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 # logging.basicConfig(filename="cipher.log", level=logging.INFO)
  17 # logger = logging.getLogger(__name__)
  18
  19 logger = logging.getLogger('cipherbreak')
  20 logger.setLevel(logging.WARNING)
  21 # logger.setLevel(logging.INFO)
  22 # logger.setLevel(logging.DEBUG)
  23
  24 # create the logging file handler
  25 fh = logging.FileHandler("cipher.log")
  26 formatter = logging.Formatter('%(asctime)s - %(name)s - %(levelname)s - %(message)s')
  27 fh.setFormatter(formatter)
  28
  29 # add handler to logger object
  30 logger.addHandler(fh)
  31
  32
  33 from cipher import *
  34 from language_models import *
  35
  36 # To time a run:
  37 #
  38 # import timeit
  39 # c5a = open('2012/5a.ciphertext', 'r').read()
  40 # timeit.timeit('keyword_break(c5a)', setup='gc.enable() ; from __main__ import c5a ; from cipher import keyword_break', number=1)
  41 # 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)
  42
  43
  44 def index_of_coincidence(text):
  45     stext = sanitise(text)
  46     counts = collections.Counter(stext)
  47     denom = len(stext) * (len(text) - 1) / 26
  48     return (
  49         sum(max(counts[l] * counts[l] - 1, 0) for l in string.ascii_lowercase)
  50         /
  51         denom
  52     )
  53
  54
  55 transpositions = collections.defaultdict(list)
  56 for word in keywords:
  57     transpositions[transpositions_of(word)] += [word]
  58
  59 def frequencies(text):
  60     """Count the number of occurrences of each character in text
  61
  62     >>> sorted(frequencies('abcdefabc').items())
  63     [('a', 2), ('b', 2), ('c', 2), ('d', 1), ('e', 1), ('f', 1)]
  64     >>> sorted(frequencies('the quick brown fox jumped over the lazy ' \
  65          'dog').items()) # doctest: +NORMALIZE_WHITESPACE
  66     [(' ', 8), ('a', 1), ('b', 1), ('c', 1), ('d', 2), ('e', 4), ('f', 1),
  67      ('g', 1), ('h', 2), ('i', 1), ('j', 1), ('k', 1), ('l', 1), ('m', 1),
  68      ('n', 1), ('o', 4), ('p', 1), ('q', 1), ('r', 2), ('t', 2), ('u', 2),
  69      ('v', 1), ('w', 1), ('x', 1), ('y', 1), ('z', 1)]
  70     >>> sorted(frequencies('The Quick BROWN fox jumped! over... the ' \
  71          '(9lazy) DOG').items()) # doctest: +NORMALIZE_WHITESPACE
  72     [(' ', 8), ('!', 1), ('(', 1), (')', 1), ('.', 3), ('9', 1), ('B', 1),
  73      ('D', 1), ('G', 1), ('N', 1), ('O', 2), ('Q', 1), ('R', 1), ('T', 1),
  74      ('W', 1), ('a', 1), ('c', 1), ('d', 1), ('e', 4), ('f', 1), ('h', 2),
  75      ('i', 1), ('j', 1), ('k', 1), ('l', 1), ('m', 1), ('o', 2), ('p', 1),
  76      ('r', 1), ('t', 1), ('u', 2), ('v', 1), ('x', 1), ('y', 1), ('z', 1)]
  77     >>> sorted(frequencies(sanitise('The Quick BROWN fox jumped! over... '\
  78          'the (9lazy) DOG')).items()) # doctest: +NORMALIZE_WHITESPACE
  79     [('a', 1), ('b', 1), ('c', 1), ('d', 2), ('e', 4), ('f', 1), ('g', 1),
  80      ('h', 2), ('i', 1), ('j', 1), ('k', 1), ('l', 1), ('m', 1), ('n', 1),
  81      ('o', 4), ('p', 1), ('q', 1), ('r', 2), ('t', 2), ('u', 2), ('v', 1),
  82      ('w', 1), ('x', 1), ('y', 1), ('z', 1)]
  83     >>> frequencies('abcdefabcdef')['x']
  84     0
  85     """
  86     return collections.Counter(c for c in text)
  87
  88
  89 def caesar_break(message, fitness=Pletters):
  90     """Breaks a Caesar cipher using frequency analysis
  91
  92     >>> caesar_break('ibxcsyorsaqcheyklxivoexlevmrimwxsfiqevvmihrsasrxliwyrh' \
  93           'ecjsppsamrkwleppfmergefifvmhixscsymjcsyqeoixlm') # doctest: +ELLIPSIS
  94     (4, -130.849989015...)
