cipherbreak.py

   1 import string
   2 import collections
   3 import norms
   4 import logging
   5 import random
   6 from itertools import zip_longest, cycle, permutations, starmap
   7 from segment import segment
   8 from multiprocessing import Pool
   9 from math import log10
  10
  11 import matplotlib.pyplot as plt
  12
  13 logger = logging.getLogger(__name__)
  14 logger.addHandler(logging.FileHandler('cipher.log'))
  15 logger.setLevel(logging.WARNING)
  16 #logger.setLevel(logging.INFO)
  17 #logger.setLevel(logging.DEBUG)
  18
  19 from cipher import *
  20 from language_models import *
  21
  22 # To time a run:
  23 #
  24 # import timeit
  25 # c5a = open('2012/5a.ciphertext', 'r').read()
  26 # timeit.timeit('keyword_break(c5a)', setup='gc.enable() ; from __main__ import c5a ; from cipher import keyword_break', number=1)
  27 # 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)
  28
  29 transpositions = collections.defaultdict(list)
  30 for word in keywords:
  31     transpositions[transpositions_of(word)] += [word]
  32
  33 def frequencies(text):
  34     """Count the number of occurrences of each character in text
  35
  36     >>> sorted(frequencies('abcdefabc').items())
  37     [('a', 2), ('b', 2), ('c', 2), ('d', 1), ('e', 1), ('f', 1)]
  38     >>> sorted(frequencies('the quick brown fox jumped over the lazy ' \
  39          'dog').items()) # doctest: +NORMALIZE_WHITESPACE
  40     [(' ', 8), ('a', 1), ('b', 1), ('c', 1), ('d', 2), ('e', 4), ('f', 1),
  41      ('g', 1), ('h', 2), ('i', 1), ('j', 1), ('k', 1), ('l', 1), ('m', 1),
  42      ('n', 1), ('o', 4), ('p', 1), ('q', 1), ('r', 2), ('t', 2), ('u', 2),
  43      ('v', 1), ('w', 1), ('x', 1), ('y', 1), ('z', 1)]
  44     >>> sorted(frequencies('The Quick BROWN fox jumped! over... the ' \
  45          '(9lazy) DOG').items()) # doctest: +NORMALIZE_WHITESPACE
  46     [(' ', 8), ('!', 1), ('(', 1), (')', 1), ('.', 3), ('9', 1), ('B', 1),
  47      ('D', 1), ('G', 1), ('N', 1), ('O', 2), ('Q', 1), ('R', 1), ('T', 1),
  48      ('W', 1), ('a', 1), ('c', 1), ('d', 1), ('e', 4), ('f', 1), ('h', 2),
  49      ('i', 1), ('j', 1), ('k', 1), ('l', 1), ('m', 1), ('o', 2), ('p', 1),
  50      ('r', 1), ('t', 1), ('u', 2), ('v', 1), ('x', 1), ('y', 1), ('z', 1)]
  51          >>> sorted(frequencies(sanitise('The Quick BROWN fox jumped! over... '\
  52          'the (9lazy) DOG')).items()) # doctest: +NORMALIZE_WHITESPACE
  53     [('a', 1), ('b', 1), ('c', 1), ('d', 2), ('e', 4), ('f', 1), ('g', 1),
  54      ('h', 2), ('i', 1), ('j', 1), ('k', 1), ('l', 1), ('m', 1), ('n', 1),
  55      ('o', 4), ('p', 1), ('q', 1), ('r', 2), ('t', 2), ('u', 2), ('v', 1),
  56      ('w', 1), ('x', 1), ('y', 1), ('z', 1)]
  57     >>> frequencies('abcdefabcdef')['x']
  58     0
  59     """
  60     return collections.Counter(c for c in text)
  61
  62
  63 def caesar_break(message, fitness=Pletters):
  64     """Breaks a Caesar cipher using frequency analysis
  65
  66     >>> caesar_break('ibxcsyorsaqcheyklxivoexlevmrimwxsfiqevvmihrsasrxliwyrh' \
  67           'ecjsppsamrkwleppfmergefifvmhixscsymjcsyqeoixlm') # doctest: +ELLIPSIS
  68     (4, -130.849989015...)
