cipherbreak.py

   1 """A set of functions to break the ciphers give in ciphers.py.
   2 """
   3
   4 import string
   5 import collections
   6 import norms
   7 import logging
   8 import random
   9 import math
  10 from itertools import starmap
  11 from segment import segment
  12 from multiprocessing import Pool
  13
  14 import matplotlib.pyplot as plt
  15
  16 logger = logging.getLogger(__name__)
  17 logger.addHandler(logging.FileHandler('cipher.log'))
  18 logger.setLevel(logging.WARNING)
  19 #logger.setLevel(logging.INFO)
  20 #logger.setLevel(logging.DEBUG)
  21
  22 from cipher import *
  23 from language_models import *
  24
  25 # To time a run:
  26 #
  27 # import timeit
  28 # c5a = open('2012/5a.ciphertext', 'r').read()
  29 # timeit.timeit('keyword_break(c5a)', setup='gc.enable() ; from __main__ import c5a ; from cipher import keyword_break', number=1)
  30 # timeit.repeat('keyword_break_mp(c5a, chunksize=500)', setup='gc.enable() ; from __main__ import c5a ; from cipher import keyword_break_mp', repeat=5, number=1)
  31
  32 transpositions = collections.defaultdict(list)
  33 for word in keywords:
  34     transpositions[transpositions_of(word)] += [word]
  35
  36 def frequencies(text):
  37     """Count the number of occurrences of each character in text
  38
  39     >>> sorted(frequencies('abcdefabc').items())
  40     [('a', 2), ('b', 2), ('c', 2), ('d', 1), ('e', 1), ('f', 1)]
  41     >>> sorted(frequencies('the quick brown fox jumped over the lazy ' \
  42          'dog').items()) # doctest: +NORMALIZE_WHITESPACE
  43     [(' ', 8), ('a', 1), ('b', 1), ('c', 1), ('d', 2), ('e', 4), ('f', 1),
  44      ('g', 1), ('h', 2), ('i', 1), ('j', 1), ('k', 1), ('l', 1), ('m', 1),
  45      ('n', 1), ('o', 4), ('p', 1), ('q', 1), ('r', 2), ('t', 2), ('u', 2),
  46      ('v', 1), ('w', 1), ('x', 1), ('y', 1), ('z', 1)]
  47     >>> sorted(frequencies('The Quick BROWN fox jumped! over... the ' \
  48          '(9lazy) DOG').items()) # doctest: +NORMALIZE_WHITESPACE
  49     [(' ', 8), ('!', 1), ('(', 1), (')', 1), ('.', 3), ('9', 1), ('B', 1),
  50      ('D', 1), ('G', 1), ('N', 1), ('O', 2), ('Q', 1), ('R', 1), ('T', 1),
  51      ('W', 1), ('a', 1), ('c', 1), ('d', 1), ('e', 4), ('f', 1), ('h', 2),
  52      ('i', 1), ('j', 1), ('k', 1), ('l', 1), ('m', 1), ('o', 2), ('p', 1),
  53      ('r', 1), ('t', 1), ('u', 2), ('v', 1), ('x', 1), ('y', 1), ('z', 1)]
  54     >>> sorted(frequencies(sanitise('The Quick BROWN fox jumped! over... '\
  55          'the (9lazy) DOG')).items()) # doctest: +NORMALIZE_WHITESPACE
  56     [('a', 1), ('b', 1), ('c', 1), ('d', 2), ('e', 4), ('f', 1), ('g', 1),
  57      ('h', 2), ('i', 1), ('j', 1), ('k', 1), ('l', 1), ('m', 1), ('n', 1),
  58      ('o', 4), ('p', 1), ('q', 1), ('r', 2), ('t', 2), ('u', 2), ('v', 1),
  59      ('w', 1), ('x', 1), ('y', 1), ('z', 1)]
  60     >>> frequencies('abcdefabcdef')['x']
  61     0
  62     """
  63     return collections.Counter(c for c in text)
  64
  65
  66 def caesar_break(message, fitness=Pletters):
  67     """Breaks a Caesar cipher using frequency analysis
  68
  69     >>> caesar_break('ibxcsyorsaqcheyklxivoexlevmrimwxsfiqevvmihrsasrxliwyrh' \
  70           'ecjsppsamrkwleppfmergefifvmhixscsymjcsyqeoixlm') # doctest: +ELLIPSIS
  71     (4, -130.849989015...)
