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field.c, mp.c: Implement the `nb_index' conversion.
[catacomb-python] / t / t-mp.py
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553d59fe
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')
e38168e2 72 me.assertEqual(repr(y), 'MP(6556380541834372447694561492436749633)')
553d59fe
MW		 73 me.assertEqual(hex(y), '0x4eeb684a0954ec4ceb255e3e9778d41')
74 me.assertEqual(oct(y), '047353320450112516611472622536175135706501')
a90a9c0e
MW		 75 try: bin
76 except NameError: pass
77 else: me.assertEqual(bin(C.MP(661438603)),
78 '0b100111011011001100000010001011')
553d59fe
MW		 79
80 def test_number(me):
81 x, y, m, zero = C.MP(169), C.MP(24), C.MP(205), C.MP(0)
82
83 me.assertEqual(-x, -169)
84 me.assertEqual(~x, -170)
85 me.assertEqual(abs(x), 169)
86 me.assertEqual(abs(-x), 169)
87
88 me.assertEqual(x + y, 193)
89 me.assertEqual(x - y, 145)
90 me.assertEqual(x*y, 4056)
91 me.assertEqual(x&y, 8)
92 me.assertEqual(x&-y, 168)
93 me.assertEqual(x | y, 185)
94 me.assertEqual(x | -y, -23)
95 me.assertEqual(x ^ y, 177)
96 me.assertEqual(x ^ -y, -191)
97
98 me.assertEqual(x << 3, 1352)
99 me.assertEqual(x << -2, 42)
100 me.assertEqual(x >> 2, 42)
101 me.assertEqual(x >> -3, 1352)
102 me.assertEqual(-x << 3, -1352)
103 me.assertEqual(-x >> 2, -43)
104
105 u = x/y; me.assertEqual((u.numer, u.denom), (169, 24))
106 me.assertEqual(x//y, 7)
107 me.assertEqual(x%y, 1)
108 me.assertEqual(divmod(x, y), (7, 1))
109 me.assertRaises(ZeroDivisionError, lambda: x/zero)
110 me.assertRaises(ZeroDivisionError, lambda: x//zero)
111 me.assertRaises(ZeroDivisionError, lambda: x%zero)
112 me.assertRaises(ZeroDivisionError, divmod, x, zero)
113
114 me.assertEqual(pow(x, y), 294632676319010105335586872991323185304149065116720321)
115 me.assertEqual(pow(x, y, m), 51)
116 me.assertRaises(ValueError, pow, x, -y)
117 me.assertEqual(pow(x, -y, m), 201)
118 me.assertRaises(ZeroDivisionError, pow, x, -y, 208)
119
120 me.assertTrue(x)
121 me.assertFalse(zero)
122
123 def test_order(me):
124 x, y = C.MP(169), C.MP(24)
125 me.assertTrue(x == x)
126 me.assertFalse(x != x)
127 me.assertFalse(x == y)
128 me.assertTrue(x != y)
129 me.assertTrue(x > y)
130 me.assertFalse(y > x)
131 me.assertFalse(x > x)
132 me.assertTrue(x >= y)
133 me.assertFalse(y >= x)
134 me.assertTrue(x >= x)
135 me.assertFalse(x <= y)
136 me.assertTrue(y <= x)
137 me.assertTrue(x <= x)
138 me.assertFalse(x < y)
139 me.assertTrue(y < x)
140 me.assertFalse(x < x)
141
77535854
MW		 142 def test_float(me):
143 x, y = C.MP(169), 24.0
144 for fn in [T.add, T.sub, T.mul, T.div]:
145 me.assertEqual(type(fn(x, y)), float)
146 me.assertEqual(type(fn(y, x)), float)
147 me.assertEqual(x, 169.0)
148 me.assertNotEqual(x, 169.1)