  69     >>> caesar_break('wxwmaxdgheetgwuxztgptedbgznitgwwhpguxyhkxbmhvvtlbhgtee' \
  70           'raxlmhiixweblmxgxwmhmaxybkbgztgwztsxwbgmxgmert') # doctest: +ELLIPSIS
  71     (19, -128.82410410...)
  72     >>> caesar_break('yltbbqnqnzvguvaxurorgenafsbezqvagbnornfgsbevpnaabjurer' \
  73           'svaquvzyvxrnznazlybequrvfohgriraabjtbaruraprur') # doctest: +ELLIPSIS
  74     (13, -126.25403935...)
  75     """
  76     sanitised_message = sanitise(message)
  77     best_shift = 0
  78     best_fit = float('-inf')
  79     for shift in range(26):
  80         plaintext = caesar_decipher(sanitised_message, shift)
  81         fit = fitness(plaintext)
  82         logger.debug('Caesar break attempt using key {0} gives fit of {1} '
  83             'and decrypt starting: {2}'.format(shift, fit,
  84                 plaintext[:50]))
  85         if fit > best_fit:
  86             best_fit = fit
  87             best_shift = shift
  88     logger.info('Caesar break best fit: key {0} gives fit of {1} and '
  89                 'decrypt starting: {2}'.format(best_shift, best_fit,
  90                     caesar_decipher(sanitised_message, best_shift)[:50]))
  91     return best_shift, best_fit
  92
  93 def affine_break(message, fitness=Pletters):
  94     """Breaks an affine cipher using frequency analysis
  95
  96     >>> affine_break('lmyfu bkuusd dyfaxw claol psfaom jfasd snsfg jfaoe ls ' \
  97           'omytd jlaxe mh jm bfmibj umis hfsul axubafkjamx. ls kffkxwsd jls ' \
  98           'ofgbjmwfkiu olfmxmtmwaokttg jlsx ls kffkxwsd jlsi zg tsxwjl. jlsx ' \
  99           'ls umfjsd jlsi zg hfsqysxog. ls dmmdtsd mx jls bats mh bkbsf. ls ' \
 100           'bfmctsd kfmyxd jls lyj, mztanamyu xmc jm clm cku tmmeaxw kj lai ' \
 101           'kxd clm ckuxj.') # doctest: +ELLIPSIS
 102     ((15, 22, True), -340.601181913...)
 103     """
 104     sanitised_message = sanitise(message)
 105     best_multiplier = 0
 106     best_adder = 0
 107     best_one_based = True
 108     best_fit = float("-inf")
 109     for one_based in [True, False]:
 110         for multiplier in [x for x in range(1, 26, 2) if x != 13]:
 111             for adder in range(26):
 112                 plaintext = affine_decipher(sanitised_message,
 113                                             multiplier, adder, one_based)
 114                 fit = fitness(plaintext)
 115                 logger.debug('Affine break attempt using key {0}x+{1} ({2}) '
 116                              'gives fit of {3} and decrypt starting: {4}'.
 117                              format(multiplier, adder, one_based, fit,
 118                                     plaintext[:50]))
 119                 if fit > best_fit:
 120                     best_fit = fit
 121                     best_multiplier = multiplier
 122                     best_adder = adder
 123                     best_one_based = one_based
 124     logger.info('Affine break best fit with key {0}x+{1} ({2}) gives fit of '
 125                 '{3} and decrypt starting: {4}'.format(
 126                     best_multiplier, best_adder, best_one_based, best_fit,
 127                     affine_decipher(sanitised_message, best_multiplier,
 128                         best_adder, best_one_based)[:50]))
 129     return (best_multiplier, best_adder, best_one_based), best_fit
 130
 131 def keyword_break(message, wordlist=keywords, fitness=Pletters):
 132     """Breaks a keyword substitution cipher using a dictionary and
 133     frequency analysis
 134
 135     >>> keyword_break(keyword_encipher('this is a test message for the ' \
 136           'keyword decipherment', 'elephant', Keyword_wrap_alphabet.from_last), \
 137           wordlist=['cat', 'elephant', 'kangaroo']) # doctest: +ELLIPSIS
 138     (('elephant', <Keyword_wrap_alphabet.from_last: 2>), -52.834575011...)