  95     >>> caesar_break('wxwmaxdgheetgwuxztgptedbgznitgwwhpguxyhkxbmhvvtlbhgtee' \
  96           'raxlmhiixweblmxgxwmhmaxybkbgztgwztsxwbgmxgmert') # doctest: +ELLIPSIS
  97     (19, -128.82410410...)
  98     >>> caesar_break('yltbbqnqnzvguvaxurorgenafsbezqvagbnornfgsbevpnaabjurer' \
  99           'svaquvzyvxrnznazlybequrvfohgriraabjtbaruraprur') # doctest: +ELLIPSIS
 100     (13, -126.25403935...)
 101     """
 102     sanitised_message = sanitise(message)
 103     best_shift = 0
 104     best_fit = float('-inf')
 105     for shift in range(26):
 106         plaintext = caesar_decipher(sanitised_message, shift)
 107         fit = fitness(plaintext)
 108         logger.debug('Caesar break attempt using key {0} gives fit of {1} '
 109                      'and decrypt starting: {2}'.format(shift, fit,
 110                                                         plaintext[:50]))
 111         if fit > best_fit:
 112             best_fit = fit
 113             best_shift = shift
 114     logger.info('Caesar break best fit: key {0} gives fit of {1} and '
 115                 'decrypt starting: {2}'.format(best_shift, best_fit,
 116                     caesar_decipher(sanitised_message, best_shift)[:50]))
 117     return best_shift, best_fit
 118
 119 def affine_break(message, fitness=Pletters):
 120     """Breaks an affine cipher using frequency analysis
 121
 122     >>> affine_break('lmyfu bkuusd dyfaxw claol psfaom jfasd snsfg jfaoe ls ' \
 123           'omytd jlaxe mh jm bfmibj umis hfsul axubafkjamx. ls kffkxwsd jls ' \
 124           'ofgbjmwfkiu olfmxmtmwaokttg jlsx ls kffkxwsd jlsi zg tsxwjl. jlsx ' \
 125           'ls umfjsd jlsi zg hfsqysxog. ls dmmdtsd mx jls bats mh bkbsf. ls ' \
 126           'bfmctsd kfmyxd jls lyj, mztanamyu xmc jm clm cku tmmeaxw kj lai ' \
 127           'kxd clm ckuxj.') # doctest: +ELLIPSIS
 128     ((15, 22, True), -340.601181913...)
 129     """
 130     sanitised_message = sanitise(message)
 131     best_multiplier = 0
 132     best_adder = 0
 133     best_one_based = True
 134     best_fit = float("-inf")
 135     for one_based in [True, False]:
 136         for multiplier in [x for x in range(1, 26, 2) if x != 13]:
 137             for adder in range(26):
 138                 plaintext = affine_decipher(sanitised_message,
 139                                             multiplier, adder, one_based)
 140                 fit = fitness(plaintext)
 141                 logger.debug('Affine break attempt using key {0}x+{1} ({2}) '
 142                              'gives fit of {3} and decrypt starting: {4}'.
