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