 139     """
 140     best_keyword = ''
 141     best_wrap_alphabet = True
 142     best_fit = float("-inf")
 143     for wrap_alphabet in Keyword_wrap_alphabet:
 144         for keyword in wordlist:
 145             plaintext = keyword_decipher(message, keyword, wrap_alphabet)
 146             fit = fitness(plaintext)
 147             logger.debug('Keyword break attempt using key {0} (wrap={1}) '
 148                          'gives fit of {2} and decrypt starting: {3}'.format(
 149                              keyword, wrap_alphabet, fit,
 150                              sanitise(plaintext)[:50]))
 151             if fit > best_fit:
 152                 best_fit = fit
 153                 best_keyword = keyword
 154                 best_wrap_alphabet = wrap_alphabet
 155     logger.info('Keyword break best fit with key {0} (wrap={1}) gives fit of '
 156                 '{2} and decrypt starting: {3}'.format(best_keyword,
 157                     best_wrap_alphabet, best_fit, sanitise(
 158                         keyword_decipher(message, best_keyword,
 159                                          best_wrap_alphabet))[:50]))
 160     return (best_keyword, best_wrap_alphabet), best_fit
 161
 162 def keyword_break_mp(message, wordlist=keywords, fitness=Pletters, chunksize=500):
 163     """Breaks a keyword substitution cipher using a dictionary and
 164     frequency analysis
 165
 166     >>> keyword_break_mp(keyword_encipher('this is a test message for the ' \
 167           'keyword decipherment', 'elephant', Keyword_wrap_alphabet.from_last), \
 168           wordlist=['cat', 'elephant', 'kangaroo']) # doctest: +ELLIPSIS
 169     (('elephant', <Keyword_wrap_alphabet.from_last: 2>), -52.834575011...)
 170     """
 171     with Pool() as pool:
 172         helper_args = [(message, word, wrap, fitness)
 173                        for word in wordlist
 174                        for wrap in Keyword_wrap_alphabet]
 175         # Gotcha: the helper function here needs to be defined at the top level
 176         #   (limitation of Pool.starmap)
 177         breaks = pool.starmap(keyword_break_worker, helper_args, chunksize)
 178         return max(breaks, key=lambda k: k[1])
 179
 180 def keyword_break_worker(message, keyword, wrap_alphabet, fitness):
 181     plaintext = keyword_decipher(message, keyword, wrap_alphabet)
 182     fit = fitness(plaintext)
 183     logger.debug('Keyword break attempt using key {0} (wrap={1}) gives fit of '
 184                  '{2} and decrypt starting: {3}'.format(keyword,
 185                      wrap_alphabet, fit, sanitise(plaintext)[:50]))
 186     return (keyword, wrap_alphabet), fit
 187
 188 def monoalphabetic_break_hillclimbing(message, max_iterations = 10000000,
 189         fitness=Pletters):
 190     ciphertext = unaccent(message).lower()
 191     alphabet = list(string.ascii_lowercase)
 192     random.shuffle(alphabet)
 193     alphabet = ''.join(alphabet)
 194     return monoalphabetic_break_hillclimbing_worker(ciphertext, alphabet,
 195         max_iterations, fitness)
 196
 197 def monoalphabetic_break_hillclimbing_mp(message, workers=10,
 198         max_iterations = 10000000, fitness=Pletters, chunksize=1):
 199     worker_args = []
 200     ciphertext = unaccent(message).lower()
 201     for i in range(workers):
 202         alphabet = list(string.ascii_lowercase)
 203         random.shuffle(alphabet)
 204         alphabet = ''.join(alphabet)
 205         worker_args.append((ciphertext, alphabet, max_iterations, fitness))
 206     with Pool() as pool:
 207         breaks = pool.starmap(monoalphabetic_break_hillclimbing_worker,
 208             worker_args, chunksize)
 209     return max(breaks, key=lambda k: k[1])
 210
 211 def monoalphabetic_break_hillclimbing_worker(message, alphabet,
 212         max_iterations, fitness):
 213     def swap(letters, i, j):
 214         if i > j:
 215             i, j = j, i
 216         if i == j:
 217             return letters
 218         else:
 219             return letters[:i] + letters[j] + letters[i+1:j] +
 220                     letters[i] + letters[j+1:]
 221     best_alphabet = alphabet
 222     best_fitness = float('-inf')
 223     for i in range(max_iterations):
 224         alphabet = swap(alphabet, random.randrange(26), random.randrange(26))
 225         cipher_translation = ''.maketrans(string.ascii_lowercase, alphabet)
 226         plaintext = message.translate(cipher_translation)
 227         if fitness(plaintext) > best_fitness:
