cipherbreak.py

   1 import string
   2 import collections
   3 import norms
   4 import logging
   5 from itertools import zip_longest, cycle, permutations, starmap
   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', Keyword_wrap_alphabet.from_last), \
 135           wordlist=['cat', 'elephant', 'kangaroo']) # doctest: +ELLIPSIS
 136     (('elephant', <Keyword_wrap_alphabet.from_last: 2>), -52.834575011...)
 137     """
 138     best_keyword = ''
 139     best_wrap_alphabet = True
 140     best_fit = float("-inf")
 141     for wrap_alphabet in Keyword_wrap_alphabet:
 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', Keyword_wrap_alphabet.from_last), \
 166           wordlist=['cat', 'elephant', 'kangaroo']) # doctest: +ELLIPSIS
 167     (('elephant', <Keyword_wrap_alphabet.from_last: 2>), -52.834575011...)
 168     """
 169     with Pool() as pool:
 170         helper_args = [(message, word, wrap, fitness)
 171                        for word in wordlist
 172                        for wrap in Keyword_wrap_alphabet]
 173         # Gotcha: the helper function here needs to be defined at the top level
 174         #   (limitation of Pool.starmap)
 175         breaks = pool.starmap(keyword_break_worker, helper_args, chunksize)
 176         return max(breaks, key=lambda k: k[1])
 177
 178 def keyword_break_worker(message, keyword, wrap_alphabet, fitness):
 179     plaintext = keyword_decipher(message, keyword, wrap_alphabet)
 180     fit = fitness(plaintext)
 181     logger.debug('Keyword break attempt using key {0} (wrap={1}) gives fit of '
 182                  '{2} and decrypt starting: {3}'.format(keyword,
 183                      wrap_alphabet, fit, sanitise(plaintext)[:50]))
 184     return (keyword, wrap_alphabet), fit
 185
 186
 187 def column_transposition_break_mp(message, translist=transpositions,
 188                      fitness=Pbigrams, chunksize=500):
 189     """Breaks a column transposition cipher using a dictionary and
 190     n-gram frequency analysis
 191
 192     >>> column_transposition_break_mp(column_transposition_encipher(sanitise( \
 193             "It is a truth universally acknowledged, that a single man in \
 194              possession of a good fortune, must be in want of a wife. However \
 195              little known the feelings or views of such a man may be on his \
 196              first entering a neighbourhood, this truth is so well fixed in the \
 197              minds of the surrounding families, that he is considered the \
 198              rightful property of some one or other of their daughters."), \
 199         'encipher'), \
 200         translist={(2, 0, 5, 3, 1, 4, 6): ['encipher'], \
 201                    (5, 0, 6, 1, 3, 4, 2): ['fourteen'], \
 202                    (6, 1, 0, 4, 5, 3, 2): ['keyword']}) # doctest: +ELLIPSIS
 203     (((2, 0, 5, 3, 1, 4, 6), False, False), -709.4646722...)
 204     >>> column_transposition_break_mp(column_transposition_encipher(sanitise( \
 205             "It is a truth universally acknowledged, that a single man in \
 206              possession of a good fortune, must be in want of a wife. However \
 207              little known the feelings or views of such a man may be on his \
 208              first entering a neighbourhood, this truth is so well fixed in the \
 209              minds of the surrounding families, that he is considered the \
 210              rightful property of some one or other of their daughters."), \
 211         'encipher'), \
 212         translist={(2, 0, 5, 3, 1, 4, 6): ['encipher'], \
 213                    (5, 0, 6, 1, 3, 4, 2): ['fourteen'], \
 214                    (6, 1, 0, 4, 5, 3, 2): ['keyword']}, \
 215         fitness=Ptrigrams) # doctest: +ELLIPSIS
 216     (((2, 0, 5, 3, 1, 4, 6), False, False), -997.0129085...)