  72     >>> caesar_break('wxwmaxdgheetgwuxztgptedbgznitgwwhpguxyhkxbmhvvtlbhgtee' \
  73           'raxlmhiixweblmxgxwmhmaxybkbgztgwztsxwbgmxgmert') # doctest: +ELLIPSIS
  74     (19, -128.82410410...)
  75     >>> caesar_break('yltbbqnqnzvguvaxurorgenafsbezqvagbnornfgsbevpnaabjurer' \
  76           'svaquvzyvxrnznazlybequrvfohgriraabjtbaruraprur') # doctest: +ELLIPSIS
  77     (13, -126.25403935...)
  78     """
  79     sanitised_message = sanitise(message)
  80     best_shift = 0
  81     best_fit = float('-inf')
  82     for shift in range(26):
  83         plaintext = caesar_decipher(sanitised_message, shift)
  84         fit = fitness(plaintext)
  85         logger.debug('Caesar break attempt using key {0} gives fit of {1} '
  86                      'and decrypt starting: {2}'.format(shift, fit,
  87                                                         plaintext[:50]))
  88         if fit > best_fit:
  89             best_fit = fit
  90             best_shift = shift
  91     logger.info('Caesar break best fit: key {0} gives fit of {1} and '
  92                 'decrypt starting: {2}'.format(best_shift, best_fit,
  93                     caesar_decipher(sanitised_message, best_shift)[:50]))
  94     return best_shift, best_fit
  95
  96 def affine_break(message, fitness=Pletters):
  97     """Breaks an affine cipher using frequency analysis
  98
  99     >>> affine_break('lmyfu bkuusd dyfaxw claol psfaom jfasd snsfg jfaoe ls ' \
 100           'omytd jlaxe mh jm bfmibj umis hfsul axubafkjamx. ls kffkxwsd jls ' \
 101           'ofgbjmwfkiu olfmxmtmwaokttg jlsx ls kffkxwsd jlsi zg tsxwjl. jlsx ' \
 102           'ls umfjsd jlsi zg hfsqysxog. ls dmmdtsd mx jls bats mh bkbsf. ls ' \
 103           'bfmctsd kfmyxd jls lyj, mztanamyu xmc jm clm cku tmmeaxw kj lai ' \
 104           'kxd clm ckuxj.') # doctest: +ELLIPSIS
 105     ((15, 22, True), -340.601181913...)
 106     """
 107     sanitised_message = sanitise(message)
 108     best_multiplier = 0
 109     best_adder = 0
 110     best_one_based = True
 111     best_fit = float("-inf")
 112     for one_based in [True, False]:
 113         for multiplier in [x for x in range(1, 26, 2) if x != 13]:
 114             for adder in range(26):
 115                 plaintext = affine_decipher(sanitised_message,
 116                                             multiplier, adder, one_based)
 117                 fit = fitness(plaintext)
 118                 logger.debug('Affine break attempt using key {0}x+{1} ({2}) '
 119                              'gives fit of {3} and decrypt starting: {4}'.
 120                              format(multiplier, adder, one_based, fit,
 121                                     plaintext[:50]))
 122                 if fit > best_fit:
 123                     best_fit = fit
 124                     best_multiplier = multiplier
 125                     best_adder = adder
 126                     best_one_based = one_based
 127     logger.info('Affine break best fit with key {0}x+{1} ({2}) gives fit of '
 128                 '{3} and decrypt starting: {4}'.format(
 129                     best_multiplier, best_adder, best_one_based, best_fit,
 130                     affine_decipher(sanitised_message, best_multiplier,
 131                                     best_adder, best_one_based)[:50]))
 132     return (best_multiplier, best_adder, best_one_based), best_fit
 133
 134 def keyword_break(message, wordlist=keywords, fitness=Pletters):
 135     """Breaks a keyword substitution cipher using a dictionary and
 136     frequency analysis.