 228             best_fitness = fitness(plaintext)
 229             best_alphabet = alphabet
 230             print(i, best_alphabet, best_fitness, plaintext)
 231     return best_alphabet, best_fitness
 232
 233
 234 def column_transposition_break_mp(message, translist=transpositions,
 235                      fitness=Pbigrams, chunksize=500):
 236     """Breaks a column transposition cipher using a dictionary and
 237     n-gram frequency analysis
 238
 239     >>> column_transposition_break_mp(column_transposition_encipher(sanitise( \
 240             "It is a truth universally acknowledged, that a single man in \
 241              possession of a good fortune, must be in want of a wife. However \
 242              little known the feelings or views of such a man may be on his \
 243              first entering a neighbourhood, this truth is so well fixed in the \
 244              minds of the surrounding families, that he is considered the \
 245              rightful property of some one or other of their daughters."), \
 246         'encipher'), \
 247         translist={(2, 0, 5, 3, 1, 4, 6): ['encipher'], \
 248                    (5, 0, 6, 1, 3, 4, 2): ['fourteen'], \
 249                    (6, 1, 0, 4, 5, 3, 2): ['keyword']}) # doctest: +ELLIPSIS
 250     (((2, 0, 5, 3, 1, 4, 6), False, False), -709.4646722...)
 251     >>> column_transposition_break_mp(column_transposition_encipher(sanitise( \
 252             "It is a truth universally acknowledged, that a single man in \
 253              possession of a good fortune, must be in want of a wife. However \
 254              little known the feelings or views of such a man may be on his \
 255              first entering a neighbourhood, this truth is so well fixed in the \
 256              minds of the surrounding families, that he is considered the \
 257              rightful property of some one or other of their daughters."), \
 258         'encipher'), \
 259         translist={(2, 0, 5, 3, 1, 4, 6): ['encipher'], \
 260                    (5, 0, 6, 1, 3, 4, 2): ['fourteen'], \
 261                    (6, 1, 0, 4, 5, 3, 2): ['keyword']}, \
 262         fitness=Ptrigrams) # doctest: +ELLIPSIS
 263     (((2, 0, 5, 3, 1, 4, 6), False, False), -997.0129085...)
 264     """
 265     with Pool() as pool:
 266         helper_args = [(message, trans, fillcolumnwise, emptycolumnwise,
 267                           fitness)
 268                        for trans in translist.keys()
 269                        for fillcolumnwise in [True, False]
 270                        for emptycolumnwise in [True, False]]
 271         # Gotcha: the helper function here needs to be defined at the top level
 272         #   (limitation of Pool.starmap)
 273         breaks = pool.starmap(column_transposition_break_worker,
 274           helper_args, chunksize)
 275         return max(breaks, key=lambda k: k[1])
 276 column_transposition_break = column_transposition_break_mp
 277
 278 def column_transposition_break_worker(message, transposition,
 279         fillcolumnwise, emptycolumnwise, fitness):
 280     plaintext = column_transposition_decipher(message, transposition,
 281         fillcolumnwise=fillcolumnwise, emptycolumnwise=emptycolumnwise)
 282     fit = fitness(sanitise(plaintext))
 283     logger.debug('Column transposition break attempt using key {0} '
 284                          'gives fit of {1} and decrypt starting: {2}'.format(
 285                              transposition, fit,
 286                              sanitise(plaintext)[:50]))
 287     return (transposition, fillcolumnwise, emptycolumnwise), fit
 288
 289
 290 def scytale_break_mp(message, max_key_length=20,
 291                      fitness=Pbigrams, chunksize=500):
 292     """Breaks a scytale cipher using a range of lengths and
 293     n-gram frequency analysis
 294
 295     >>> scytale_break_mp(scytale_encipher(sanitise( \
 296             "It is a truth universally acknowledged, that a single man in \
 297              possession of a good fortune, must be in want of a wife. However \
 298              little known the feelings or views of such a man may be on his \
 299              first entering a neighbourhood, this truth is so well fixed in the \
 300              minds of the surrounding families, that he is considered the \
 301              rightful property of some one or other of their daughters."), \
 302         5)) # doctest: +ELLIPSIS
 303     (5, -709.4646722...)
