127), 1)
379
380###--------------------------------------------------------------------------
381class TestMPCRT (U.TestCase):
382
383 def test(me):
384
385 c = C.MPCRT(5, 7, 11)
386 me.assertEqual(c.moduli, [5, 7, 11])
387 me.assertEqual(c.product, 385)
388 me.assertEqual(c.solve([2, 3, 4]), 367)
389 me.assertEqual(c.solve([2, -4, -7]), 367)
390
391 me.assertRaises(ValueError, C.MPCRT, [6, 15, 35])
392
393###--------------------------------------------------------------------------
394class TestGF (U.TestCase):
395
396 def test_make(me):
397 x = C.GF(5)
398 k = C.PrimeField(17)
399 kk = C.BinPolyField(C.GF(0x13))
400 E = k.ec(-3, 1)
401 me.assertTrue(C.GF(x) is x)
402 me.assertEqual(C.GF(k(8)), C.GF(8))
403 me.assertEqual(C.GF(kk(8)), C.GF(8))
404 me.assertEqual(C.GF(E(1, 4)), C.GF(1))
405 me.assertRaises(TypeError, C.GF, E())
406
7032ee7c 407 me.assertNotEqual(x, 5) # no implicit conversion to int
ffad1322
MW		 408 me.assertEqual(int(x), 5)
409 y = C.GF(0x4eeb684a0954ec4ceb255e3e9778d41)
410 me.assertEqual(type(int(y)), T.long)
411
412 me.assertEqual(C.GF('0x4eeb684a0954ec4ceb255e3e9778d41'), y)
413 me.assertEqual(C.GF('4eeb684a0954ec4ceb255e3e9778d41', 16), y)
414 me.assertEqual(C.GF('0b0', 16), C.GF(176)) # not 0
415
416 me.assertEqual(C.GF('047353320450112516611472622536175135706501'), y)
417 me.assertEqual(C.GF('0o47353320450112516611472622536175135706501'), y)
418 me.assertEqual(C.GF('047353320450112516611472622536175135706501', 8), y)
419 me.assertEqual(C.GF('47353320450112516611472622536175135706501', 8), y)
420
421 t = C.GF(661438603)
422 me.assertEqual(C.GF('0b100111011011001100000010001011'), t)
423 me.assertEqual(C.GF('100111011011001100000010001011', 2), t)
424
425 def test_string(me):
426 y = C.GF(0x4eeb684a0954ec4ceb255e3e9778d41)
427 me.assertEqual(str(y), '0x4eeb684a0954ec4ceb255e3e9778d41')
e8cd4ca5 428 me.assertEqual(repr(y), 'GF(0x4eeb684a0954ec4ceb255e3e9778d41)')
ffad1322 429 me.assertEqual(hex(y), '0x4eeb684a0954ec4ceb255e3e9778d41')
d472b9a1
MW		 430 me.assertEqual(oct(y), T.py23('0', '0o') +
431 '47353320450112516611472622536175135706501')
8aafc119
MW		 432 try: bin
433 except NameError: pass
434 else: me.assertEqual(bin(C.GF(661438603)),
435 '0b100111011011001100000010001011')
ffad1322
MW		 436
437 def test_number(me):
438 x, y, m, zero = C.GF(0xa9), C.GF(0x18), C.GF(0x11b), C.GF(0)
439
440 me.assertEqual(x, -x)
441 me.assertEqual(abs(x), x)
442
443 me.assertEqual(x + y, C.GF(0xb1))
444 me.assertEqual(x - y, C.GF(0xb1))
445 me.assertEqual(x*y, C.GF(0xfd8))
446 me.assertEqual(x&y, C.GF(0x8))
447 me.assertEqual(x | y, C.GF(0xb9))
448 me.assertEqual(x ^ y, C.GF(0xb1))
449
450 me.assertEqual(x << 3, C.GF(0x548))
451 me.assertEqual(x << -2, C.GF(0x2a))
452 me.assertEqual(x >> 2, C.GF(0x2a))
453 me.assertEqual(x >> -3, C.GF(0x548))
454
455 u = x/y; me.assertEqual((u.numer, u.denom), (C.GF(0x67), C.GF(0x8)))
456 me.assertEqual(x//y, C.GF(0xc))
457 me.assertEqual(x%y, C.GF(0x9))
458 me.assertEqual(divmod(x, y), (C.GF(0xc), C.GF(0x9)))
459 me.assertRaises(ZeroDivisionError, lambda: x/zero)
460 me.assertRaises(ZeroDivisionError, lambda: x//zero)
461 me.assertRaises(ZeroDivisionError, lambda: x%zero)
462 me.assertRaises(ZeroDivisionError, divmod, x, zero)
463
464 me.assertEqual(pow(x, 24),
465 C.GF(0x1000100000001010000010101000101010001000001))
466 me.assertEqual(pow(x, 24, m), C.GF(0x78))
467 me.assertEqual(pow(x, -24, m), C.GF(0xb6))
468 me.assertRaises(ZeroDivisionError, pow, x, -24, C.GF(0x18))
469
470 me.assertTrue(x)
471 me.assertFalse(zero)
472
473 def test_order(me):
474 x, y, z = C.GF(0xa9), C.GF(0x18), C.GF(0xb3)
475 me.assertTrue(x == x)
476 me.assertFalse(x != x)
477 me.assertFalse(x == y)
478 me.assertTrue(x != y)
479 me.assertTrue(x > y)
480 me.assertFalse(y > x)
