cipherbreak.py

   1 import string
   2 import collections
   3 import norms
   4 import logging
   5 from itertools import zip_longest, cycle, permutations
   6 from segment import segment
   7 from multiprocessing import Pool
   8 from math import log10
   9
  10 import matplotlib.pyplot as plt
  11
  12 logger = logging.getLogger(__name__)
  13 logger.addHandler(logging.FileHandler('cipher.log'))
  14 logger.setLevel(logging.WARNING)
  15 #logger.setLevel(logging.INFO)
  16 #logger.setLevel(logging.DEBUG)
  17
  18 from cipher import *
  19 from language_models import *
  20
  21 # To time a run:
  22 #
  23 # import timeit
  24 # c5a = open('2012/5a.ciphertext', 'r').read()
  25 # timeit.timeit('keyword_break(c5a)', setup='gc.enable() ; from __main__ import c5a ; from cipher import keyword_break', number=1)
  26 # 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)
  27
  28 transpositions = collections.defaultdict(list)
  29 for word in keywords:
  30     transpositions[transpositions_of(word)] += [word]
  31
  32 def frequencies(text):
  33     """Count the number of occurrences of each character in text
  34
  35     >>> sorted(frequencies('abcdefabc').items())
  36     [('a', 2), ('b', 2), ('c', 2), ('d', 1), ('e', 1), ('f', 1)]
  37     >>> sorted(frequencies('the quick brown fox jumped over the lazy ' \
  38          'dog').items()) # doctest: +NORMALIZE_WHITESPACE
  39     [(' ', 8), ('a', 1), ('b', 1), ('c', 1), ('d', 2), ('e', 4), ('f', 1),
  40      ('g', 1), ('h', 2), ('i', 1), ('j', 1), ('k', 1), ('l', 1), ('m', 1),
  41      ('n', 1), ('o', 4), ('p', 1), ('q', 1), ('r', 2), ('t', 2), ('u', 2),
  42      ('v', 1), ('w', 1), ('x', 1), ('y', 1), ('z', 1)]
  43     >>> sorted(frequencies('The Quick BROWN fox jumped! over... the ' \
  44          '(9lazy) DOG').items()) # doctest: +NORMALIZE_WHITESPACE
  45     [(' ', 8), ('!', 1), ('(', 1), (')', 1), ('.', 3), ('9', 1), ('B', 1),
  46      ('D', 1), ('G', 1), ('N', 1), ('O', 2), ('Q', 1), ('R', 1), ('T', 1),
  47      ('W', 1), ('a', 1), ('c', 1), ('d', 1), ('e', 4), ('f', 1), ('h', 2),
  48      ('i', 1), ('j', 1), ('k', 1), ('l', 1), ('m', 1), ('o', 2), ('p', 1),
  49      ('r', 1), ('t', 1), ('u', 2), ('v', 1), ('x', 1), ('y', 1), ('z', 1)]
  50     >>> sorted(frequencies(sanitise('The Quick BROWN fox jumped! over... ' \
  51          'the (9lazy) DOG')).items()) # doctest: +NORMALIZE_WHITESPACE
  52     [('a', 1), ('b', 1), ('c', 1), ('d', 2), ('e', 4), ('f', 1), ('g', 1),
  53      ('h', 2), ('i', 1), ('j', 1), ('k', 1), ('l', 1), ('m', 1), ('n', 1),
  54      ('o', 4), ('p', 1), ('q', 1), ('r', 2), ('t', 2), ('u', 2), ('v', 1),
  55      ('w', 1), ('x', 1), ('y', 1), ('z', 1)]
  56     >>> frequencies('abcdefabcdef')['x']
  57     0
  58     """
  59     return collections.Counter(c for c in text)
  60
  61
  62 def caesar_break(message, fitness=Pletters):
  63     """Breaks a Caesar cipher using frequency analysis
  64
  65     >>> caesar_break('ibxcsyorsaqcheyklxivoexlevmrimwxsfiqevvmihrsasrxliwyrh' \
  66           'ecjsppsamrkwleppfmergefifvmhixscsymjcsyqeoixlm') # doctest: +ELLIPSIS
  67     (4, -130.849989015...)
  68     >>> caesar_break('wxwmaxdgheetgwuxztgptedbgznitgwwhpguxyhkxbmhvvtlbhgtee' \
  69           'raxlmhiixweblmxgxwmhmaxybkbgztgwztsxwbgmxgmert') # doctest: +ELLIPSIS
  70     (19, -128.82410410...)
