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d7ab1bab | 1 | # -*-python-*- |
2 | # | |
3 | # $Id$ | |
4 | # | |
5 | # Setup for Catacomb/Python bindings | |
6 | # | |
7 | # (c) 2004 Straylight/Edgeware | |
8 | # | |
9 | ||
10 | #----- Licensing notice ----------------------------------------------------- | |
11 | # | |
12 | # This file is part of the Python interface to Catacomb. | |
13 | # | |
14 | # Catacomb/Python is free software; you can redistribute it and/or modify | |
15 | # it under the terms of the GNU General Public License as published by | |
16 | # the Free Software Foundation; either version 2 of the License, or | |
17 | # (at your option) any later version. | |
18 | # | |
19 | # Catacomb/Python is distributed in the hope that it will be useful, | |
20 | # but WITHOUT ANY WARRANTY; without even the implied warranty of | |
21 | # MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the | |
22 | # GNU General Public License for more details. | |
23 | # | |
24 | # You should have received a copy of the GNU General Public License | |
25 | # along with Catacomb/Python; if not, write to the Free Software Foundation, | |
26 | # Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA. | |
27 | ||
ed8cc62d MW |
28 | #----- Imports -------------------------------------------------------------- |
29 | ||
d7ab1bab | 30 | import _base |
31 | import types as _types | |
32 | from binascii import hexlify as _hexify, unhexlify as _unhexify | |
46e6ad89 | 33 | from sys import argv as _argv |
34 | ||
ed8cc62d MW |
35 | #----- Basic stuff ---------------------------------------------------------- |
36 | ||
37 | ## For the benefit of the default keyreporter, we need the program na,e. | |
46e6ad89 | 38 | _base._ego(_argv[0]) |
d7ab1bab | 39 | |
ed8cc62d MW |
40 | ## Initialize the module. Drag in the static methods of the various |
41 | ## classes; create names for the various known crypto algorithms. | |
d7ab1bab | 42 | def _init(): |
43 | d = globals() | |
44 | b = _base.__dict__; | |
45 | for i in b: | |
46 | if i[0] != '_': | |
47 | d[i] = b[i]; | |
48 | for i in ['MP', 'GF', 'Field', | |
49 | 'ECPt', 'ECPtCurve', 'ECCurve', 'ECInfo', | |
ed8cc62d MW |
50 | 'DHInfo', 'BinDHInfo', 'RSAPriv', 'BBSPriv', |
51 | 'PrimeFilter', 'RabinMiller', | |
46e6ad89 | 52 | 'Group', 'GE', |
53 | 'KeyData']: | |
d7ab1bab | 54 | c = d[i] |
55 | pre = '_' + i + '_' | |
56 | plen = len(pre) | |
57 | for j in b: | |
58 | if j[:plen] == pre: | |
59 | setattr(c, j[plen:], classmethod(b[j])) | |
ed8cc62d MW |
60 | for i in [gcciphers, gchashes, gcmacs, gcprps]: |
61 | for c in i.itervalues(): | |
d7ab1bab | 62 | d[c.name.replace('-', '_')] = c |
ed8cc62d MW |
63 | for c in gccrands.itervalues(): |
64 | d[c.name.replace('-', '_') + 'rand'] = c | |
d7ab1bab | 65 | _init() |
66 | ||
ed8cc62d MW |
67 | ## A handy function for our work: add the methods of a named class to an |
68 | ## existing class. This is how we write the Python-implemented parts of our | |
69 | ## mostly-C types. | |
d7ab1bab | 70 | def _augment(c, cc): |
71 | for i in cc.__dict__: | |
72 | a = cc.__dict__[i] | |
73 | if type(a) is _types.MethodType: | |
74 | a = a.im_func | |
75 | elif type(a) not in (_types.FunctionType, staticmethod, classmethod): | |
76 | continue | |