149 me.assertNotEqual(x, 168.9)
150 me.assertTrue(x > 168.9)
151 me.assertTrue(x < 169.1)
152 z = 1.0
153 while z == z + 1: z *= 2.0
154 me.assertNotEqual(C.MP(int(z)) + 1, z)
155
553d59fe
MW		 156 def test_bits(me):
157 x, y, zero = C.MP(169), C.MP(-24), C.MP(0)
158 me.assertTrue(x.testbit(0))
159 me.assertFalse(x.testbit(1))
160 me.assertFalse(x.testbit(1000))
161 me.assertFalse(y.testbit(0))
162 me.assertTrue(y.testbit(3))
163 me.assertTrue(y.testbit(1000))
164
165 me.assertEqual(x.setbit(0), x)
166 me.assertEqual(x.clearbit(0), 168)
167 me.assertEqual(x.setbit(1), 171)
168 me.assertEqual(x.clearbit(1), x)
169 me.assertEqual(y.setbit(0), -23)
170 me.assertEqual(y.clearbit(0), y)
171 me.assertEqual(y.setbit(3), y)
172 me.assertEqual(y.clearbit(3), -32)
173 me.assertEqual(y.setbit(1000), y)
174
175 me.assertEqual(x.nbits, 8)
176 me.assertEqual(y.nbits, 5)
177 me.assertEqual(zero.nbits, 0)
178
179 def test_loadstore(me):
180 x = C.MP(0x0123456789ab)
181 y = -x
182 u = C.MP(0xfedcba9876)
183
184 me.assertEqual(x.noctets, 6)
185 me.assertEqual(x.noctets2c, 6)
186 me.assertEqual(y.noctets, 6)
187 me.assertEqual(y.noctets2c, 6)
188 me.assertEqual(u.noctets, 5)
189 me.assertEqual(u.noctets2c, 6)
190
191 me.assertEqual(x, C.MP.loadb(C.bytes("0123456789ab")))
192 me.assertEqual(x, C.MP.loadb2c(C.bytes("0123456789ab")))
193 me.assertEqual(y, C.MP.loadb2c(C.bytes("fedcba987655")))
194
195 me.assertEqual(x.storeb(), C.bytes("0123456789ab"))
196 me.assertEqual(x.storeb(3), C.bytes("6789ab"))
197 me.assertEqual(x.storeb(8), C.bytes("00000123456789ab"))
198 me.assertEqual(x.storeb2c(), C.bytes("0123456789ab"))
199 me.assertEqual(x.storeb2c(3), C.bytes("6789ab"))
200 me.assertEqual(x.storeb2c(8), C.bytes("00000123456789ab"))
201 me.assertEqual(u.storeb2c(), C.bytes("00fedcba9876"))
202 me.assertEqual(y.storeb2c(), C.bytes("fedcba987655"))
203 me.assertEqual(y.storeb2c(3), C.bytes("987655"))
204 me.assertEqual(y.storeb2c(8), C.bytes("fffffedcba987655"))
205
206 me.assertEqual(x, C.MP.loadl(C.bytes("ab8967452301")))
207 me.assertEqual(x, C.MP.loadl2c(C.bytes("ab8967452301")))
208 me.assertEqual(y, C.MP.loadl2c(C.bytes("557698badcfe")))
209
210 me.assertEqual(x.storel(), C.bytes("ab8967452301"))
211 me.assertEqual(x.storel(3), C.bytes("ab8967"))
212 me.assertEqual(x.storel(8), C.bytes("ab89674523010000"))
213 me.assertEqual(x.storel2c(), C.bytes("ab8967452301"))
214 me.assertEqual(x.storel2c(3), C.bytes("ab8967"))
215 me.assertEqual(x.storel2c(8), C.bytes("ab89674523010000"))
216 me.assertEqual(u.storel2c(), C.bytes("7698badcfe00"))
217 me.assertEqual(y.storel2c(), C.bytes("557698badcfe"))
218 me.assertEqual(y.storel2c(3), C.bytes("557698"))
219 me.assertEqual(y.storel2c(8), C.bytes("557698badcfeffff"))
220