481 me.assertFalse(x > x)
482 me.assertFalse(x > z)
483 me.assertFalse(z > x)
484 me.assertTrue(x >= y)
485 me.assertFalse(y >= x)
486 me.assertTrue(x >= x)
487 me.assertTrue(x >= z)
488 me.assertTrue(z >= x)
489 me.assertFalse(x <= y)
490 me.assertTrue(y <= x)
491 me.assertTrue(x <= x)
492 me.assertTrue(x <= z)
493 me.assertTrue(z <= x)
494 me.assertFalse(x < y)
495 me.assertTrue(y < x)
496 me.assertFalse(x < x)
497 me.assertFalse(x < z)
498 me.assertFalse(z < x)
499
500 def test_bits(me):
501 x, zero = C.GF(0xa9), C.GF(0)
502 me.assertTrue(x.testbit(0))
503 me.assertFalse(x.testbit(1))
504 me.assertFalse(x.testbit(1000))
505
506 me.assertEqual(x.setbit(0), x)
507 me.assertEqual(x.clearbit(0), C.GF(0xa8))
508 me.assertEqual(x.setbit(1), C.GF(0xab))
509 me.assertEqual(x.clearbit(1), x)
510
511 me.assertEqual(x.nbits, 8)
512 me.assertEqual(x.degree, 7)
513 me.assertEqual(zero.nbits, 0)
514 me.assertEqual(zero.degree, -1)
515
516 def test_loadstore(me):
517 x = C.GF(0x0123456789ab)
518
519 me.assertEqual(x.noctets, 6)
520
521 me.assertEqual(x, C.GF.loadb(C.bytes("0123456789ab")))
522
523 me.assertEqual(x.storeb(), C.bytes("0123456789ab"))
524 me.assertEqual(x.storeb(3), C.bytes("6789ab"))
525 me.assertEqual(x.storeb(8), C.bytes("00000123456789ab"))
526
527 me.assertEqual(x, C.GF.loadl(C.bytes("ab8967452301")))
528
529 me.assertEqual(x.storel(), C.bytes("ab8967452301"))
530 me.assertEqual(x.storel(3), C.bytes("ab8967"))
531 me.assertEqual(x.storel(8), C.bytes("ab89674523010000"))
532
533 me.assertEqual(x.tobuf(), C.bytes("00060123456789ab"))
534 me.assertEqual((x, T.bin("abcd")),
535 C.GF.frombuf(C.bytes("00060123456789ab61626364")))
536
537 def test_numbertheory(me):
538 p, x, y = C.GF(0x11b), C.GF(0xa9), C.GF(0x18)
539
540 me.assertEqual(x.sqr(), C.GF(0x4441))
541
542 me.assertEqual(x.gcd(y), C.GF(0x3))
543 me.assertEqual(x.gcdx(y), (C.GF(0x3), C.GF(0x3), C.GF(0x15)))
544 me.assertEqual(p.modinv(x), C.GF(0xc8))
545
546 me.assertTrue(p.irreduciblep())
547 me.assertFalse(x.irreduciblep())
548
549###--------------------------------------------------------------------------
550class TestGFReduce (U.TestCase):
551
552 def test(me):
553 p = C.GF(0x87).setbit(128)
554 me.assertTrue(p.irreduciblep())
555 m = C.GFReduce(p)
556
557 x = C.GF(0xce46b4c1d3a1523520b1bb6eb5c61883)
558 y = C.GF(0xb5b0b3566b8e03f4b4a2b1ac413f8566)
559 xy = C.GF(0x28e5b895c11b08edc2fe7e1be5694c64)
560
561 me.assertEqual(m.reduce(x*y), xy)
562 me.assertEqual(m.trace(x), 0)
563 me.assertEqual(m.trace(y), 1)
564 me.assertEqual(m.sqrt(x), C.GF(0xa277ee4bf770e5974cf1e31b1ccb54a1))
565 me.assertEqual(m.halftrace(y), C.GF(0x9cea73e79ffd190dd3c81d33e58d8e6f))
566 me.assertEqual(m.quadsolve(x), C.GF(0x9664c09d23d168147a438de6a813c784))
567
568###--------------------------------------------------------------------------
569class TestGFN (U.TestCase):
570
571 def test(me):
572 p = C.GF(0x87).setbit(128)
573 beta = C.GF(0xc50f387e37194d4a4b41e157a3e2b5e1)
574 y = C.GF(0xdaca76dc2578a63c788a2ce0fc7878f6)
575 yy = C.GF(0x298a98f955100f054fcee3433f96b00e)
576 zero, one, fff = C.GF(0), C.GF(1), C.GF(T.long(2)**128 - 1)
577 me.assertTrue(p.irreduciblep())
578
579 gfn = C.GFN(p, beta)
580 me.assertEqual(gfn.p, p)
581 me.assertEqual(gfn.beta, beta)
582 me.assertEqual(gfn.pton(zero), zero)
583 me.assertEqual(gfn.ntop(zero), zero)
584 me.assertEqual(gfn.pton(one), fff)
585 me.assertEqual(gfn.ntop(fff), one)
586 me.assertEqual(gfn.pton(y), yy)
587 me.assertEqual(gfn.ntop(yy), y)
588
589 ## Doesn't generate a normal basis.
590 me.assertRaises(ValueError, C.GFN, p, y)
591
592###----- That's all, folks --------------------------------------------------
593
594if __name__ == "__main__": U.main()
Catacomb cryptographic library -- Python bindings