| 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 | |
| 28 | #----- Imports -------------------------------------------------------------- |
| 29 | |
| 30 | import _base |
| 31 | import types as _types |
| 32 | from binascii import hexlify as _hexify, unhexlify as _unhexify |
| 33 | from sys import argv as _argv |
| 34 | |
| 35 | #----- Basic stuff ---------------------------------------------------------- |
| 36 | |
| 37 | ## For the benefit of the default keyreporter, we need the program na,e. |
| 38 | _base._ego(_argv[0]) |
| 39 | |
| 40 | ## Initialize the module. Drag in the static methods of the various |
| 41 | ## classes; create names for the various known crypto algorithms. |
| 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', |
| 50 | 'DHInfo', 'BinDHInfo', 'RSAPriv', 'BBSPriv', |
| 51 | 'PrimeFilter', 'RabinMiller', |
| 52 | 'Group', 'GE', |
| 53 | 'KeyData']: |
| 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])) |
| 60 | for i in [gcciphers, gchashes, gcmacs, gcprps]: |
| 61 | for c in i.itervalues(): |
| 62 | d[c.name.replace('-', '_')] = c |
| 63 | for c in gccrands.itervalues(): |
| 64 | d[c.name.replace('-', '_') + 'rand'] = c |
| 65 | _init() |
| 66 | |
| 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. |
| 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 | |
| 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 | |
| 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 | |
| 101 | #----- Multiprecision integers and binary polynomials ----------------------- |
| 102 | |
| 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' |
| 115 | return MPMul.product(xrange(1, x + 1)) |
| 116 | factorial = staticmethod(factorial) |
| 117 | _augment(MP, _tmp) |
| 118 | |
| 119 | class _tmp: |
| 120 | def zerop(x): return x == 0 |
| 121 | def reduce(x): return GFReduce(x) |
| 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) |
| 126 | _augment(GF, _tmp) |
| 127 | |
| 128 | class _tmp: |
| 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: |
| 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 | |
| 157 | #----- Elliptic curves ------------------------------------------------------ |
| 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): |
| 167 | return me(*args) |
| 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 | |
| 196 | #----- Key sizes ------------------------------------------------------------ |
| 197 | |
| 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 | |
| 226 | #----- Abstract groups ------------------------------------------------------ |
| 227 | |
| 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 | |
| 252 | #----- RSA encoding techniques ---------------------------------------------- |
| 253 | |
| 254 | class PKCS1Crypt (object): |
| 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 | |
| 263 | class PKCS1Sig (object): |
| 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 | |
| 272 | class OAEP (object): |
| 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 | |
| 283 | class PSS (object): |
| 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 | |
| 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 |
| 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 | |
| 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 ---------------------------------------------------- |