77 | setattr(c, i, a) | |
78 | ||
ed8cc62d MW |
79 | ## Parsing functions tend to return the object parsed and the remainder of |
80 | ## the input. This checks that the remainder is input and, if so, returns | |
81 | ## just the object. | |
82 | def _checkend(r): | |
83 | x, rest = r | |
84 | if rest != '': | |
85 | raise SyntaxError, 'junk at end of string' | |
86 | return x | |
87 | ||
88 | #----- Bytestrings ---------------------------------------------------------- | |
89 | ||
d7ab1bab | 90 | class _tmp: |
91 | def fromhex(x): | |
92 | return ByteString(_unhexify(x)) | |
93 | fromhex = staticmethod(fromhex) | |
94 | def __hex__(me): | |
95 | return _hexify(me) | |
96 | def __repr__(me): | |
97 | return 'bytes(%r)' % hex(me) | |
98 | _augment(ByteString, _tmp) | |
99 | bytes = ByteString.fromhex | |
100 | ||
ed8cc62d MW |
101 | #----- Multiprecision integers and binary polynomials ----------------------- |
102 | ||
d7ab1bab | 103 | class _tmp: |
104 | def negp(x): return x < 0 | |
105 | def posp(x): return x > 0 | |
106 | def zerop(x): return x == 0 | |
107 | def oddp(x): return x.testbit(0) | |
108 | def evenp(x): return not x.testbit(0) | |
109 | def mont(x): return MPMont(x) | |
110 | def barrett(x): return MPBarrett(x) | |
111 | def reduce(x): return MPReduce(x) | |
112 | def factorial(x): | |
113 | 'factorial(X) -> X!' | |
114 | if x < 0: raise ValueError, 'factorial argument must be > 0' | |
ed8cc62d | 115 | return MPMul.product(xrange(1, x + 1)) |
d7ab1bab | 116 | factorial = staticmethod(factorial) |
117 | _augment(MP, _tmp) | |
118 | ||
d7ab1bab | 119 | class _tmp: |
fbc145f3 | 120 | def zerop(x): return x == 0 |
ed8cc62d | 121 | def reduce(x): return GFReduce(x) |
fbc145f3 MW |
122 | def trace(x, y): return x.reduce().trace(y) |
123 | def halftrace(x, y): return x.reduce().halftrace(y) | |
124 | def modsqrt(x, y): return x.reduce().sqrt(y) | |
125 | def quadsolve(x, y): return x.reduce().quadsolve(y) | |
d7ab1bab | 126 | _augment(GF, _tmp) |
127 | ||
128 | class _tmp: | |
ed8cc62d MW |
129 | def product(*arg): |
130 | 'product(ITERABLE) or product(I, ...) -> PRODUCT' | |
131 | return MPMul(*arg).done() | |
132 | product = staticmethod(product) | |
133 | _augment(MPMul, _tmp) | |
134 | ||
135 | #----- Abstract fields ------------------------------------------------------ | |
136 | ||
137 | class _tmp: | |
d7ab1bab | 138 | def fromstring(str): return _checkend(Field.parse(str)) |
139 | fromstring = staticmethod(fromstring) | |
140 | _augment(Field, _tmp) | |
141 | ||
142 | class _tmp: | |
143 | def __repr__(me): return '%s(%sL)' % (type(me).__name__, me.p) | |
144 | def ec(me, a, b): return ECPrimeProjCurve(me, a, b) | |
145 | _augment(PrimeField, _tmp) | |
146 | ||
147 | class _tmp: | |
148 | def __repr__(me): return '%s(%sL)' % (type(me).__name__, hex(me.p)) | |
149 | def ec(me, a, b): return ECBinProjCurve(me, a, b) | |
150 | _augment(BinField, _tmp) | |
151 | ||
152 | class _tmp: | |
153 | def __str__(me): return str(me.value) | |
154 | def __repr__(me): return '%s(%s)' % (repr(me.field), repr(me.value)) | |
155 | _augment(FE, _tmp) | |
156 | ||
ed8cc62d | 157 | #----- Elliptic curves ------------------------------------------------------ |
d7ab1bab | 158 | |
159 | class _tmp: | |