 137
 138     >>> keyword_break(keyword_encipher('this is a test message for the ' \
 139           'keyword decipherment', 'elephant', KeywordWrapAlphabet.from_last), \
 140           wordlist=['cat', 'elephant', 'kangaroo']) # doctest: +ELLIPSIS
 141     (('elephant', <KeywordWrapAlphabet.from_last: 2>), -52.834575011...)
 142     """
 143     best_keyword = ''
 144     best_wrap_alphabet = True
 145     best_fit = float("-inf")
 146     for wrap_alphabet in KeywordWrapAlphabet:
 147         for keyword in wordlist:
 148             plaintext = keyword_decipher(message, keyword, wrap_alphabet)
 149             fit = fitness(plaintext)
 150             logger.debug('Keyword break attempt using key {0} (wrap={1}) '
 151                          'gives fit of {2} and decrypt starting: {3}'.format(
 152                              keyword, wrap_alphabet, fit,
 153                              sanitise(plaintext)[:50]))
 154             if fit > best_fit:
 155                 best_fit = fit
 156                 best_keyword = keyword
 157                 best_wrap_alphabet = wrap_alphabet
 158     logger.info('Keyword break best fit with key {0} (wrap={1}) gives fit of '
 159                 '{2} and decrypt starting: {3}'.format(best_keyword,
 160                     best_wrap_alphabet, best_fit, sanitise(
 161                         keyword_decipher(message, best_keyword,
 162                                          best_wrap_alphabet))[:50]))
 163     return (best_keyword, best_wrap_alphabet), best_fit
 164
 165 def keyword_break_mp(message, wordlist=keywords, fitness=Pletters,
 166                      number_of_solutions=1, chunksize=500):
 167     """Breaks a keyword substitution cipher using a dictionary and
 168     frequency analysis
 169
 170     >>> keyword_break_mp(keyword_encipher('this is a test message for the ' \
 171           'keyword decipherment', 'elephant', KeywordWrapAlphabet.from_last), \
 172           wordlist=['cat', 'elephant', 'kangaroo']) # doctest: +ELLIPSIS
 173     (('elephant', <KeywordWrapAlphabet.from_last: 2>), -52.834575011...)
 174     >>> keyword_break_mp(keyword_encipher('this is a test message for the ' \
 175           'keyword decipherment', 'elephant', KeywordWrapAlphabet.from_last), \
 176           wordlist=['cat', 'elephant', 'kangaroo'], \
 177           number_of_solutions=2) # doctest: +ELLIPSIS, +NORMALIZE_WHITESPACE
 178     [(('elephant', <KeywordWrapAlphabet.from_last: 2>), -52.834575011...),
 179     (('elephant', <KeywordWrapAlphabet.from_largest: 3>), -52.834575011...)]
 180     """
 181     with Pool() as pool:
 182         helper_args = [(message, word, wrap, fitness)
 183                        for word in wordlist
 184                        for wrap in KeywordWrapAlphabet]
 185         # Gotcha: the helper function here needs to be defined at the top level
 186         #   (limitation of Pool.starmap)
 187         breaks = pool.starmap(keyword_break_worker, helper_args, chunksize)
 188         if number_of_solutions == 1:
 189             return max(breaks, key=lambda k: k[1])
 190         else:
 191             return sorted(breaks, key=lambda k: k[1], reverse=True)[:number_of_solutions]
 192
 193 def keyword_break_worker(message, keyword, wrap_alphabet, fitness):
 194     plaintext = keyword_decipher(message, keyword, wrap_alphabet)
 195     fit = fitness(plaintext)
 196     logger.debug('Keyword break attempt using key {0} (wrap={1}) gives fit of '
 197                  '{2} and decrypt starting: {3}'.format(keyword,
 198                      wrap_alphabet, fit, sanitise(plaintext)[:50]))
 199     return (keyword, wrap_alphabet), fit
 200
 201 def monoalphabetic_break_hillclimbing(message, max_iterations=10000000,
 202         fitness=Pletters):
 203     ciphertext = unaccent(message).lower()
 204     alphabet = list(string.ascii_lowercase)
 205     random.shuffle(alphabet)
 206     alphabet = ''.join(alphabet)
