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 column_transposition_break_mp(message, translist=transpositions,
 248                                   fitness=Pbigrams, chunksize=500):
 249     """Breaks a column transposition cipher using a dictionary and
 250     n-gram frequency analysis
 251
 252     >>> column_transposition_break_mp(column_transposition_encipher(sanitise( \
 253             "It is a truth universally acknowledged, that a single man in \
 254              possession of a good fortune, must be in want of a wife. However \
 255              little known the feelings or views of such a man may be on his \
 256              first entering a neighbourhood, this truth is so well fixed in \
 257              the minds of the surrounding families, that he is considered the \
 258              rightful property of some one or other of their daughters."), \
 259         'encipher'), \
 260         translist={(2, 0, 5, 3, 1, 4, 6): ['encipher'], \
 261                    (5, 0, 6, 1, 3, 4, 2): ['fourteen'], \
 262                    (6, 1, 0, 4, 5, 3, 2): ['keyword']}) # doctest: +ELLIPSIS
 263     (((2, 0, 5, 3, 1, 4, 6), False, False), -709.4646722...)
 264     >>> column_transposition_break_mp(column_transposition_encipher(sanitise( \
 265             "It is a truth universally acknowledged, that a single man in \
 266              possession of a good fortune, must be in want of a wife. However \
 267              little known the feelings or views of such a man may be on his \
 268              first entering a neighbourhood, this truth is so well fixed in \
 269              the minds of the surrounding families, that he is considered the \
 270              rightful property of some one or other of their daughters."), \
 271         'encipher'), \
 272         translist={(2, 0, 5, 3, 1, 4, 6): ['encipher'], \
 273                    (5, 0, 6, 1, 3, 4, 2): ['fourteen'], \
 274                    (6, 1, 0, 4, 5, 3, 2): ['keyword']}, \
 275         fitness=Ptrigrams) # doctest: +ELLIPSIS
 276     (((2, 0, 5, 3, 1, 4, 6), False, False), -997.0129085...)
 277     """
 278     with Pool() as pool:
 279         helper_args = [(message, trans, fillcolumnwise, emptycolumnwise,
 280                         fitness)
 281                        for trans in translist.keys()
 282                        for fillcolumnwise in [True, False]
 283                        for emptycolumnwise in [True, False]]
 284         # Gotcha: the helper function here needs to be defined at the top level
 285         #   (limitation of Pool.starmap)
 286         breaks = pool.starmap(column_transposition_break_worker,
 287                               helper_args, chunksize)
 288         return max(breaks, key=lambda k: k[1])
 289 column_transposition_break = column_transposition_break_mp
 290
 291 def column_transposition_break_worker(message, transposition,
 292         fillcolumnwise, emptycolumnwise, fitness):
 293     plaintext = column_transposition_decipher(message, transposition,
 294         fillcolumnwise=fillcolumnwise, emptycolumnwise=emptycolumnwise)
 295     fit = fitness(sanitise(plaintext))
 296     logger.debug('Column transposition break attempt using key {0} '
 297                          'gives fit of {1} and decrypt starting: {2}'.format(
 298                              transposition, fit,
 299                              sanitise(plaintext)[:50]))
 300     return (transposition, fillcolumnwise, emptycolumnwise), fit
 301
 302
 303 def scytale_break_mp(message, max_key_length=20,
 304                      fitness=Pbigrams, chunksize=500):
 305     """Breaks a scytale cipher using a range of lengths and
 306     n-gram frequency analysis
 307
 308     >>> scytale_break_mp(scytale_encipher(sanitise( \
 309             "It is a truth universally acknowledged, that a single man in \
 310              possession of a good fortune, must be in want of a wife. However \
 311              little known the feelings or views of such a man may be on his \
 312              first entering a neighbourhood, this truth is so well fixed in \
 313              the minds of the surrounding families, that he is considered the \
 314              rightful property of some one or other of their daughters."), \
 315         5)) # doctest: +ELLIPSIS
 316     (5, -709.4646722...)
 317     >>> scytale_break_mp(scytale_encipher(sanitise( \
 318             "It is a truth universally acknowledged, that a single man in \
 319              possession of a good fortune, must be in want of a wife. However \
 320              little known the feelings or views of such a man may be on his \
 321              first entering a neighbourhood, this truth is so well fixed in \
 322              the minds of the surrounding families, that he is considered the \
 323              rightful property of some one or other of their daughters."), \
 324         5), \
 325         fitness=Ptrigrams) # doctest: +ELLIPSIS
 326     (5, -997.0129085...)
 327     """
 328     with Pool() as pool:
 329         helper_args = [(message, trans, False, True, fitness)
 330             for trans in
 331                 [[col for col in range(math.ceil(len(message)/rows))]
 332                     for rows in range(1,max_key_length+1)]]
 333         # Gotcha: the helper function here needs to be defined at the top level
 334         #   (limitation of Pool.starmap)
 335         breaks = pool.starmap(column_transposition_break_worker,
 336                               helper_args, chunksize)
 337         best = max(breaks, key=lambda k: k[1])
 338         return math.trunc(len(message) / len(best[0][0])), best[1]
 339 scytale_break = scytale_break_mp
 340
 341
 342 def vigenere_keyword_break_mp(message, wordlist=keywords, fitness=Pletters,
 343                               chunksize=500):
 344     """Breaks a vigenere cipher using a dictionary and frequency analysis.