160 | def __repr__(me): | |
161 | return '%s(%r, %s, %s)' % (type(me).__name__, me.field, me.a, me.b) | |
162 | def frombuf(me, s): | |
163 | return ecpt.frombuf(me, s) | |
164 | def fromraw(me, s): | |
165 | return ecpt.fromraw(me, s) | |
166 | def pt(me, *args): | |
5f959e50 | 167 | return me(*args) |
d7ab1bab | 168 | _augment(ECCurve, _tmp) |
169 | ||
170 | class _tmp: | |
171 | def __repr__(me): | |
172 | if not me: return 'ECPt()' | |
173 | return 'ECPt(%s, %s)' % (me.ix, me.iy) | |
174 | def __str__(me): | |
175 | if not me: return 'inf' | |
176 | return '(%s, %s)' % (me.ix, me.iy) | |
177 | _augment(ECPt, _tmp) | |
178 | ||
179 | class _tmp: | |
180 | def __repr__(me): | |
181 | return 'ECInfo(curve = %r, G = %r, r = %s, h = %s)' % \ | |
182 | (me.curve, me.G, me.r, me.h) | |
183 | def group(me): | |
184 | return ECGroup(me) | |
185 | _augment(ECInfo, _tmp) | |
186 | ||
187 | class _tmp: | |
188 | def __repr__(me): | |
189 | if not me: return '%r()' % (me.curve) | |
190 | return '%r(%s, %s)' % (me.curve, me.x, me.y) | |
191 | def __str__(me): | |
192 | if not me: return 'inf' | |
193 | return '(%s, %s)' % (me.x, me.y) | |
194 | _augment(ECPtCurve, _tmp) | |
195 | ||
ed8cc62d MW |
196 | #----- Key sizes ------------------------------------------------------------ |
197 | ||
d7ab1bab | 198 | class _tmp: |
199 | def __repr__(me): return 'KeySZAny(%d)' % me.default | |
200 | def check(me, sz): return True | |
201 | def best(me, sz): return sz | |
202 | _augment(KeySZAny, _tmp) | |
203 | ||
204 | class _tmp: | |
205 | def __repr__(me): | |
206 | return 'KeySZRange(%d, %d, %d, %d)' % \ | |
207 | (me.default, me.min, me.max, me.mod) | |
208 | def check(me, sz): return me.min <= sz <= me.max and sz % me.mod == 0 | |
209 | def best(me, sz): | |
210 | if sz < me.min: raise ValueError, 'key too small' | |
211 | elif sz > me.max: return me.max | |
212 | else: return sz - (sz % me.mod) | |
213 | _augment(KeySZRange, _tmp) | |
214 | ||
215 | class _tmp: | |
216 | def __repr__(me): return 'KeySZSet(%d, %s)' % (me.default, me.set) | |
217 | def check(me, sz): return sz in me.set | |
218 | def best(me, sz): | |
219 | found = -1 | |
220 | for i in me.set: | |
221 | if found < i <= sz: found = i | |
222 | if found < 0: raise ValueError, 'key too small' | |
223 | return found | |
224 | _augment(KeySZSet, _tmp) | |
225 | ||
ed8cc62d MW |
226 | #----- Abstract groups ------------------------------------------------------ |
227 | ||
d7ab1bab | 228 | class _tmp: |
229 | def __repr__(me): | |
230 | return '%s(p = %s, r = %s, g = %s)' % \ | |
231 | (type(me).__name__, me.p, me.r, me.g) | |
232 | _augment(FGInfo, _tmp) | |
233 | ||
234 | class _tmp: | |
235 | def group(me): return PrimeGroup(me) | |
236 | _augment(DHInfo, _tmp) | |
237 | ||
238 | class _tmp: | |
239 | def group(me): return BinGroup(me) | |
240 | _augment(BinDHInfo, _tmp) | |
241 | ||
242 | class _tmp: | |
243 | def __repr__(me): | |
244 | return '%s(%r)' % (type(me).__name__, me.info) | |
245 | _augment(Group, _tmp) | |
246 | ||
247 | class _tmp: | |
248 | def __repr__(me): | |
249 | return '%r(%r)' % (me.group, str(me)) | |
250 | _augment(GE, _tmp) | |
251 | ||
ed8cc62d MW |
252 | #----- RSA encoding techniques ---------------------------------------------- |
253 | ||