 217     """
 218     with Pool() as pool:
 219         helper_args = [(message, trans, fillcolumnwise, emptycolumnwise,
 220                           fitness)
 221                        for trans in translist.keys()
 222                        for fillcolumnwise in [True, False]
 223                        for emptycolumnwise in [True, False]]
 224         # Gotcha: the helper function here needs to be defined at the top level
 225         #   (limitation of Pool.starmap)
 226         breaks = pool.starmap(column_transposition_break_worker,
 227           helper_args, chunksize)
 228         return max(breaks, key=lambda k: k[1])
 229 column_transposition_break = column_transposition_break_mp
 230
 231 def column_transposition_break_worker(message, transposition,
 232         fillcolumnwise, emptycolumnwise, fitness):
 233     plaintext = column_transposition_decipher(message, transposition,
 234         fillcolumnwise=fillcolumnwise, emptycolumnwise=emptycolumnwise)
 235     fit = fitness(sanitise(plaintext))
 236     logger.debug('Column transposition break attempt using key {0} '
 237                          'gives fit of {1} and decrypt starting: {2}'.format(
 238                              transposition, fit,
 239                              sanitise(plaintext)[:50]))
 240     return (transposition, fillcolumnwise, emptycolumnwise), fit
 241
 242
 243 def scytale_break_mp(message, max_key_length=20,
 244                      fitness=Pbigrams, chunksize=500):
 245     """Breaks a scytale cipher using a range of lengths and
 246     n-gram frequency analysis
 247
 248     >>> scytale_break_mp(scytale_encipher(sanitise( \
 249             "It is a truth universally acknowledged, that a single man in \
 250              possession of a good fortune, must be in want of a wife. However \
 251              little known the feelings or views of such a man may be on his \
 252              first entering a neighbourhood, this truth is so well fixed in the \
 253              minds of the surrounding families, that he is considered the \
 254              rightful property of some one or other of their daughters."), \
 255         5)) # doctest: +ELLIPSIS
 256     (5, -709.4646722...)
 257     >>> scytale_break_mp(scytale_encipher(sanitise( \
 258             "It is a truth universally acknowledged, that a single man in \
 259              possession of a good fortune, must be in want of a wife. However \
 260              little known the feelings or views of such a man may be on his \
 261              first entering a neighbourhood, this truth is so well fixed in the \
 262              minds of the surrounding families, that he is considered the \
 263              rightful property of some one or other of their daughters."), \
 264         5), \
 265         fitness=Ptrigrams) # doctest: +ELLIPSIS
 266     (5, -997.0129085...)
 267     """
 268     with Pool() as pool:
 269         helper_args = [(message, trans, False, True, fitness)
 270             for trans in
 271                 [[col for col in range(math.ceil(len(message)/rows))]
 272                     for rows in range(1,max_key_length+1)]]
 273         # Gotcha: the helper function here needs to be defined at the top level
 274         #   (limitation of Pool.starmap)
 275         breaks = pool.starmap(column_transposition_break_worker,
 276           helper_args, chunksize)
 277         best = max(breaks, key=lambda k: k[1])
 278         return math.trunc(len(message) / len(best[0][0])), best[1]
 279 scytale_break = scytale_break_mp
 280
 281
 282 def vigenere_keyword_break_mp(message, wordlist=keywords, fitness=Pletters,
 283                      chunksize=500):
 284     """Breaks a vigenere cipher using a dictionary and
 285     frequency analysis
 286
 287     >>> vigenere_keyword_break_mp(vigenere_encipher(sanitise('this is a test ' \
 288              'message for the vigenere decipherment'), 'cat'), \
 289              wordlist=['cat', 'elephant', 'kangaroo']) # doctest: +ELLIPSIS
 290     ('cat', -52.947271216...)