  71     >>> caesar_break('yltbbqnqnzvguvaxurorgenafsbezqvagbnornfgsbevpnaabjurer' \
  72           'svaquvzyvxrnznazlybequrvfohgriraabjtbaruraprur') # doctest: +ELLIPSIS
  73     (13, -126.25403935...)
  74     """
  75     sanitised_message = sanitise(message)
  76     best_shift = 0
  77     best_fit = float('-inf')
  78     for shift in range(26):
  79         plaintext = caesar_decipher(sanitised_message, shift)
  80         fit = fitness(plaintext)
  81         logger.debug('Caesar break attempt using key {0} gives fit of {1} '
  82                       'and decrypt starting: {2}'.format(shift, fit, plaintext[:50]))
  83         if fit > best_fit:
  84             best_fit = fit
  85             best_shift = shift
  86     logger.info('Caesar break best fit: key {0} gives fit of {1} and '
  87                 'decrypt starting: {2}'.format(best_shift, best_fit,
  88                     caesar_decipher(sanitised_message, best_shift)[:50]))
  89     return best_shift, best_fit
  90
  91 def affine_break(message, fitness=Pletters):
  92     """Breaks an affine cipher using frequency analysis
  93
  94     >>> affine_break('lmyfu bkuusd dyfaxw claol psfaom jfasd snsfg jfaoe ls ' \
  95           'omytd jlaxe mh jm bfmibj umis hfsul axubafkjamx. ls kffkxwsd jls ' \
  96           'ofgbjmwfkiu olfmxmtmwaokttg jlsx ls kffkxwsd jlsi zg tsxwjl. jlsx ' \
  97           'ls umfjsd jlsi zg hfsqysxog. ls dmmdtsd mx jls bats mh bkbsf. ls ' \
  98           'bfmctsd kfmyxd jls lyj, mztanamyu xmc jm clm cku tmmeaxw kj lai ' \
  99           'kxd clm ckuxj.') # doctest: +ELLIPSIS
 100     ((15, 22, True), -340.601181913...)
 101     """
 102     sanitised_message = sanitise(message)
 103     best_multiplier = 0
 104     best_adder = 0
 105     best_one_based = True
 106     best_fit = float("-inf")
 107     for one_based in [True, False]:
 108         for multiplier in [x for x in range(1, 26, 2) if x != 13]:
 109             for adder in range(26):
 110                 plaintext = affine_decipher(sanitised_message,
 111                                             multiplier, adder, one_based)
 112                 fit = fitness(plaintext)
 113                 logger.debug('Affine break attempt using key {0}x+{1} ({2}) '
 114                              'gives fit of {3} and decrypt starting: {4}'.
 115                              format(multiplier, adder, one_based, fit,
 116                                     plaintext[:50]))
 117                 if fit > best_fit:
 118                     best_fit = fit
 119                     best_multiplier = multiplier
 120                     best_adder = adder
 121                     best_one_based = one_based
 122     logger.info('Affine break best fit with key {0}x+{1} ({2}) gives fit of {3} '
 123                 'and decrypt starting: {4}'.format(
 124                     best_multiplier, best_adder, best_one_based, best_fit,
 125                     affine_decipher(sanitised_message, best_multiplier,
 126                         best_adder, best_one_based)[:50]))
 127     return (best_multiplier, best_adder, best_one_based), best_fit
 128
 129 def keyword_break(message, wordlist=keywords, fitness=Pletters):
 130     """Breaks a keyword substitution cipher using a dictionary and
 131     frequency analysis
 132
 133     >>> keyword_break(keyword_encipher('this is a test message for the ' \
 134           'keyword decipherment', 'elephant', 1), \
 135           wordlist=['cat', 'elephant', 'kangaroo']) # doctest: +ELLIPSIS
 136     (('elephant', 1), -52.834575011...)