254 | class PKCS1Crypt (object): | |
d7ab1bab | 255 | def __init__(me, ep = '', rng = rand): |
256 | me.ep = ep | |
257 | me.rng = rng | |
258 | def encode(me, msg, nbits): | |
259 | return _base._p1crypt_encode(msg, nbits, me.ep, me.rng) | |
260 | def decode(me, ct, nbits): | |
261 | return _base._p1crypt_decode(ct, nbits, me.ep, me.rng) | |
262 | ||
ed8cc62d | 263 | class PKCS1Sig (object): |
d7ab1bab | 264 | def __init__(me, ep = '', rng = rand): |
265 | me.ep = ep | |
266 | me.rng = rng | |
267 | def encode(me, msg, nbits): | |
268 | return _base._p1sig_encode(msg, nbits, me.ep, me.rng) | |
269 | def decode(me, msg, sig, nbits): | |
270 | return _base._p1sig_decode(msg, sig, nbits, me.ep, me.rng) | |
271 | ||
ed8cc62d | 272 | class OAEP (object): |
d7ab1bab | 273 | def __init__(me, mgf = sha_mgf, hash = sha, ep = '', rng = rand): |
274 | me.mgf = mgf | |
275 | me.hash = hash | |
276 | me.ep = ep | |
277 | me.rng = rng | |
278 | def encode(me, msg, nbits): | |
279 | return _base._oaep_encode(msg, nbits, me.mgf, me.hash, me.ep, me.rng) | |
280 | def decode(me, ct, nbits): | |
281 | return _base._oaep_decode(ct, nbits, me.mgf, me.hash, me.ep, me.rng) | |
282 | ||
ed8cc62d | 283 | class PSS (object): |
d7ab1bab | 284 | def __init__(me, mgf = sha_mgf, hash = sha, saltsz = None, rng = rand): |
285 | me.mgf = mgf | |
286 | me.hash = hash | |
287 | if saltsz is None: | |
288 | saltsz = hash.hashsz | |
289 | me.saltsz = saltsz | |
290 | me.rng = rng | |
291 | def encode(me, msg, nbits): | |
292 | return _base._pss_encode(msg, nbits, me.mgf, me.hash, me.saltsz, me.rng) | |
293 | def decode(me, msg, sig, nbits): | |
294 | return _base._pss_decode(msg, sig, nbits, | |
295 | me.mgf, me.hash, me.saltsz, me.rng) | |
296 | ||
297 | class _tmp: | |
298 | def encrypt(me, msg, enc): | |
299 | return me.pubop(enc.encode(msg, me.n.nbits)) | |
300 | def verify(me, msg, sig, enc): | |
301 | if msg is None: return enc.decode(msg, me.pubop(sig), me.n.nbits) | |
302 | try: | |
303 | x = enc.decode(msg, me.pubop(sig), me.n.nbits) | |
304 | return x is None or x == msg | |
305 | except ValueError: | |
306 | return False | |
307 | _augment(RSAPub, _tmp) | |
308 | ||
309 | class _tmp: | |
310 | def decrypt(me, ct, enc): return enc.decode(me.privop(ct), me.n.nbits) | |
311 | def sign(me, msg, enc): return me.privop(enc.encode(msg, me.n.nbits)) | |
312 | _augment(RSAPriv, _tmp) | |
313 | ||
ed8cc62d MW |
314 | #----- Built-in named curves and prime groups ------------------------------- |
315 | ||
316 | class _groupmap (object): | |
317 | def __init__(me, map, nth): | |
318 | me.map = map | |
319 | me.nth = nth | |
320 | me.i = [None] * (max(map.values()) + 1) | |
321 | def __repr__(me): | |
322 | return '{%s}' % ', '.join(['%r: %r' % (k, me[k]) for k in me]) | |
323 | def __contains__(me, k): | |
324 | return k in me.map | |
325 | def __getitem__(me, k): | |
326 | i = me.map[k] | |
327 | if me.i[i] is None: | |
328 | me.i[i] = me.nth(i) | |
329 | return me.i[i] | |
330 | def __setitem__(me, k, v): | |
331 | raise TypeError, "immutable object" | |
332 | def __iter__(me): | |
333 | return iter(me.map) | |
334 | def keys(me): | |
335 | return [k for k in me] | |
336 | def values(me): | |
337 | return [me[k] for k in me] | |