 143                              format(multiplier, adder, one_based, fit,
 144                                     plaintext[:50]))
 145                 if fit > best_fit:
 146                     best_fit = fit
 147                     best_multiplier = multiplier
 148                     best_adder = adder
 149                     best_one_based = one_based
 150     logger.info('Affine break best fit with key {0}x+{1} ({2}) gives fit of '
 151                 '{3} and decrypt starting: {4}'.format(
 152                     best_multiplier, best_adder, best_one_based, best_fit,
 153                     affine_decipher(sanitised_message, best_multiplier,
 154                                     best_adder, best_one_based)[:50]))
 155     return (best_multiplier, best_adder, best_one_based), best_fit
 156
 157 def keyword_break(message, wordlist=keywords, fitness=Pletters):
 158     """Breaks a keyword substitution cipher using a dictionary and
 159     frequency analysis.
 160
 161     >>> keyword_break(keyword_encipher('this is a test message for the ' \
 162           'keyword decipherment', 'elephant', KeywordWrapAlphabet.from_last), \
 163           wordlist=['cat', 'elephant', 'kangaroo']) # doctest: +ELLIPSIS
 164     (('elephant', <KeywordWrapAlphabet.from_last: 2>), -52.834575011...)
 165     """
 166     best_keyword = ''
 167     best_wrap_alphabet = True
 168     best_fit = float("-inf")
 169     for wrap_alphabet in KeywordWrapAlphabet:
 170         for keyword in wordlist:
 171             plaintext = keyword_decipher(message, keyword, wrap_alphabet)
 172             fit = fitness(plaintext)
 173             logger.debug('Keyword break attempt using key {0} (wrap={1}) '
 174                          'gives fit of {2} and decrypt starting: {3}'.format(
 175                              keyword, wrap_alphabet, fit,
 176                              sanitise(plaintext)[:50]))
 177             if fit > best_fit:
 178                 best_fit = fit
 179                 best_keyword = keyword
 180                 best_wrap_alphabet = wrap_alphabet
 181     logger.info('Keyword break best fit with key {0} (wrap={1}) gives fit of '
 182                 '{2} and decrypt starting: {3}'.format(best_keyword,
 183                     best_wrap_alphabet, best_fit, sanitise(
 184                         keyword_decipher(message, best_keyword,
 185                                          best_wrap_alphabet))[:50]))
 186     return (best_keyword, best_wrap_alphabet), best_fit
 187
 188 def keyword_break_mp(message, wordlist=keywords, fitness=Pletters,
 189                      number_of_solutions=1, chunksize=500):
 190     """Breaks a keyword substitution cipher using a dictionary and
 191     frequency analysis
 192
 193     >>> keyword_break_mp(keyword_encipher('this is a test message for the ' \
 194           'keyword decipherment', 'elephant', KeywordWrapAlphabet.from_last), \
 195           wordlist=['cat', 'elephant', 'kangaroo']) # doctest: +ELLIPSIS
 196     (('elephant', <KeywordWrapAlphabet.from_last: 2>), -52.834575011...)
 197     >>> keyword_break_mp(keyword_encipher('this is a test message for the ' \
 198           'keyword decipherment', 'elephant', KeywordWrapAlphabet.from_last), \
 199           wordlist=['cat', 'elephant', 'kangaroo'], \
 200           number_of_solutions=2) # doctest: +ELLIPSIS, +NORMALIZE_WHITESPACE
 201     [(('elephant', <KeywordWrapAlphabet.from_last: 2>), -52.834575011...),
 202     (('elephant', <KeywordWrapAlphabet.from_largest: 3>), -52.834575011...)]