221 me.assertEqual(x.tobuf(), C.bytes("00060123456789ab"))
222 me.assertEqual((x, T.bin("abcd")),
223 C.MP.frombuf(C.bytes("00060123456789ab61626364")))
224
225 def test_numbertheory(me):
226 p, x, y, z = C.MP(173), C.MP(169), C.MP(24), C.MP(20)
227
228 me.assertEqual(x.odd(), (0, x))
229 me.assertEqual(y.odd(), (3, 3))
230
231 me.assertEqual(x.sqr(), 28561)
232 me.assertEqual(x.sqrt(), 13)
233 me.assertEqual(y.sqrt(), 4)
234
235 me.assertEqual(x.gcd(y), 1)
236 me.assertEqual(x.gcdx(y), (1, -23, 162))
237 me.assertEqual(y.gcdx(x), (1, -7, 1))
238 me.assertEqual(x.modinv(y), 162)
239 me.assertEqual(y.modinv(x), 1)
240
241 me.assertEqual(x.jacobi(y), 1)
242 me.assertEqual(x.jacobi(13), 0)
243 me.assertEqual(y.jacobi(x), 1)
244 me.assertEqual(p.jacobi(y), 1)
245 me.assertEqual(p.jacobi(z), -1)
246 me.assertEqual(p.modsqrt(y), 71)
247 me.assertRaises(ValueError, p.modsqrt, z)
248
249 me.assertEqual(y.leastcongruent(x, 32), 184)
250
251 me.assertTrue(p.primep())
252 me.assertFalse(x.primep())
253
254 def test_bang(me):
255 me.assertEqual(C.MP.factorial(0), 1)
256 me.assertEqual \
257 (C.MP.factorial(50),
258 30414093201713378043612608166064768844377641568960512000000000000)
259 me.assertRaises((ValueError, OverflowError), C.MP.factorial, -1)
260
261 def test_fib(me):
262 me.assertEqual(C.MP.fibonacci(-2), -1)
263 me.assertEqual(C.MP.fibonacci(-1), +1)
264 me.assertEqual(C.MP.fibonacci( 0), 0)
265 me.assertEqual(C.MP.fibonacci(+1), +1)
266 me.assertEqual(C.MP.fibonacci(+2), +1)
267 me.assertEqual(C.MP.fibonacci(50), 12586269025)
268
269###--------------------------------------------------------------------------
270class TestMPMul (U.TestCase):
271
272 def test(me):
273 m = C.MPMul()
274 me.assertTrue(m.livep)
275 m.factor(1, 2, 3)
276 m.factor([4, 5, 6])
277 me.assertEqual(m.done(), 720)
278 me.assertFalse(m.livep)
279
280 me.assertEqual(C.MPMul(T.range(1, 7)).done(), 720)
281 me.assertEqual(C.MP.factorial(6), 720)
282
283###--------------------------------------------------------------------------
284class TestMPMont (U.TestCase):
285
286 def test(me):
287
288 me.assertRaises(ValueError,
289 C.MPMont, 35315021952044908656941308411353985942)
290 me.assertRaises(ValueError, C.MPMont, -9)
291
292 p = C.MP(269464705320809171350781605680038324101)
293 g = C.MP(2) # lucky chance
294 x = C.MP(211184293914316080585277908844600399612)
295 y = C.MP(154454671298730680774195646814344206562)
296 xy = C.MP(209444562478584646216087606217820187655)
297 me.assertTrue(p.primep())
298 m = C.MPMont(p)
299 me.assertEqual(m.m, p)
300
301 ## The precise values of m.r and m.r2 are dependent on the internal
302 ## bignum representation. But we expect m.r to be congruent to some
303 ## power of two. (It should be 2^128.)