 207     return monoalphabetic_break_hillclimbing_worker(ciphertext, alphabet,
 208                                                     max_iterations, fitness)
 209
 210 def monoalphabetic_break_hillclimbing_mp(message, workers=10,
 211         max_iterations = 10000000, fitness=Pletters, chunksize=1):
 212     worker_args = []
 213     ciphertext = unaccent(message).lower()
 214     for i in range(workers):
 215         alphabet = list(string.ascii_lowercase)
 216         random.shuffle(alphabet)
 217         alphabet = ''.join(alphabet)
 218         worker_args.append((ciphertext, alphabet, max_iterations, fitness))
 219     with Pool() as pool:
 220         breaks = pool.starmap(monoalphabetic_break_hillclimbing_worker,
 221                               worker_args, chunksize)
 222     return max(breaks, key=lambda k: k[1])
 223
 224 def monoalphabetic_break_hillclimbing_worker(message, alphabet,
 225         max_iterations, fitness):
 226     def swap(letters, i, j):
 227         if i > j:
 228             i, j = j, i
 229         if i == j:
 230             return letters
 231         else:
 232             return (letters[:i] + letters[j] + letters[i+1:j] + letters[i] +
 233                     letters[j+1:])
 234     best_alphabet = alphabet
 235     best_fitness = float('-inf')
 236     for i in range(max_iterations):
 237         alphabet = swap(alphabet, random.randrange(26), random.randrange(26))
 238         cipher_translation = ''.maketrans(string.ascii_lowercase, alphabet)
 239         plaintext = message.translate(cipher_translation)
 240         if fitness(plaintext) > best_fitness:
 241             best_fitness = fitness(plaintext)
 242             best_alphabet = alphabet
 243             print(i, best_alphabet, best_fitness, plaintext)
 244     return best_alphabet, best_fitness
 245
 246
 247 def vigenere_keyword_break_mp(message, wordlist=keywords, fitness=Pletters,
 248                               chunksize=500):
 249     """Breaks a vigenere cipher using a dictionary and frequency analysis.
 250
 251     >>> vigenere_keyword_break_mp(vigenere_encipher(sanitise('this is a test ' \
 252              'message for the vigenere decipherment'), 'cat'), \
 253              wordlist=['cat', 'elephant', 'kangaroo']) # doctest: +ELLIPSIS
 254     ('cat', -52.947271216...)
 255     """
 256     with Pool() as pool:
 257         helper_args = [(message, word, fitness)
 258                        for word in wordlist]
 259         # Gotcha: the helper function here needs to be defined at the top level
 260         #   (limitation of Pool.starmap)
 261         breaks = pool.starmap(vigenere_keyword_break_worker, helper_args,
 262                               chunksize)
 263         return max(breaks, key=lambda k: k[1])
 264 vigenere_keyword_break = vigenere_keyword_break_mp
 265
 266 def vigenere_keyword_break_worker(message, keyword, fitness):
 267     plaintext = vigenere_decipher(message, keyword)
 268     fit = fitness(plaintext)
 269     logger.debug('Vigenere keyword break attempt using key {0} gives fit of '
 270                  '{1} and decrypt starting: {2}'.format(keyword,
 271                      fit, sanitise(plaintext)[:50]))
 272     return keyword, fit
 273
 274
 275 def vigenere_frequency_break(message, max_key_length=20, fitness=Pletters):
 276     """Breaks a Vigenere cipher with frequency analysis
 277
 278     >>> vigenere_frequency_break(vigenere_encipher(sanitise("It is time to " \
 279             "run. She is ready and so am I. I stole Daniel's pocketbook this " \
 280             "afternoon when he left his jacket hanging on the easel in the " \
 281             "attic. I jump every time I hear a footstep on the stairs, " \
 282             "certain that the theft has been discovered and that I will " \
 283             "be caught. The SS officer visits less often now that he is " \
 284             "sure"), 'florence')) # doctest: +ELLIPSIS
 285     ('florence', -307.5473096791...)