 203     """
 204     with Pool() as pool:
 205         helper_args = [(message, word, wrap, fitness)
 206                        for word in wordlist
 207                        for wrap in KeywordWrapAlphabet]
 208         # Gotcha: the helper function here needs to be defined at the top level
 209         #   (limitation of Pool.starmap)
 210         breaks = pool.starmap(keyword_break_worker, helper_args, chunksize)
 211         if number_of_solutions == 1:
 212             return max(breaks, key=lambda k: k[1])
 213         else:
 214             return sorted(breaks, key=lambda k: k[1], reverse=True)[:number_of_solutions]
 215
 216 def keyword_break_worker(message, keyword, wrap_alphabet, fitness):
 217     plaintext = keyword_decipher(message, keyword, wrap_alphabet)
 218     fit = fitness(plaintext)
 219     logger.debug('Keyword break attempt using key {0} (wrap={1}) gives fit of '
 220                  '{2} and decrypt starting: {3}'.format(keyword,
 221                      wrap_alphabet, fit, sanitise(plaintext)[:50]))
 222     return (keyword, wrap_alphabet), fit
 223
 224 def monoalphabetic_break_hillclimbing(message, max_iterations=10000000,
 225         alphabet=None, fitness=Pletters):
 226     ciphertext = unaccent(message).lower()
 227     if not alphabet:
 228         alphabet = list(string.ascii_lowercase)
 229         random.shuffle(alphabet)
 230         alphabet = cat(alphabet)
 231     return monoalphabetic_break_hillclimbing_worker(ciphertext, alphabet,
 232                                                     max_iterations, fitness)
 233
 234 def monoalphabetic_break_hillclimbing_mp(message, workers=10,
 235         max_iterations = 10000000, alphabet=None, fitness=Pletters, chunksize=1):
 236     worker_args = []
 237     ciphertext = unaccent(message).lower()
 238     for i in range(workers):
 239         if alphabet:
 240             this_alphabet = alphabet
 241         else:
 242             this_alphabet = list(string.ascii_lowercase)
 243             random.shuffle(this_alphabet)
 244             this_alphabet = cat(this_alphabet)
 245         worker_args.append((ciphertext, this_alphabet, max_iterations, fitness))
 246     with Pool() as pool:
 247         breaks = pool.starmap(monoalphabetic_break_hillclimbing_worker,
 248                               worker_args, chunksize)
 249     return max(breaks, key=lambda k: k[1])
 250
 251 def monoalphabetic_break_hillclimbing_worker(message, alphabet,
 252         max_iterations, fitness):
 253     def swap(letters, i, j):
 254         if i > j:
 255             i, j = j, i
 256         if i == j:
 257             return letters
 258         else:
 259             return (letters[:i] + letters[j] + letters[i+1:j] + letters[i] +
 260                     letters[j+1:])
 261     best_alphabet = alphabet
 262     best_fitness = float('-inf')
 263     for i in range(max_iterations):
 264         alphabet = swap(alphabet, random.randrange(26), random.randrange(26))
 265         cipher_translation = ''.maketrans(string.ascii_lowercase, alphabet)
 266         plaintext = message.translate(cipher_translation)
 267         if fitness(plaintext) > best_fitness:
 268             best_fitness = fitness(plaintext)
 269             best_alphabet = alphabet
 270             print(i, best_alphabet, best_fitness, plaintext)
 271     return best_alphabet, best_fitness
 272
 273
 274 def vigenere_keyword_break_mp(message, wordlist=keywords, fitness=Pletters,
 275                               chunksize=500):
 276     """Breaks a vigenere cipher using a dictionary and frequency analysis.
 277
 278     >>> vigenere_keyword_break_mp(vigenere_encipher(sanitise('this is a test ' \
 279              'message for the vigenere decipherment'), 'cat'), \
 280              wordlist=['cat', 'elephant', 'kangaroo']) # doctest: +ELLIPSIS
 281     ('cat', -52.9472712...)