304 t = p.modinv(m.r)
305 for i in T.range(1025):
306 if t == 1: break
307 t *= 2
308 if t >= p: t -= p
309 else:
310 me.fail("m.r is not a small-ish power of 2")
311 me.assertEqual(m.r2, pow(2, 2*i, p))
312 me.assertEqual(m.ext(m.r), 1)
313 me.assertEqual(m.reduce(m.r), 1)
314
315 me.assertEqual(m.ext(m.int(x)), x)
316 me.assertEqual(m.int(x), m.mul(x, m.r2))
317 me.assertEqual(m.mul(m.int(x), y), xy)
318 me.assertEqual(m.ext(m.mul(m.int(x), m.int(y))), xy)
319
320 me.assertEqual(m.exp(2, p - 1), 1)
321 me.assertEqual(m.expr(m.int(2), p - 1), m.r)
322
323 q, r, s, z = 32, 128, 2048, pow(g, 156, p)
324 me.assertEqual(m.mexp([(q, 9), (r, 8), (s, 5)]), z)
325 me.assertEqual(m.mexp(q, 9, r, 8, s, 5), z)
326
327 q, r, s, z = T.imap(m.int, [32, 128, 2048, pow(g, 156, p)])
328 me.assertEqual(m.mexpr([(q, 9), (r, 8), (s, 5)]), z)
329 me.assertEqual(m.mexpr(q, 9, r, 8, s, 5), z)
330
331###--------------------------------------------------------------------------
332class TestMPBarrett (U.TestCase):
333
334 def test(me):
335
336 p = C.MP(269464705320809171350781605680038324101)
337 g = C.MP(2) # lucky chance
338 x = C.MP(211184293914316080585277908844600399612)
339 y = C.MP(154454671298730680774195646814344206562)
340 xy = C.MP(209444562478584646216087606217820187655)
341 me.assertTrue(p.primep())
342 m = C.MPBarrett(p)
343 me.assertEqual(m.m, p)
344
345 me.assertEqual(m.reduce(x*y), xy)
346
347 me.assertEqual(m.exp(2, p - 1), 1)
348
349 q, r, s, z = 32, 128, 2048, pow(g, 156, p)
350 me.assertEqual(m.mexp([(q, 9), (r, 8), (s, 5)]), z)
351 me.assertEqual(m.mexp(q, 9, r, 8, s, 5), z)
352
353###--------------------------------------------------------------------------
354class TestMPReduce (U.TestCase):
355
356 def test(me):
357
358 p = C.MP(2)**127 - 1
359 g = C.MP(2) # lucky chance
360 x = C.MP(94827182170881245766374991987593163418)
361 y = C.MP(106025009945795266831396608563402138277)
362 xy = C.MP(80027041045616838298103413933629021123)
363 me.assertTrue(p.primep())
364 m = C.MPReduce(p)
365 me.assertEqual(m.m, p)
366
367 me.assertEqual(m.reduce(x*y), xy)
368
369 me.assertEqual(m.exp(2, 127), 1)
370
371###--------------------------------------------------------------------------
372class TestMPCRT (U.TestCase):
373
374 def test(me):
375
376 c = C.MPCRT(5, 7, 11)
377 me.assertEqual(c.moduli, [5, 7, 11])
378 me.assertEqual(c.product, 385)
379 me.assertEqual(c.solve([2, 3, 4]), 367)
380 me.assertEqual(c.solve([2, -4, -7]), 367)
381
382 me.assertRaises(ValueError, C.MPCRT, [6, 15, 35])
383
384###--------------------------------------------------------------------------
385class TestGF (U.TestCase):
386
387 def test_make(me):
388 x = C.GF(5)
389 k = C.PrimeField(17)
390 kk = C.BinPolyField(C.GF(0x13))
391 E = k.ec(-3, 1)
392 me.assertTrue(C.GF(x) is x)
393 me.assertEqual(C.GF(k(8)), C.GF(8))
394 me.assertEqual(C.GF(kk(8)), C.GF(8))
395 me.assertEqual(C.GF(E(1, 4)), C.GF(1))
396 me.assertRaises(TypeError, C.GF, E())
397
398 me.assertEqual(int(x), 5)
399 y = C.GF(0x4eeb684a0954ec4ceb255e3e9778d41)
400 me.assertEqual(type(int(y)), T.long)
401
402 me.assertEqual(C.GF('0x4eeb684a0954ec4ceb255e3e9778d41'), y)