 345
 346     >>> vigenere_keyword_break_mp(vigenere_encipher(sanitise('this is a test ' \
 347              'message for the vigenere decipherment'), 'cat'), \
 348              wordlist=['cat', 'elephant', 'kangaroo']) # doctest: +ELLIPSIS
 349     ('cat', -52.947271216...)
 350     """
 351     with Pool() as pool:
 352         helper_args = [(message, word, fitness)
 353                        for word in wordlist]
 354         # Gotcha: the helper function here needs to be defined at the top level
 355         #   (limitation of Pool.starmap)
 356         breaks = pool.starmap(vigenere_keyword_break_worker, helper_args,
 357                               chunksize)
 358         return max(breaks, key=lambda k: k[1])
 359 vigenere_keyword_break = vigenere_keyword_break_mp
 360
 361 def vigenere_keyword_break_worker(message, keyword, fitness):
 362     plaintext = vigenere_decipher(message, keyword)
 363     fit = fitness(plaintext)
 364     logger.debug('Vigenere keyword break attempt using key {0} gives fit of '
 365                  '{1} and decrypt starting: {2}'.format(keyword,
 366                      fit, sanitise(plaintext)[:50]))
 367     return keyword, fit
 368
 369
 370
 371 def vigenere_frequency_break(message, max_key_length=20, fitness=Pletters):
 372     """Breaks a Vigenere cipher with frequency analysis
 373
 374     >>> vigenere_frequency_break(vigenere_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 that he is " \
 380             "sure"), 'florence')) # doctest: +ELLIPSIS
 381     ('florence', -307.5473096791...)
 382     """
 383     def worker(message, key_length, fitness):
 384         splits = every_nth(sanitised_message, key_length)
 385         key = ''.join([chr(caesar_break(s)[0] + ord('a')) for s in splits])
 386         plaintext = vigenere_decipher(message, key)
 387         fit = fitness(plaintext)
 388         return key, fit
 389     sanitised_message = sanitise(message)
 390     results = starmap(worker, [(sanitised_message, i, fitness)
 391                                for i in range(1, max_key_length+1)])
 392     return max(results, key=lambda k: k[1])
 393
 394
 395 def beaufort_frequency_break(message, max_key_length=20, fitness=Pletters):
 396     """Breaks a Beaufort cipher with frequency analysis
 397
 398     >>> beaufort_frequency_break(beaufort_encipher(sanitise("It is time to " \
 399             "run. She is ready and so am I. I stole Daniel's pocketbook this " \
 400             "afternoon when he left his jacket hanging on the easel in the " \
 401             "attic. I jump every time I hear a footstep on the stairs, " \
 402             "certain that the theft has been discovered and that I will " \
 403             "be caught. The SS officer visits less often now " \
 404             "that he is sure"), 'florence')) # doctest: +ELLIPSIS
 405     ('florence', -307.5473096791...)
 406     """
 407     def worker(message, key_length, fitness):
 408         splits = every_nth(sanitised_message, key_length)
 409         key = ''.join([chr(-caesar_break(s)[0] % 26 + ord('a'))
 410                        for s in splits])
 411         plaintext = beaufort_decipher(message, key)
 412         fit = fitness(plaintext)
 413         return key, fit
 414     sanitised_message = sanitise(message)
 415     results = starmap(worker, [(sanitised_message, i, fitness)
 416                                for i in range(1, max_key_length+1)])
 417     return max(results, key=lambda k: k[1])
 418
 419
 420 def pocket_enigma_break_by_crib(message, wheel_spec, crib, crib_position):
 421     """Break a pocket enigma using a crib (some plaintext that's expected to
 422     be in a certain position). Returns a list of possible starting wheel
 423     positions that could produce the crib.
 424
 425     >>> pocket_enigma_break_by_crib('kzpjlzmoga', 1, 'h', 0)
 426     ['a', 'f', 'q']
 427     >>> pocket_enigma_break_by_crib('kzpjlzmoga', 1, 'he', 0)
 428     ['a']
 429     >>> pocket_enigma_break_by_crib('kzpjlzmoga', 1, 'll', 2)
 430     ['a']
 431     >>> pocket_enigma_break_by_crib('kzpjlzmoga', 1, 'l', 2)
 432     ['a']
 433     >>> pocket_enigma_break_by_crib('kzpjlzmoga', 1, 'l', 3)
 434     ['a', 'j', 'n']
 435     >>> pocket_enigma_break_by_crib('aaaaa', 1, 'l', 3)
 436     []
 437     """
 438     pe = PocketEnigma(wheel=wheel_spec)
 439     possible_positions = []
 440     for p in string.ascii_lowercase:
 441         pe.set_position(p)
 442         plaintext = pe.decipher(message)
 443         if plaintext[crib_position:crib_position+len(crib)] == crib:
 444             possible_positions += [p]
 445     return possible_positions
 446
 447
 448 def plot_frequency_histogram(freqs, sort_key=None):
 449     x = range(len(freqs.keys()))
 450     y = [freqs[l] for l in sorted(freqs.keys(), key=sort_key)]
 451     f = plt.figure()
 452     ax = f.add_axes([0.1, 0.1, 0.9, 0.9])
 453     ax.bar(x, y, align='center')
 454     ax.set_xticks(x)
 455     ax.set_xticklabels(sorted(freqs.keys(), key=sort_key))
 456     f.show()
 457
 458
 459 if __name__ == "__main__":
 460     import doctest
 461     doctest.testmod()