 286     """
 287     def worker(message, key_length, fitness):
 288         splits = every_nth(sanitised_message, key_length)
 289         key = ''.join([chr(caesar_break(s)[0] + ord('a')) for s in splits])
 290         plaintext = vigenere_decipher(message, key)
 291         fit = fitness(plaintext)
 292         return key, fit
 293     sanitised_message = sanitise(message)
 294     results = starmap(worker, [(sanitised_message, i, fitness)
 295                                for i in range(1, max_key_length+1)])
 296     return max(results, key=lambda k: k[1])
 297
 298
 299 def beaufort_frequency_break(message, max_key_length=20, fitness=Pletters):
 300     """Breaks a Beaufort cipher with frequency analysis
 301
 302     >>> beaufort_frequency_break(beaufort_encipher(sanitise("It is time to " \
 303             "run. She is ready and so am I. I stole Daniel's pocketbook this " \
 304             "afternoon when he left his jacket hanging on the easel in the " \
 305             "attic. I jump every time I hear a footstep on the stairs, " \
 306             "certain that the theft has been discovered and that I will " \
 307             "be caught. The SS officer visits less often now " \
 308             "that he is sure"), 'florence')) # doctest: +ELLIPSIS
 309     ('florence', -307.5473096791...)
 310     """
 311     def worker(message, key_length, fitness):
 312         splits = every_nth(sanitised_message, key_length)
 313         key = ''.join([chr(-caesar_break(s)[0] % 26 + ord('a'))
 314                        for s in splits])
 315         plaintext = beaufort_decipher(message, key)
 316         fit = fitness(plaintext)
 317         return key, fit
 318     sanitised_message = sanitise(message)
 319     results = starmap(worker, [(sanitised_message, i, fitness)
 320                                for i in range(1, max_key_length+1)])
 321     return max(results, key=lambda k: k[1])
 322
 323
 324 def column_transposition_break_mp(message, translist=transpositions,
 325                                   fitness=Pbigrams, chunksize=500):
 326     """Breaks a column transposition cipher using a dictionary and
 327     n-gram frequency analysis
 328
 329     >>> column_transposition_break_mp(column_transposition_encipher(sanitise( \
 330             "It is a truth universally acknowledged, that a single man in \
 331              possession of a good fortune, must be in want of a wife. However \
 332              little known the feelings or views of such a man may be on his \
 333              first entering a neighbourhood, this truth is so well fixed in \
 334              the minds of the surrounding families, that he is considered the \
 335              rightful property of some one or other of their daughters."), \
 336         'encipher'), \
 337         translist={(2, 0, 5, 3, 1, 4, 6): ['encipher'], \
 338                    (5, 0, 6, 1, 3, 4, 2): ['fourteen'], \
 339                    (6, 1, 0, 4, 5, 3, 2): ['keyword']}) # doctest: +ELLIPSIS
 340     (((2, 0, 5, 3, 1, 4, 6), False, False), -709.4646722...)
 341     >>> column_transposition_break_mp(column_transposition_encipher(sanitise( \
 342             "It is a truth universally acknowledged, that a single man in \
 343              possession of a good fortune, must be in want of a wife. However \
 344              little known the feelings or views of such a man may be on his \
 345              first entering a neighbourhood, this truth is so well fixed in \
 346              the minds of the surrounding families, that he is considered the \
 347              rightful property of some one or other of their daughters."), \
 348         'encipher'), \
 349         translist={(2, 0, 5, 3, 1, 4, 6): ['encipher'], \
 350                    (5, 0, 6, 1, 3, 4, 2): ['fourteen'], \
 351                    (6, 1, 0, 4, 5, 3, 2): ['keyword']}, \
 352         fitness=Ptrigrams) # doctest: +ELLIPSIS
 353     (((2, 0, 5, 3, 1, 4, 6), False, False), -997.0129085...)