338 | eccurves = _groupmap(_base._eccurves, ECInfo._curven) | |
339 | primegroups = _groupmap(_base._pgroups, DHInfo._groupn) | |
340 | bingroups = _groupmap(_base._bingroups, BinDHInfo._groupn) | |
341 | ||
342 | #----- Prime number generation ---------------------------------------------- | |
343 | ||
344 | class PrimeGenEventHandler (object): | |
345 | def pg_begin(me, ev): | |
346 | return me.pg_try(ev) | |
347 | def pg_done(me, ev): | |
348 | return PGEN_DONE | |
349 | def pg_abort(me, ev): | |
350 | return PGEN_TRY | |
351 | def pg_fail(me, ev): | |
352 | return PGEN_TRY | |
353 | def pg_pass(me, ev): | |
354 | return PGEN_TRY | |
d7ab1bab | 355 | |
356 | class SophieGermainStepJump (object): | |
357 | def pg_begin(me, ev): | |
358 | me.lf = PrimeFilter(ev.x) | |
359 | me.hf = me.lf.muladd(2, 1) | |
360 | return me.cont(ev) | |
361 | def pg_try(me, ev): | |
362 | me.step() | |
363 | return me.cont(ev) | |
364 | def cont(me, ev): | |
365 | while me.lf.status == PGEN_FAIL or me.hf.status == PGEN_FAIL: | |
366 | me.step() | |
367 | if me.lf.status == PGEN_ABORT or me.hf.status == PGEN_ABORT: | |
368 | return PGEN_ABORT | |
369 | ev.x = me.lf.x | |
370 | if me.lf.status == PGEN_DONE and me.hf.status == PGEN_DONE: | |
371 | return PGEN_DONE | |
372 | return PGEN_TRY | |
373 | def pg_done(me, ev): | |
374 | del me.lf | |
375 | del me.hf | |
376 | ||
377 | class SophieGermainStepper (SophieGermainStepJump): | |
378 | def __init__(me, step): | |
379 | me.lstep = step; | |
380 | me.hstep = 2 * step | |
381 | def step(me): | |
382 | me.lf.step(me.lstep) | |
383 | me.hf.step(me.hstep) | |
384 | ||
385 | class SophieGermainJumper (SophieGermainStepJump): | |
386 | def __init__(me, jump): | |
387 | me.ljump = PrimeFilter(jump); | |
388 | me.hjump = me.ljump.muladd(2, 0) | |
389 | def step(me): | |
390 | me.lf.jump(me.ljump) | |
391 | me.hf.jump(me.hjump) | |
392 | def pg_done(me, ev): | |
393 | del me.ljump | |
394 | del me.hjump | |
395 | SophieGermainStepJump.pg_done(me, ev) | |
396 | ||
397 | class SophieGermainTester (object): | |
398 | def __init__(me): | |
399 | pass | |
400 | def pg_begin(me, ev): | |
401 | me.lr = RabinMiller(ev.x) | |
402 | me.hr = RabinMiller(2 * ev.x + 1) | |
403 | def pg_try(me, ev): | |
404 | lst = me.lr.test(ev.rng.range(me.lr.x)) | |
405 | if lst != PGEN_PASS and lst != PGEN_DONE: | |
406 | return lst | |
407 | rst = me.hr.test(ev.rng.range(me.hr.x)) | |
408 | if rst != PGEN_PASS and rst != PGEN_DONE: | |
409 | return rst | |
410 | if lst == PGEN_DONE and rst == PGEN_DONE: | |
411 | return PGEN_DONE | |
412 | return PGEN_PASS | |
413 | def pg_done(me, ev): | |
414 | del me.lr | |
415 | del me.hr | |
416 | ||
d7ab1bab | 417 | class PrimitiveStepper (PrimeGenEventHandler): |
418 | def __init__(me): | |
419 | pass | |
420 | def pg_try(me, ev): | |
421 | ev.x = me.i.next() | |
422 | return PGEN_TRY | |
423 | def pg_begin(me, ev): | |
424 | me.i = iter(smallprimes) | |
425 | return me.pg_try(ev) | |
426 | ||
427 | class PrimitiveTester (PrimeGenEventHandler): | |
428 | def __init__(me, mod, hh = [], exp = None): | |
429 | me.mod = MPMont(mod) | |
430 | me.exp = exp | |
431 | me.hh = hh | |
432 | def pg_try(me, ev): | |
433 | x = ev.x | |
434 | if me.exp is not None: | |
435 | x = me.mod.exp(x, me.exp) | |