 137     """
 138     best_keyword = ''
 139     best_wrap_alphabet = True
 140     best_fit = float("-inf")
 141     for wrap_alphabet in range(3):
 142         for keyword in wordlist:
 143             plaintext = keyword_decipher(message, keyword, wrap_alphabet)
 144             fit = fitness(plaintext)
 145             logger.debug('Keyword break attempt using key {0} (wrap={1}) '
 146                          'gives fit of {2} and decrypt starting: {3}'.format(
 147                              keyword, wrap_alphabet, fit,
 148                              sanitise(plaintext)[:50]))
 149             if fit > best_fit:
 150                 best_fit = fit
 151                 best_keyword = keyword
 152                 best_wrap_alphabet = wrap_alphabet
 153     logger.info('Keyword break best fit with key {0} (wrap={1}) gives fit of '
 154                 '{2} and decrypt starting: {3}'.format(best_keyword,
 155                     best_wrap_alphabet, best_fit, sanitise(
 156                         keyword_decipher(message, best_keyword,
 157                                          best_wrap_alphabet))[:50]))
 158     return (best_keyword, best_wrap_alphabet), best_fit
 159
 160 def keyword_break_mp(message, wordlist=keywords, fitness=Pletters, chunksize=500):
 161     """Breaks a keyword substitution cipher using a dictionary and
 162     frequency analysis
 163
 164     >>> keyword_break_mp(keyword_encipher('this is a test message for the ' \
 165           'keyword decipherment', 'elephant', 1), \
 166           wordlist=['cat', 'elephant', 'kangaroo']) # doctest: +ELLIPSIS
 167     (('elephant', 1), -52.834575011...)
 168     """
 169     with Pool() as pool:
 170         helper_args = [(message, word, wrap, fitness)
 171                        for word in wordlist for wrap in range(3)]
 172         # Gotcha: the helper function here needs to be defined at the top level
 173         #   (limitation of Pool.starmap)
 174         breaks = pool.starmap(keyword_break_worker, helper_args, chunksize)
 175         return max(breaks, key=lambda k: k[1])
 176
 177 def keyword_break_worker(message, keyword, wrap_alphabet, fitness):
 178     plaintext = keyword_decipher(message, keyword, wrap_alphabet)
 179     fit = fitness(plaintext)
 180     logger.debug('Keyword break attempt using key {0} (wrap={1}) gives fit of '
 181                  '{2} and decrypt starting: {3}'.format(keyword,
 182                      wrap_alphabet, fit, sanitise(plaintext)[:50]))
 183     return (keyword, wrap_alphabet), fit
 184
 185 def scytale_break(message, fitness=Pbigrams):
 186     """Breaks a Scytale cipher
 187
 188     >>> scytale_break('tfeulchtrtteehwahsdehneoifeayfsondmwpltmaoalhikotoere' \
 189            'dcweatehiplwxsnhooacgorrcrcraotohsgullasenylrendaianeplscdriioto' \
 190            'aek') # doctest: +ELLIPSIS
 191     (6, -281.276219108...)
 192     """
 193     best_key = 0
 194     best_fit = float("-inf")
 195     for key in range(1, 20):
 196         if len(message) % key == 0:
 197             plaintext = scytale_decipher(message, key)
 198             fit = fitness(sanitise(plaintext))
 199             logger.debug('Scytale break attempt using key {0} gives fit of '
 200                          '{1} and decrypt starting: {2}'.format(key,
 201                              fit, sanitise(plaintext)[:50]))
 202             if fit > best_fit:
 203                 best_fit = fit
 204                 best_key = key
 205     logger.info('Scytale break best fit with key {0} gives fit of {1} and '
 206                 'decrypt starting: {2}'.format(best_key, best_fit,
 207                     sanitise(scytale_decipher(message, best_key))[:50]))
 208     return best_key, best_fit
 209
 210
 211 def column_transposition_break_mp(message, translist=transpositions,
 212                      fitness=Pbigrams, chunksize=500):
 213     """Breaks a column transposition cipher using a dictionary and
 214     n-gram frequency analysis
 215     """
 216     # >>> column_transposition_break_mp(column_transposition_encipher(sanitise( \
 217     #         "It is a truth universally acknowledged, that a single man in \
 218     #          possession of a good fortune, must be in want of a wife. However \
 219     #          little known the feelings or views of such a man may be on his \
 220     #          first entering a neighbourhood, this truth is so well fixed in the \
 221     #          minds of the surrounding families, that he is considered the \
 222     #          rightful property of some one or other of their daughters."), \
 223     #     'encipher'), \
 224     #     translist={(2, 0, 5, 3, 1, 4, 6): ['encipher'], \
 225     #                (5, 0, 6, 1, 3, 4, 2): ['fourteen'], \
 226     #                (6, 1, 0, 4, 5, 3, 2): ['keyword']}) # doctest: +ELLIPSIS
 227     # (((2, 0, 5, 3, 1, 4, 6), False), 0.0628106372...)