 354     """
 355     with Pool() as pool:
 356         helper_args = [(message, trans, fillcolumnwise, emptycolumnwise,
 357                         fitness)
 358                        for trans in translist.keys()
 359                        for fillcolumnwise in [True, False]
 360                        for emptycolumnwise in [True, False]]
 361         # Gotcha: the helper function here needs to be defined at the top level
 362         #   (limitation of Pool.starmap)
 363         breaks = pool.starmap(column_transposition_break_worker,
 364                               helper_args, chunksize)
 365         return max(breaks, key=lambda k: k[1])
 366 column_transposition_break = column_transposition_break_mp
 367
 368 def column_transposition_break_worker(message, transposition,
 369         fillcolumnwise, emptycolumnwise, fitness):
 370     plaintext = column_transposition_decipher(message, transposition,
 371         fillcolumnwise=fillcolumnwise, emptycolumnwise=emptycolumnwise)
 372     fit = fitness(sanitise(plaintext))
 373     logger.debug('Column transposition break attempt using key {0} '
 374                          'gives fit of {1} and decrypt starting: {2}'.format(
 375                              transposition, fit,
 376                              sanitise(plaintext)[:50]))
 377     return (transposition, fillcolumnwise, emptycolumnwise), fit
 378
 379
 380 def scytale_break_mp(message, max_key_length=20,
 381                      fitness=Pbigrams, chunksize=500):
 382     """Breaks a scytale cipher using a range of lengths and
 383     n-gram frequency analysis
 384
 385     >>> scytale_break_mp(scytale_encipher(sanitise( \
 386             "It is a truth universally acknowledged, that a single man in \
 387              possession of a good fortune, must be in want of a wife. However \
 388              little known the feelings or views of such a man may be on his \
 389              first entering a neighbourhood, this truth is so well fixed in \
 390              the minds of the surrounding families, that he is considered the \
 391              rightful property of some one or other of their daughters."), \
 392         5)) # doctest: +ELLIPSIS
 393     (5, -709.4646722...)
 394     >>> scytale_break_mp(scytale_encipher(sanitise( \
 395             "It is a truth universally acknowledged, that a single man in \
 396              possession of a good fortune, must be in want of a wife. However \
 397              little known the feelings or views of such a man may be on his \
 398              first entering a neighbourhood, this truth is so well fixed in \
 399              the minds of the surrounding families, that he is considered the \
 400              rightful property of some one or other of their daughters."), \
 401         5), \
 402         fitness=Ptrigrams) # doctest: +ELLIPSIS
 403     (5, -997.0129085...)
 404     """
 405     with Pool() as pool:
 406         helper_args = [(message, trans, False, True, fitness)
 407             for trans in
 408                 [[col for col in range(math.ceil(len(message)/rows))]
 409                     for rows in range(1,max_key_length+1)]]
 410         # Gotcha: the helper function here needs to be defined at the top level
 411         #   (limitation of Pool.starmap)
 412         breaks = pool.starmap(column_transposition_break_worker,
 413                               helper_args, chunksize)
 414         best = max(breaks, key=lambda k: k[1])
 415         return math.trunc(len(message) / len(best[0][0])), best[1]
 416 scytale_break = scytale_break_mp
 417
 418
 419 def railfence_break(message, max_key_length=20,
 420                      fitness=Pletters, chunksize=500):
 421     """Breaks a hill cipher using a matrix of given rank and letter frequencies
 422
 423
 424     """
 425
 426     sanitised_message = sanitise(message)
 427     results = starmap(worker, [(sanitised_message, i, fitness)
 428                                for i in range(2, max_key_length+1)])
 429     return max(results, key=lambda k: k[1])
 430
 431
 432 def railfence_break(message, max_key_length=20,
 433                      fitness=Pbigrams, chunksize=500):
 434     """Breaks a railfence cipher using a range of lengths and
 435     n-gram frequency analysis
 436
 437     >>> railfence_break(railfence_encipher(sanitise( \
 438             "It is a truth universally acknowledged, that a single man in \
 439              possession of a good fortune, must be in want of a wife. However \
 440              little known the feelings or views of such a man may be on his \
 441              first entering a neighbourhood, this truth is so well fixed in \
 442              the minds of the surrounding families, that he is considered the \
 443              rightful property of some one or other of their daughters."), \
 444         7)) # doctest: +ELLIPSIS
 445     (7, -709.46467226...)
 446     >>> railfence_break(railfence_encipher(sanitise( \
 447             "It is a truth universally acknowledged, that a single man in \
 448              possession of a good fortune, must be in want of a wife. However \
 449              little known the feelings or views of such a man may be on his \
 450              first entering a neighbourhood, this truth is so well fixed in \
 451              the minds of the surrounding families, that he is considered the \
 452              rightful property of some one or other of their daughters."), \
 453         7), \
 454         fitness=Ptrigrams) # doctest: +ELLIPSIS
 455     (7, -997.0129085...)