436 | if x == 1: return PGEN_FAIL | |
437 | for h in me.hh: | |
438 | if me.mod.exp(x, h) == 1: return PGEN_FAIL | |
439 | ev.x = x | |
440 | return PGEN_DONE | |
441 | ||
442 | class SimulStepper (PrimeGenEventHandler): | |
443 | def __init__(me, mul = 2, add = 1, step = 2): | |
444 | me.step = step | |
445 | me.mul = mul | |
446 | me.add = add | |
447 | def _stepfn(me, step): | |
448 | if step <= 0: | |
449 | raise ValueError, 'step must be positive' | |
450 | if step <= MPW_MAX: | |
451 | return lambda f: f.step(step) | |
452 | j = PrimeFilter(step) | |
453 | return lambda f: f.jump(j) | |
454 | def pg_begin(me, ev): | |
455 | x = ev.x | |
456 | me.lf = PrimeFilter(x) | |
457 | me.hf = PrimeFilter(x * me.mul + me.add) | |
458 | me.lstep = me._stepfn(me.step) | |
459 | me.hstep = me._stepfn(me.step * me.mul) | |
460 | SimulStepper._cont(me, ev) | |
461 | def pg_try(me, ev): | |
462 | me._step() | |
463 | me._cont(ev) | |
464 | def _step(me): | |
465 | me.lstep(me.lf) | |
466 | me.hstep(me.hf) | |
467 | def _cont(me, ev): | |
468 | while me.lf.status == PGEN_FAIL or me.hf.status == PGEN_FAIL: | |
469 | me._step() | |
470 | if me.lf.status == PGEN_ABORT or me.hf.status == PGEN_ABORT: | |
471 | return PGEN_ABORT | |
472 | ev.x = me.lf.x | |
473 | if me.lf.status == PGEN_DONE and me.hf.status == PGEN_DONE: | |
474 | return PGEN_DONE | |
475 | return PGEN_TRY | |
476 | def pg_done(me, ev): | |
477 | del me.lf | |
478 | del me.hf | |
479 | del me.lstep | |
480 | del me.hstep | |
481 | ||
482 | class SimulTester (PrimeGenEventHandler): | |
483 | def __init__(me, mul = 2, add = 1): | |
484 | me.mul = mul | |
485 | me.add = add | |
486 | def pg_begin(me, ev): | |
487 | x = ev.x | |
488 | me.lr = RabinMiller(x) | |
489 | me.hr = RabinMiller(x * me.mul + me.add) | |
490 | def pg_try(me, ev): | |
491 | lst = me.lr.test(ev.rng.range(me.lr.x)) | |
492 | if lst != PGEN_PASS and lst != PGEN_DONE: | |
493 | return lst | |
494 | rst = me.hr.test(ev.rng.range(me.hr.x)) | |
495 | if rst != PGEN_PASS and rst != PGEN_DONE: | |
496 | return rst | |
497 | if lst == PGEN_DONE and rst == PGEN_DONE: | |
498 | return PGEN_DONE | |
499 | return PGEN_PASS | |
500 | def pg_done(me, ev): | |
501 | del me.lr | |
502 | del me.hr | |
503 | ||
504 | def sgprime(start, step = 2, name = 'p', event = pgen_nullev, nsteps = 0): | |
505 | start = MP(start) | |
506 | return pgen(start, name, SimulStepper(step = step), SimulTester(), event, | |
507 | nsteps, RabinMiller.iters(start.nbits)) | |
508 | ||
509 | def findprimitive(mod, hh = [], exp = None, name = 'g', event = pgen_nullev): | |
510 | return pgen(0, name, PrimitiveStepper(), PrimitiveTester(mod, hh, exp), | |
511 | event, 0, 1) | |
512 | ||
513 | def kcdsaprime(pbits, qbits, rng = rand, | |
514 | event = pgen_nullev, name = 'p', nsteps = 0): | |
515 | hbits = pbits - qbits | |
516 | h = pgen(rng.mp(hbits, 1), name + ' [h]', | |
517 | PrimeGenStepper(2), PrimeGenTester(), | |
518 | event, nsteps, RabinMiller.iters(hbits)) | |
519 | q = pgen(rng.mp(qbits, 1), name, SimulStepper(2 * h, 1, 2), | |
520 | SimulTester(2 * h, 1), event, nsteps, RabinMiller.iters(qbits)) | |
521 | p = 2 * q * h + 1 | |
522 | return p, q, h | |
523 | ||
524 | #----- That's all, folks ---------------------------------------------------- |