 304     >>> scytale_break_mp(scytale_encipher(sanitise( \
 305             "It is a truth universally acknowledged, that a single man in \
 306              possession of a good fortune, must be in want of a wife. However \
 307              little known the feelings or views of such a man may be on his \
 308              first entering a neighbourhood, this truth is so well fixed in the \
 309              minds of the surrounding families, that he is considered the \
 310              rightful property of some one or other of their daughters."), \
 311         5), \
 312         fitness=Ptrigrams) # doctest: +ELLIPSIS
 313     (5, -997.0129085...)
 314     """
 315     with Pool() as pool:
 316         helper_args = [(message, trans, False, True, fitness)
 317             for trans in
 318                 [[col for col in range(math.ceil(len(message)/rows))]
 319                     for rows in range(1,max_key_length+1)]]
 320         # Gotcha: the helper function here needs to be defined at the top level
 321         #   (limitation of Pool.starmap)
 322         breaks = pool.starmap(column_transposition_break_worker,
 323           helper_args, chunksize)
 324         best = max(breaks, key=lambda k: k[1])
 325         return math.trunc(len(message) / len(best[0][0])), best[1]
 326 scytale_break = scytale_break_mp
 327
 328
 329 def vigenere_keyword_break_mp(message, wordlist=keywords, fitness=Pletters,
 330                      chunksize=500):
 331     """Breaks a vigenere cipher using a dictionary and
 332     frequency analysis
 333
 334     >>> vigenere_keyword_break_mp(vigenere_encipher(sanitise('this is a test ' \
 335              'message for the vigenere decipherment'), 'cat'), \
 336              wordlist=['cat', 'elephant', 'kangaroo']) # doctest: +ELLIPSIS
 337     ('cat', -52.947271216...)
 338     """
 339     with Pool() as pool:
 340         helper_args = [(message, word, fitness)
 341                        for word in wordlist]
 342         # Gotcha: the helper function here needs to be defined at the top level
 343         #   (limitation of Pool.starmap)
 344         breaks = pool.starmap(vigenere_keyword_break_worker, helper_args, chunksize)
 345         return max(breaks, key=lambda k: k[1])
 346 vigenere_keyword_break = vigenere_keyword_break_mp
 347
 348 def vigenere_keyword_break_worker(message, keyword, fitness):
 349     plaintext = vigenere_decipher(message, keyword)
 350     fit = fitness(plaintext)
 351     logger.debug('Vigenere keyword break attempt using key {0} gives fit of '
 352                  '{1} and decrypt starting: {2}'.format(keyword,
 353                      fit, sanitise(plaintext)[:50]))
 354     return keyword, fit
 355
 356
 357
 358 def vigenere_frequency_break(message, max_key_length=20, fitness=Pletters):
 359     """Breaks a Vigenere cipher with frequency analysis
 360
 361     >>> vigenere_frequency_break(vigenere_encipher(sanitise("It is time to " \
 362             "run. She is ready and so am I. I stole Daniel's pocketbook this " \
 363             "afternoon when he left his jacket hanging on the easel in the " \
 364             "attic. I jump every time I hear a footstep on the stairs, " \
 365             "certain that the theft has been discovered and that I will " \
 366             "be caught. The SS officer visits less often now that he is " \
 367             "sure"), 'florence')) # doctest: +ELLIPSIS
 368     ('florence', -307.5473096791...)