403 me.assertEqual(C.GF('4eeb684a0954ec4ceb255e3e9778d41', 16), y)
404 me.assertEqual(C.GF('0b0', 16), C.GF(176)) # not 0
405
406 me.assertEqual(C.GF('047353320450112516611472622536175135706501'), y)
407 me.assertEqual(C.GF('0o47353320450112516611472622536175135706501'), y)
408 me.assertEqual(C.GF('047353320450112516611472622536175135706501', 8), y)
409 me.assertEqual(C.GF('47353320450112516611472622536175135706501', 8), y)
410
411 t = C.GF(661438603)
412 me.assertEqual(C.GF('0b100111011011001100000010001011'), t)
413 me.assertEqual(C.GF('100111011011001100000010001011', 2), t)
414
415 def test_string(me):
416 y = C.GF(0x4eeb684a0954ec4ceb255e3e9778d41)
417 me.assertEqual(str(y), '0x4eeb684a0954ec4ceb255e3e9778d41')
e38168e2 418 me.assertEqual(repr(y), 'GF(0x4eeb684a0954ec4ceb255e3e9778d41)')
553d59fe
MW		 419 me.assertEqual(hex(y), '0x4eeb684a0954ec4ceb255e3e9778d41')
420 me.assertEqual(oct(y), '047353320450112516611472622536175135706501')
a90a9c0e
MW		 421 try: bin
422 except NameError: pass
423 else: me.assertEqual(bin(C.GF(661438603)),
424 '0b100111011011001100000010001011')
553d59fe
MW		 425
426 def test_number(me):
427 x, y, m, zero = C.GF(0xa9), C.GF(0x18), C.GF(0x11b), C.GF(0)
428
429 me.assertEqual(x, -x)
430 me.assertEqual(abs(x), x)
431
432 me.assertEqual(x + y, C.GF(0xb1))
433 me.assertEqual(x - y, C.GF(0xb1))
434 me.assertEqual(x*y, C.GF(0xfd8))
435 me.assertEqual(x&y, C.GF(0x8))
436 me.assertEqual(x | y, C.GF(0xb9))
437 me.assertEqual(x ^ y, C.GF(0xb1))
438
439 me.assertEqual(x << 3, C.GF(0x548))
440 me.assertEqual(x << -2, C.GF(0x2a))
441 me.assertEqual(x >> 2, C.GF(0x2a))
442 me.assertEqual(x >> -3, C.GF(0x548))
443
444 u = x/y; me.assertEqual((u.numer, u.denom), (C.GF(0x67), C.GF(0x8)))
445 me.assertEqual(x//y, C.GF(0xc))
446 me.assertEqual(x%y, C.GF(0x9))
447 me.assertEqual(divmod(x, y), (C.GF(0xc), C.GF(0x9)))
448 me.assertRaises(ZeroDivisionError, lambda: x/zero)
449 me.assertRaises(ZeroDivisionError, lambda: x//zero)
450 me.assertRaises(ZeroDivisionError, lambda: x%zero)
451 me.assertRaises(ZeroDivisionError, divmod, x, zero)
452
453 me.assertEqual(pow(x, 24),
454 C.GF(0x1000100000001010000010101000101010001000001))
455 me.assertEqual(pow(x, 24, m), C.GF(0x78))
456 me.assertEqual(pow(x, -24, m), C.GF(0xb6))
457 me.assertRaises(ZeroDivisionError, pow, x, -24, C.GF(0x18))
458
459 me.assertTrue(x)
460 me.assertFalse(zero)
461
462 def test_order(me):
463 x, y, z = C.GF(0xa9), C.GF(0x18), C.GF(0xb3)
464 me.assertTrue(x == x)
465 me.assertFalse(x != x)
466 me.assertFalse(x == y)
467 me.assertTrue(x != y)
468 me.assertTrue(x > y)
469 me.assertFalse(y > x)
470 me.assertFalse(x > x)
471 me.assertFalse(x > z)
472 me.assertFalse(z > x)
473 me.assertTrue(x >= y)
474 me.assertFalse(y >= x)
475 me.assertTrue(x >= x)
476 me.assertTrue(x >= z)
477 me.assertTrue(z >= x)
478 me.assertFalse(x <= y)
479 me.assertTrue(y <= x)
480 me.assertTrue(x <= x)
481 me.assertTrue(x <= z)
482 me.assertTrue(z <= x)
483 me.assertFalse(x < y)
484 me.assertTrue(y < x)
485 me.assertFalse(x < x)
486 me.assertFalse(x < z)
487 me.assertFalse(z < x)
488
489 def test_bits(me):
490 x, zero = C.GF(0xa9), C.GF(0)
491 me.assertTrue(x.testbit(0))
492 me.assertFalse(x.testbit(1))