 282     """
 283     with Pool() as pool:
 284         helper_args = [(message, word, fitness)
 285                        for word in wordlist]
 286         # Gotcha: the helper function here needs to be defined at the top level
 287         #   (limitation of Pool.starmap)
 288         breaks = pool.starmap(vigenere_keyword_break_worker, helper_args,
 289                               chunksize)
 290         return max(breaks, key=lambda k: k[1])
 291 vigenere_keyword_break = vigenere_keyword_break_mp
 292
 293 def vigenere_keyword_break_worker(message, keyword, fitness):
 294     plaintext = vigenere_decipher(message, keyword)
 295     fit = fitness(plaintext)
 296     logger.debug('Vigenere keyword break attempt using key {0} gives fit of '
 297                  '{1} and decrypt starting: {2}'.format(keyword,
 298                      fit, sanitise(plaintext)[:50]))
 299     return keyword, fit
 300
 301
 302 def vigenere_frequency_break(message, max_key_length=20, fitness=Pletters):
 303     """Breaks a Vigenere cipher with frequency analysis
 304
 305     >>> vigenere_frequency_break(vigenere_encipher(sanitise("It is time to " \
 306             "run. She is ready and so am I. I stole Daniel's pocketbook this " \
 307             "afternoon when he left his jacket hanging on the easel in the " \
 308             "attic. I jump every time I hear a footstep on the stairs, " \
 309             "certain that the theft has been discovered and that I will " \
 310             "be caught. The SS officer visits less often now that he is " \
 311             "sure"), 'florence')) # doctest: +ELLIPSIS
 312     ('florence', -307.5473096...)
 313     """
 314     def worker(message, key_length, fitness):
 315         splits = every_nth(sanitised_message, key_length)
 316         key = cat([unpos(caesar_break(s)[0]) for s in splits])
 317         plaintext = vigenere_decipher(message, key)
 318         fit = fitness(plaintext)
 319         return key, fit
 320     sanitised_message = sanitise(message)
 321     results = starmap(worker, [(sanitised_message, i, fitness)
 322                                for i in range(1, max_key_length+1)])
 323     return max(results, key=lambda k: k[1])
 324
 325
 326 def beaufort_sub_break(message, fitness=Pletters):
 327     """Breaks one chunk of a Beaufort cipher with frequency analysis
 328
 329     >>> beaufort_sub_break('samwpplggnnmmyaazgympjapopnwiywwomwspgpjmefwmawx' \
 330       'jafjhxwwwdigxshnlywiamhyshtasxptwueahhytjwsn') # doctest: +ELLIPSIS
 331     (0, -117.4492...)
 332     >>> beaufort_sub_break('eyprzjjzznxymrygryjqmqhznjrjjapenejznawngnnezgza' \
 333       'dgndknaogpdjneadadazlhkhxkryevrronrmdjnndjlo') # doctest: +ELLIPSIS
 334     (17, -114.9598...)
 335     """
 336     best_shift = 0
 337     best_fit = float('-inf')
 338     for key in range(26):
 339         plaintext = [unpos(key - pos(l)) for l in message]
 340         fit = fitness(plaintext)
 341         logger.debug('Beaufort sub break attempt using key {0} gives fit of {1} '
 342                      'and decrypt starting: {2}'.format(key, fit,
 343                                                         plaintext[:50]))
 344         if fit > best_fit:
 345             best_fit = fit
 346             best_key = key
 347     logger.info('Beaufort sub break best fit: key {0} gives fit of {1} and '
 348                 'decrypt starting: {2}'.format(best_key, best_fit,
 349                     cat([unpos(best_key - pos(l)) for l in message[:50]])))
 350     return best_key, best_fit
 351
 352
 353 def beaufort_frequency_break(message, max_key_length=20, fitness=Pletters):
 354     """Breaks a Beaufort cipher with frequency analysis
 355
 356     >>> beaufort_frequency_break(beaufort_encipher(sanitise("It is time to " \
 357             "run. She is ready and so am I. I stole Daniel's pocketbook this " \
 358             "afternoon when he left his jacket hanging on the easel in the " \
 359             "attic. I jump every time I hear a footstep on the stairs, " \
 360             "certain that the theft has been discovered and that I will " \
 361             "be caught. The SS officer visits less often now " \
 362             "that he is sure"), 'florence')) # doctest: +ELLIPSIS
 363     ('florence', -307.5473096791...)