 456     """
 457     def worker(message, height, fitness):
 458         plaintext = railfence_decipher(message, height)
 459         fit = fitness(plaintext)
 460         return height, fit
 461
 462     sanitised_message = sanitise(message)
 463     results = starmap(worker, [(sanitised_message, i, fitness)
 464                                for i in range(2, max_key_length+1)])
 465     return max(results, key=lambda k: k[1])
 466
 467
 468 def hill_break(message, matrix_size=2, fitness=Pletters,
 469     number_of_solutions=1, chunksize=500):
 470
 471     all_matrices = [np.matrix(list(m))
 472         for m in itertools.product([list(r)
 473             for r in itertools.product(range(26), repeat=matrix_size)],
 474         repeat=matrix_size)]
 475     valid_matrices = [m for m, d in
 476         zip(all_matrices, (int(round(linalg.det(m))) for m in all_matrices))
 477                   if d != 0
 478                   if d % 2 != 0
 479                   if d % 13 != 0 ]
 480     with Pool() as pool:
 481         helper_args = [(message, matrix, fitness)
 482                        for matrix in valid_matrices]
 483         # Gotcha: the helper function here needs to be defined at the top level
 484         #   (limitation of Pool.starmap)
 485         breaks = pool.starmap(hill_break_worker, helper_args, chunksize)
 486         if number_of_solutions == 1:
 487             return max(breaks, key=lambda k: k[1])
 488         else:
 489             return sorted(breaks, key=lambda k: k[1], reverse=True)[:number_of_solutions]
 490
 491 def hill_break_worker(message, matrix, fitness):
 492     plaintext = hill_decipher(matrix, message)
 493     fit = fitness(plaintext)
 494     logger.debug('Hill cipher break attempt using key {0} gives fit of '
 495                  '{1} and decrypt starting: {2}'.format(matrix,
 496                      fit, sanitise(plaintext)[:50]))
 497     return matrix, fit
 498
 499
 500 def pocket_enigma_break_by_crib(message, wheel_spec, crib, crib_position):
 501     """Break a pocket enigma using a crib (some plaintext that's expected to
 502     be in a certain position). Returns a list of possible starting wheel
 503     positions that could produce the crib.
 504
 505     >>> pocket_enigma_break_by_crib('kzpjlzmoga', 1, 'h', 0)
 506     ['a', 'f', 'q']
 507     >>> pocket_enigma_break_by_crib('kzpjlzmoga', 1, 'he', 0)
 508     ['a']
 509     >>> pocket_enigma_break_by_crib('kzpjlzmoga', 1, 'll', 2)
 510     ['a']
 511     >>> pocket_enigma_break_by_crib('kzpjlzmoga', 1, 'l', 2)
 512     ['a']
 513     >>> pocket_enigma_break_by_crib('kzpjlzmoga', 1, 'l', 3)
 514     ['a', 'j', 'n']
 515     >>> pocket_enigma_break_by_crib('aaaaa', 1, 'l', 3)
 516     []
 517     """
 518     pe = PocketEnigma(wheel=wheel_spec)
 519     possible_positions = []
 520     for p in string.ascii_lowercase:
 521         pe.set_position(p)
 522         plaintext = pe.decipher(message)
 523         if plaintext[crib_position:crib_position+len(crib)] == crib:
 524             possible_positions += [p]
 525     return possible_positions
 526
 527
 528 def plot_frequency_histogram(freqs, sort_key=None):
 529     x = range(len(freqs.keys()))
 530     y = [freqs[l] for l in sorted(freqs.keys(), key=sort_key)]
 531     f = plt.figure()
 532     ax = f.add_axes([0.1, 0.1, 0.9, 0.9])
 533     ax.bar(x, y, align='center')
 534     ax.set_xticks(x)
 535     ax.set_xticklabels(sorted(freqs.keys(), key=sort_key))
 536     f.show()
 537
 538
 539 if __name__ == "__main__":
 540     import doctest
 541     doctest.testmod()