493 me.assertFalse(x.testbit(1000))
494
495 me.assertEqual(x.setbit(0), x)
496 me.assertEqual(x.clearbit(0), C.GF(0xa8))
497 me.assertEqual(x.setbit(1), C.GF(0xab))
498 me.assertEqual(x.clearbit(1), x)
499
500 me.assertEqual(x.nbits, 8)
501 me.assertEqual(x.degree, 7)
502 me.assertEqual(zero.nbits, 0)
503 me.assertEqual(zero.degree, -1)
504
505 def test_loadstore(me):
506 x = C.GF(0x0123456789ab)
507
508 me.assertEqual(x.noctets, 6)
509
510 me.assertEqual(x, C.GF.loadb(C.bytes("0123456789ab")))
511
512 me.assertEqual(x.storeb(), C.bytes("0123456789ab"))
513 me.assertEqual(x.storeb(3), C.bytes("6789ab"))
514 me.assertEqual(x.storeb(8), C.bytes("00000123456789ab"))
515
516 me.assertEqual(x, C.GF.loadl(C.bytes("ab8967452301")))
517
518 me.assertEqual(x.storel(), C.bytes("ab8967452301"))
519 me.assertEqual(x.storel(3), C.bytes("ab8967"))
520 me.assertEqual(x.storel(8), C.bytes("ab89674523010000"))
521
522 me.assertEqual(x.tobuf(), C.bytes("00060123456789ab"))
523 me.assertEqual((x, T.bin("abcd")),
524 C.GF.frombuf(C.bytes("00060123456789ab61626364")))
525
526 def test_numbertheory(me):
527 p, x, y = C.GF(0x11b), C.GF(0xa9), C.GF(0x18)
528
529 me.assertEqual(x.sqr(), C.GF(0x4441))
530
531 me.assertEqual(x.gcd(y), C.GF(0x3))
532 me.assertEqual(x.gcdx(y), (C.GF(0x3), C.GF(0x3), C.GF(0x15)))
533 me.assertEqual(p.modinv(x), C.GF(0xc8))
534
535 me.assertTrue(p.irreduciblep())
536 me.assertFalse(x.irreduciblep())
537
538###--------------------------------------------------------------------------
539class TestGFReduce (U.TestCase):
540
541 def test(me):
542 p = C.GF(0x87).setbit(128)
543 me.assertTrue(p.irreduciblep())
544 m = C.GFReduce(p)
545
546 x = C.GF(0xce46b4c1d3a1523520b1bb6eb5c61883)
547 y = C.GF(0xb5b0b3566b8e03f4b4a2b1ac413f8566)
548 xy = C.GF(0x28e5b895c11b08edc2fe7e1be5694c64)
549
550 me.assertEqual(m.reduce(x*y), xy)
551 me.assertEqual(m.trace(x), 0)
552 me.assertEqual(m.trace(y), 1)
553 me.assertEqual(m.sqrt(x), C.GF(0xa277ee4bf770e5974cf1e31b1ccb54a1))
554 me.assertEqual(m.halftrace(y), C.GF(0x9cea73e79ffd190dd3c81d33e58d8e6f))
555 me.assertEqual(m.quadsolve(x), C.GF(0x9664c09d23d168147a438de6a813c784))
556
557###--------------------------------------------------------------------------
558class TestGFN (U.TestCase):
559
560 def test(me):
561 p = C.GF(0x87).setbit(128)
562 beta = C.GF(0xc50f387e37194d4a4b41e157a3e2b5e1)
563 y = C.GF(0xdaca76dc2578a63c788a2ce0fc7878f6)
564 yy = C.GF(0x298a98f955100f054fcee3433f96b00e)
565 zero, one, fff = C.GF(0), C.GF(1), C.GF(T.long(2)**128 - 1)
566 me.assertTrue(p.irreduciblep())
567
568 gfn = C.GFN(p, beta)
569 me.assertEqual(gfn.p, p)
570 me.assertEqual(gfn.beta, beta)
571 me.assertEqual(gfn.pton(zero), zero)
572 me.assertEqual(gfn.ntop(zero), zero)
573 me.assertEqual(gfn.pton(one), fff)
574 me.assertEqual(gfn.ntop(fff), one)
575 me.assertEqual(gfn.pton(y), yy)
576 me.assertEqual(gfn.ntop(yy), y)
577
578 ## Doesn't generate a normal basis.
579 me.assertRaises(ValueError, C.GFN, p, y)
580
581###----- That's all, folks --------------------------------------------------
582
583if __name__ == "__main__": U.main()
Catacomb cryptographic library -- Python bindings