 364     """
 365     def worker(message, key_length, fitness):
 366         splits = every_nth(message, key_length)
 367         key = cat([unpos(beaufort_sub_break(s)[0]) for s in splits])
 368         plaintext = beaufort_decipher(message, key)
 369         fit = fitness(plaintext)
 370         return key, fit
 371     sanitised_message = sanitise(message)
 372     results = starmap(worker, [(sanitised_message, i, fitness)
 373                                for i in range(1, max_key_length+1)])
 374     return max(results, key=lambda k: k[1])
 375
 376
 377 def beaufort_variant_frequency_break(message, max_key_length=20, fitness=Pletters):
 378     """Breaks a Beaufort cipher with frequency analysis
 379
 380     >>> beaufort_variant_frequency_break(beaufort_variant_encipher(sanitise("It is time to " \
 381             "run. She is ready and so am I. I stole Daniel's pocketbook this " \
 382             "afternoon when he left his jacket hanging on the easel in the " \
 383             "attic. I jump every time I hear a footstep on the stairs, " \
 384             "certain that the theft has been discovered and that I will " \
 385             "be caught. The SS officer visits less often now " \
 386             "that he is sure"), 'florence')) # doctest: +ELLIPSIS
 387     ('florence', -307.5473096791...)
 388     """
 389     def worker(message, key_length, fitness):
 390         splits = every_nth(sanitised_message, key_length)
 391         key = cat([unpos(-caesar_break(s)[0]) for s in splits])
 392         plaintext = beaufort_variant_decipher(message, key)
 393         fit = fitness(plaintext)
 394         return key, fit
 395     sanitised_message = sanitise(message)
 396     results = starmap(worker, [(sanitised_message, i, fitness)
 397                                for i in range(1, max_key_length+1)])
 398     return max(results, key=lambda k: k[1])
 399
 400 def polybius_break_mp(message, column_labels, row_labels,
 401                       letters_to_merge=None,
 402                       wordlist=keywords, fitness=Pletters,
 403                       number_of_solutions=1, chunksize=500):
 404     """Breaks a Polybius substitution cipher using a dictionary and
 405     frequency analysis
 406
 407     >>> polybius_break_mp(polybius_encipher('this is a test message for the ' \
 408           'polybius decipherment', 'elephant', 'abcde', 'abcde'), \
 409           'abcde', 'abcde', \
 410           wordlist=['cat', 'elephant', 'kangaroo']) # doctest: +ELLIPSIS, +NORMALIZE_WHITESPACE
 411     (('elephant', <KeywordWrapAlphabet.from_a: 1>, 'abcde', 'abcde', False), \
 412     -54.53880...)
 413     >>> polybius_break_mp(polybius_encipher('this is a test message for the ' \
 414           'polybius decipherment', 'elephant', 'abcde', 'abcde', column_first=True), \
 415           'abcde', 'abcde', \
 416           wordlist=['cat', 'elephant', 'kangaroo']) # doctest: +ELLIPSIS, +NORMALIZE_WHITESPACE
 417     (('elephant', <KeywordWrapAlphabet.from_a: 1>, 'abcde', 'abcde', True), \
 418     -54.53880...)
 419     >>> polybius_break_mp(polybius_encipher('this is a test message for the ' \
 420           'polybius decipherment', 'elephant', 'abcde', 'abcde', column_first=False), \
 421           'abcde', 'abcde', \
 422           wordlist=['cat', 'elephant', 'kangaroo']) # doctest: +ELLIPSIS, +NORMALIZE_WHITESPACE
 423     (('elephant', <KeywordWrapAlphabet.from_a: 1>, 'abcde', 'abcde', False), \
 424     -54.53880...)