 228     # >>> column_transposition_break_mp(column_transposition_encipher(sanitise( \
 229     #         "It is a truth universally acknowledged, that a single man in \
 230     #          possession of a good fortune, must be in want of a wife. However \
 231     #          little known the feelings or views of such a man may be on his \
 232     #          first entering a neighbourhood, this truth is so well fixed in the \
 233     #          minds of the surrounding families, that he is considered the \
 234     #          rightful property of some one or other of their daughters."), \
 235     #     'encipher'), \
 236     #     translist={(2, 0, 5, 3, 1, 4, 6): ['encipher'], \
 237     #                (5, 0, 6, 1, 3, 4, 2): ['fourteen'], \
 238     #                (6, 1, 0, 4, 5, 3, 2): ['keyword']}, \
 239     #     target_counts=normalised_english_trigram_counts) # doctest: +ELLIPSIS
 240     # (((2, 0, 5, 3, 1, 4, 6), False), 0.0592259560...)
 241     # """
 242     with Pool() as pool:
 243         helper_args = [(message, trans, columnwise, fitness)
 244                        for trans in translist.keys()
 245                        for columnwise in [True, False]]
 246         # Gotcha: the helper function here needs to be defined at the top level
 247         #   (limitation of Pool.starmap)
 248         breaks = pool.starmap(column_transposition_break_worker,
 249           helper_args, chunksize)
 250         return max(breaks, key=lambda k: k[1])
 251 column_transposition_break = column_transposition_break_mp
 252
 253 def column_transposition_break_worker(message, transposition, columnwise,
 254                                         fitness):
 255     plaintext = column_transposition_decipher(message, transposition, columnwise=columnwise)
 256     fit = fitness(sanitise(plaintext))
 257     logger.debug('Column transposition break attempt using key {0} '
 258                          'gives fit of {1} and decrypt starting: {2}'.format(
 259                              transposition, fit,
 260                              sanitise(plaintext)[:50]))
 261     return (transposition, columnwise), fit
 262
 263
 264 def transposition_break_exhaustive(message, fitness=Pbigrams):
 265     best_transposition = ''
 266     best_pw = float('-inf')
 267     for keylength in range(1, 21):
 268         if len(message) % keylength == 0:
 269             for transposition in permutations(range(keylength)):
 270                 for columnwise in [True, False]:
 271                     plaintext = column_transposition_decipher(message,
 272                         transposition, columnwise=columnwise)
 273                     fit=fitness(plaintext)
 274                     logger.debug('Column transposition break attempt using key {0} {1} '
 275                          'gives fit of {2} and decrypt starting: {3}'.format(
 276                              transposition, columnwise, pw,
 277                              sanitise(plaintext)[:50]))
 278                     if fit > best_fit:
 279                         best_transposition = transposition
 280                         best_columnwise = columnwise
 281                         best_fit = fit
 282     return (best_transposition, best_columnwise), best_pw
 283
 284
 285 def vigenere_keyword_break(message, wordlist=keywords, fitness=Pletters):
 286     """Breaks a vigenere cipher using a dictionary and
 287     frequency analysis
 288
 289     >>> vigenere_keyword_break(vigenere_encipher(sanitise('this is a test ' \
 290              'message for the vigenere decipherment'), 'cat'), \
 291              wordlist=['cat', 'elephant', 'kangaroo']) # doctest: +ELLIPSIS
 292     ('cat', -52.947271216...)
 293     """
 294     best_keyword = ''
 295     best_fit = float("-inf")
 296     for keyword in wordlist:
 297         plaintext = vigenere_decipher(message, keyword)
 298         fit = fitness(plaintext)
 299         logger.debug('Vigenere break attempt using key {0} '
 300                          'gives fit of {1} and decrypt starting: {2}'.format(
 301                              keyword, fit,
 302                              sanitise(plaintext)[:50]))
 303         if fit > best_fit:
 304             best_fit = fit
 305             best_keyword = keyword
 306     logger.info('Vigenere break best fit with key {0} gives fit '
 307                 'of {1} and decrypt starting: {2}'.format(best_keyword,
 308                     best_fit, sanitise(
 309                         vigenere_decipher(message, best_keyword))[:50]))
 310     return best_keyword, best_fit
 311
 312 def vigenere_keyword_break_mp(message, wordlist=keywords, fitness=Pletters,
 313                      chunksize=500):
 314     """Breaks a vigenere cipher using a dictionary and
 315     frequency analysis
 316
 317     >>> vigenere_keyword_break_mp(vigenere_encipher(sanitise('this is a test ' \
 318              'message for the vigenere decipherment'), 'cat'), \
 319              wordlist=['cat', 'elephant', 'kangaroo']) # doctest: +ELLIPSIS
 320     ('cat', -52.947271216...)