 369     """
 370     def worker(message, key_length, fitness):
 371         splits = every_nth(sanitised_message, key_length)
 372         key = ''.join([chr(caesar_break(s)[0] + ord('a')) for s in splits])
 373         plaintext = vigenere_decipher(message, key)
 374         fit = fitness(plaintext)
 375         return key, fit
 376     sanitised_message = sanitise(message)
 377     results = starmap(worker, [(sanitised_message, i, fitness)
 378         for i in range(1, max_key_length+1)])
 379     return max(results, key=lambda k: k[1])
 380
 381
 382 def beaufort_frequency_break(message, max_key_length=20, fitness=Pletters):
 383     """Breaks a Beaufort cipher with frequency analysis
 384
 385     >>> beaufort_frequency_break(beaufort_encipher(sanitise("It is time to " \
 386             "run. She is ready and so am I. I stole Daniel's pocketbook this " \
 387             "afternoon when he left his jacket hanging on the easel in the " \
 388             "attic. I jump every time I hear a footstep on the stairs, " \
 389             "certain that the theft has been discovered and that I will " \
 390             "be caught. The SS officer visits less often now " \
 391             "that he is sure"), 'florence')) # doctest: +ELLIPSIS
 392     ('florence', -307.5473096791...)
 393     """
 394     def worker(message, key_length, fitness):
 395         splits = every_nth(sanitised_message, key_length)
 396         key = ''.join([chr(-caesar_break(s)[0] % 26 + ord('a')) for s in splits])
 397         plaintext = beaufort_decipher(message, key)
 398         fit = fitness(plaintext)
 399         return key, fit
 400     sanitised_message = sanitise(message)
 401     results = starmap(worker, [(sanitised_message, i, fitness)
 402         for i in range(1, max_key_length+1)])
 403     return max(results, key=lambda k: k[1])
 404
 405
 406 def pocket_enigma_break_by_crib(message, wheel_spec, crib, crib_position):
 407     """Break a pocket enigma using a crib (some plaintext that's expected to
 408     be in a certain position). Returns a list of possible starting wheel
 409     positions that could produce the crib.
 410
 411     >>> pocket_enigma_break_by_crib('kzpjlzmoga', 1, 'h', 0)
 412     ['a', 'f', 'q']
 413     >>> pocket_enigma_break_by_crib('kzpjlzmoga', 1, 'he', 0)
 414     ['a']
 415     >>> pocket_enigma_break_by_crib('kzpjlzmoga', 1, 'll', 2)
 416     ['a']
 417     >>> pocket_enigma_break_by_crib('kzpjlzmoga', 1, 'l', 2)
 418     ['a']
 419     >>> pocket_enigma_break_by_crib('kzpjlzmoga', 1, 'l', 3)
 420     ['a', 'j', 'n']
 421     >>> pocket_enigma_break_by_crib('aaaaa', 1, 'l', 3)
 422     []
 423     """
 424     pe = PocketEnigma(wheel=wheel_spec)
 425     possible_positions = []
 426     for p in string.ascii_lowercase:
 427         pe.set_position(p)
 428         plaintext = pe.decipher(message)
 429         if plaintext[crib_position:crib_position+len(crib)] == crib:
 430             possible_positions += [p]
 431     return possible_positions
 432
 433
 434 def plot_frequency_histogram(freqs, sort_key=None):
 435     x = range(len(freqs.keys()))
 436     y = [freqs[l] for l in sorted(freqs.keys(), key=sort_key)]
 437     f = plt.figure()
 438     ax = f.add_axes([0.1, 0.1, 0.9, 0.9])
 439     ax.bar(x, y, align='center')
 440     ax.set_xticks(x)
 441     ax.set_xticklabels(sorted(freqs.keys(), key=sort_key))
 442     f.show()
 443
 444
 445 if __name__ == "__main__":
 446     import doctest
 447     doctest.testmod()