 425     >>> polybius_break_mp(polybius_encipher('this is a test message for the ' \
 426           'polybius decipherment', 'elephant', 'abcde', 'pqrst', column_first=True), \
 427           'abcde', 'pqrst', \
 428           wordlist=['cat', 'elephant', 'kangaroo']) # doctest: +ELLIPSIS, +NORMALIZE_WHITESPACE
 429     (('elephant', <KeywordWrapAlphabet.from_a: 1>, 'abcde', 'pqrst', True), \
 430     -54.53880...)
 431     """
 432     if letters_to_merge is None:
 433         letters_to_merge = {'j': 'i'}
 434     with Pool() as pool:
 435         helper_args = [(message, word, wrap,
 436                         column_labels, row_labels, column_first,
 437                         letters_to_merge,
 438                         fitness)
 439                        for word in wordlist
 440                        for wrap in KeywordWrapAlphabet
 441                        for column_first in [False, True]]
 442         # Gotcha: the helper function here needs to be defined at the top level
 443         #   (limitation of Pool.starmap)
 444         breaks = pool.starmap(polybius_break_worker, helper_args, chunksize)
 445         if number_of_solutions == 1:
 446             return max(breaks, key=lambda k: k[1])
 447         else:
 448             return sorted(breaks, key=lambda k: k[1], reverse=True)[:number_of_solutions]
 449
 450 def polybius_break_worker(message, keyword, wrap_alphabet,
 451                           column_order, row_order, column_first,
 452                           letters_to_merge,
 453                           fitness):
 454     plaintext = polybius_decipher(message, keyword,
 455                                   column_order, row_order,
 456                                   column_first=column_first,
 457                                   letters_to_merge=letters_to_merge,
 458                                   wrap_alphabet=wrap_alphabet)
 459     if plaintext:
 460         fit = fitness(plaintext)
 461     else:
 462         fit = float('-inf')
 463     logger.debug('Polybius break attempt using key {0} (wrap={1}, merging {2}), '
 464                  'columns as {3}, rows as {4} (column_first={5}) '
 465                  'gives fit of {6} and decrypt starting: '
 466                  '{7}'.format(keyword, wrap_alphabet, letters_to_merge,
 467                               column_order, row_order, column_first,
 468                               fit, sanitise(plaintext)[:50]))
 469     return (keyword, wrap_alphabet, column_order, row_order, column_first), fit
 470
 471
 472 def column_transposition_break_mp(message, translist=transpositions,
 473                                   fitness=Pbigrams, chunksize=500):
 474     """Breaks a column transposition cipher using a dictionary and
 475     n-gram frequency analysis
 476
 477     >>> column_transposition_break_mp(column_transposition_encipher(sanitise( \
 478             "It is a truth universally acknowledged, that a single man in \
 479              possession of a good fortune, must be in want of a wife. However \
 480              little known the feelings or views of such a man may be on his \
 481              first entering a neighbourhood, this truth is so well fixed in \
 482              the minds of the surrounding families, that he is considered the \
 483              rightful property of some one or other of their daughters."), \
 484         'encipher'), \
 485         translist={(2, 0, 5, 3, 1, 4, 6): ['encipher'], \
 486                    (5, 0, 6, 1, 3, 4, 2): ['fourteen'], \
 487                    (6, 1, 0, 4, 5, 3, 2): ['keyword']}) # doctest: +ELLIPSIS
 488     (((2, 0, 5, 3, 1, 4, 6), False, False), -709.4646722...)
 489     >>> column_transposition_break_mp(column_transposition_encipher(sanitise( \
 490             "It is a truth universally acknowledged, that a single man in \
 491              possession of a good fortune, must be in want of a wife. However \
 492              little known the feelings or views of such a man may be on his \
 493              first entering a neighbourhood, this truth is so well fixed in \
 494              the minds of the surrounding families, that he is considered the \
 495              rightful property of some one or other of their daughters."), \
 496         'encipher'), \
 497         translist={(2, 0, 5, 3, 1, 4, 6): ['encipher'], \
 498                    (5, 0, 6, 1, 3, 4, 2): ['fourteen'], \
 499                    (6, 1, 0, 4, 5, 3, 2): ['keyword']}, \
 500         fitness=Ptrigrams) # doctest: +ELLIPSIS
 501     (((2, 0, 5, 3, 1, 4, 6), False, False), -997.0129085...)