 321     """
 322     with Pool() as pool:
 323         helper_args = [(message, word, fitness)
 324                        for word in wordlist]
 325         # Gotcha: the helper function here needs to be defined at the top level
 326         #   (limitation of Pool.starmap)
 327         breaks = pool.starmap(vigenere_keyword_break_worker, helper_args, chunksize)
 328         return max(breaks, key=lambda k: k[1])
 329
 330 def vigenere_keyword_break_worker(message, keyword, fitness):
 331     plaintext = vigenere_decipher(message, keyword)
 332     fit = fitness(plaintext)
 333     logger.debug('Vigenere keyword break attempt using key {0} gives fit of '
 334                  '{1} and decrypt starting: {2}'.format(keyword,
 335                      fit, sanitise(plaintext)[:50]))
 336     return keyword, fit
 337
 338
 339
 340 def vigenere_frequency_break(message, fitness=Pletters):
 341     """Breaks a Vigenere cipher with frequency analysis
 342
 343     >>> vigenere_frequency_break(vigenere_encipher(sanitise("It is time to " \
 344             "run. She is ready and so am I. I stole Daniel's pocketbook this " \
 345             "afternoon when he left his jacket hanging on the easel in the " \
 346             "attic. I jump every time I hear a footstep on the stairs, " \
 347             "certain that the theft has been discovered and that I will " \
 348             "be caught. The SS officer visits less often now that he is " \
 349             "sure"), 'florence')) # doctest: +ELLIPSIS
 350     ('florence', -307.5473096791...)
 351     """
 352     best_fit = float("-inf")
 353     best_key = ''
 354     sanitised_message = sanitise(message)
 355     for trial_length in range(1, 20):
 356         splits = every_nth(sanitised_message, trial_length)
 357         key = ''.join([chr(caesar_break(s)[0] + ord('a')) for s in splits])
 358         plaintext = vigenere_decipher(sanitised_message, key)
 359         fit = fitness(plaintext)
 360         logger.debug('Vigenere key length of {0} ({1}) gives fit of {2}'.
 361                      format(trial_length, key, fit))
 362         if fit > best_fit:
 363             best_fit = fit
 364             best_key = key
 365     logger.info('Vigenere break best fit with key {0} gives fit '
 366                 'of {1} and decrypt starting: {2}'.format(best_key,
 367                     best_fit, sanitise(
 368                         vigenere_decipher(message, best_key))[:50]))
 369     return best_key, best_fit
 370
 371 def beaufort_frequency_break(message, fitness=Pletters):
 372     """Breaks a Beaufort cipher with frequency analysis
 373
 374     >>> beaufort_frequency_break(beaufort_encipher(sanitise("It is time to " \
 375             "run. She is ready and so am I. I stole Daniel's pocketbook this " \
 376             "afternoon when he left his jacket hanging on the easel in the " \
 377             "attic. I jump every time I hear a footstep on the stairs, " \
 378             "certain that the theft has been discovered and that I will " \
 379             "be caught. The SS officer visits less often now " \
 380             "that he is sure"), 'florence')) # doctest: +ELLIPSIS
 381     ('florence', -307.5473096791...)
 382     """
 383     best_fit = float("-inf")
 384     best_key = ''
 385     sanitised_message = sanitise(message)
 386     for trial_length in range(1, 20):
 387         splits = every_nth(sanitised_message, trial_length)
 388         key = ''.join([chr(-caesar_break(s)[0] % 26 + ord('a')) for s in splits])
 389         plaintext = beaufort_decipher(sanitised_message, key)
 390         fit = fitness(plaintext)
 391         logger.debug('Beaufort key length of {0} ({1}) gives fit of {2}'.
 392                      format(trial_length, key, fit))
 393         if fit > best_fit:
 394             best_fit = fit
 395             best_key = key
 396     logger.info('Beaufort break best fit with key {0} gives fit '
 397                 'of {1} and decrypt starting: {2}'.format(best_key,
 398                     best_fit, sanitise(
 399                         beaufort_decipher(message, best_key))[:50]))
 400     return best_key, best_fit
 401
 402
 403
 404 def plot_frequency_histogram(freqs, sort_key=None):
 405     x = range(len(freqs.keys()))
 406     y = [freqs[l] for l in sorted(freqs.keys(), key=sort_key)]
 407     f = plt.figure()
 408     ax = f.add_axes([0.1, 0.1, 0.9, 0.9])
 409     ax.bar(x, y, align='center')
 410     ax.set_xticks(x)
 411     ax.set_xticklabels(sorted(freqs.keys(), key=sort_key))
 412     f.show()
 413
 414
 415 if __name__ == "__main__":
 416     import doctest
 417     doctest.testmod()
 418