 291     """
 292     with Pool() as pool:
 293         helper_args = [(message, word, fitness)
 294                        for word in wordlist]
 295         # Gotcha: the helper function here needs to be defined at the top level
 296         #   (limitation of Pool.starmap)
 297         breaks = pool.starmap(vigenere_keyword_break_worker, helper_args, chunksize)
 298         return max(breaks, key=lambda k: k[1])
 299 vigenere_keyword_break = vigenere_keyword_break_mp
 300
 301 def vigenere_keyword_break_worker(message, keyword, fitness):
 302     plaintext = vigenere_decipher(message, keyword)
 303     fit = fitness(plaintext)
 304     logger.debug('Vigenere keyword break attempt using key {0} gives fit of '
 305                  '{1} and decrypt starting: {2}'.format(keyword,
 306                      fit, sanitise(plaintext)[:50]))
 307     return keyword, fit
 308
 309
 310
 311 def vigenere_frequency_break(message, max_key_length=20, fitness=Pletters):
 312     """Breaks a Vigenere cipher with frequency analysis
 313
 314     >>> vigenere_frequency_break(vigenere_encipher(sanitise("It is time to " \
 315             "run. She is ready and so am I. I stole Daniel's pocketbook this " \
 316             "afternoon when he left his jacket hanging on the easel in the " \
 317             "attic. I jump every time I hear a footstep on the stairs, " \
 318             "certain that the theft has been discovered and that I will " \
 319             "be caught. The SS officer visits less often now that he is " \
 320             "sure"), 'florence')) # doctest: +ELLIPSIS
 321     ('florence', -307.5473096791...)
 322     """
 323     def worker(message, key_length, fitness):
 324         splits = every_nth(sanitised_message, key_length)
 325         key = ''.join([chr(caesar_break(s)[0] + ord('a')) for s in splits])
 326         plaintext = vigenere_decipher(message, key)
 327         fit = fitness(plaintext)
 328         return key, fit
 329     sanitised_message = sanitise(message)
 330     results = starmap(worker, [(sanitised_message, i, fitness)
 331         for i in range(1, max_key_length+1)])
 332     return max(results, key=lambda k: k[1])
 333
 334
 335 def beaufort_frequency_break(message, max_key_length=20, fitness=Pletters):
 336     """Breaks a Beaufort cipher with frequency analysis
 337
 338     >>> beaufort_frequency_break(beaufort_encipher(sanitise("It is time to " \
 339             "run. She is ready and so am I. I stole Daniel's pocketbook this " \
 340             "afternoon when he left his jacket hanging on the easel in the " \
 341             "attic. I jump every time I hear a footstep on the stairs, " \
 342             "certain that the theft has been discovered and that I will " \
 343             "be caught. The SS officer visits less often now " \
 344             "that he is sure"), 'florence')) # doctest: +ELLIPSIS
 345     ('florence', -307.5473096791...)
 346     """
 347     def worker(message, key_length, fitness):
 348         splits = every_nth(sanitised_message, key_length)
 349         key = ''.join([chr(-caesar_break(s)[0] % 26 + ord('a')) for s in splits])
 350         plaintext = beaufort_decipher(message, key)
 351         fit = fitness(plaintext)
 352         return key, fit
 353     sanitised_message = sanitise(message)
 354     results = starmap(worker, [(sanitised_message, i, fitness)
 355         for i in range(1, max_key_length+1)])
 356     return max(results, key=lambda k: k[1])
 357
 358
 359 def plot_frequency_histogram(freqs, sort_key=None):
 360     x = range(len(freqs.keys()))
 361     y = [freqs[l] for l in sorted(freqs.keys(), key=sort_key)]
 362     f = plt.figure()
 363     ax = f.add_axes([0.1, 0.1, 0.9, 0.9])
 364     ax.bar(x, y, align='center')
 365     ax.set_xticks(x)
 366     ax.set_xticklabels(sorted(freqs.keys(), key=sort_key))
 367     f.show()
 368
 369
 370 if __name__ == "__main__":
 371     import doctest
 372     doctest.testmod()
 373