 502     """
 503     with Pool() as pool:
 504         helper_args = [(message, trans, fillcolumnwise, emptycolumnwise,
 505                         fitness)
 506                        for trans in translist
 507                        for fillcolumnwise in [True, False]
 508                        for emptycolumnwise in [True, False]]
 509         # Gotcha: the helper function here needs to be defined at the top level
 510         #   (limitation of Pool.starmap)
 511         breaks = pool.starmap(column_transposition_break_worker,
 512                               helper_args, chunksize)
 513         return max(breaks, key=lambda k: k[1])
 514 column_transposition_break = column_transposition_break_mp
 515
 516 def column_transposition_break_worker(message, transposition,
 517         fillcolumnwise, emptycolumnwise, fitness):
 518     plaintext = column_transposition_decipher(message, transposition,
 519         fillcolumnwise=fillcolumnwise, emptycolumnwise=emptycolumnwise)
 520     fit = fitness(sanitise(plaintext))
 521     logger.debug('Column transposition break attempt using key {0} '
 522                          'gives fit of {1} and decrypt starting: {2}'.format(
 523                              transposition, fit,
 524                              sanitise(plaintext)[:50]))
 525     return (transposition, fillcolumnwise, emptycolumnwise), fit
 526
 527
 528 def scytale_break_mp(message, max_key_length=20,
 529                      fitness=Pbigrams, chunksize=500):
 530     """Breaks a scytale cipher using a range of lengths and
 531     n-gram frequency analysis
 532
 533     >>> scytale_break_mp(scytale_encipher(sanitise( \
 534             "It is a truth universally acknowledged, that a single man in \
 535              possession of a good fortune, must be in want of a wife. However \
 536              little known the feelings or views of such a man may be on his \
 537              first entering a neighbourhood, this truth is so well fixed in \
 538              the minds of the surrounding families, that he is considered the \
 539              rightful property of some one or other of their daughters."), \
 540         5)) # doctest: +ELLIPSIS
 541     (5, -709.4646722...)
 542     >>> scytale_break_mp(scytale_encipher(sanitise( \
 543             "It is a truth universally acknowledged, that a single man in \
 544              possession of a good fortune, must be in want of a wife. However \
 545              little known the feelings or views of such a man may be on his \
 546              first entering a neighbourhood, this truth is so well fixed in \
 547              the minds of the surrounding families, that he is considered the \
 548              rightful property of some one or other of their daughters."), \
 549         5), \
 550         fitness=Ptrigrams) # doctest: +ELLIPSIS
 551     (5, -997.0129085...)
 552     """
 553     with Pool() as pool:
 554         helper_args = [(message, trans, False, True, fitness)
 555             for trans in
 556                 [[col for col in range(math.ceil(len(message)/rows))]
 557                     for rows in range(1,max_key_length+1)]]
 558         # Gotcha: the helper function here needs to be defined at the top level
 559         #   (limitation of Pool.starmap)
 560         breaks = pool.starmap(column_transposition_break_worker,
 561                               helper_args, chunksize)
 562         best = max(breaks, key=lambda k: k[1])
 563         return math.trunc(len(message) / len(best[0][0])), best[1]
 564 scytale_break = scytale_break_mp
 565
 566
 567 def railfence_break(message, max_key_length=20,
 568                      fitness=Pletters, chunksize=500):
 569     """Breaks a hill cipher using a matrix of given rank and letter frequencies
 570
 571
 572     """
 573
 574     sanitised_message = sanitise(message)
 575     results = starmap(worker, [(sanitised_message, i, fitness)
 576                                for i in range(2, max_key_length+1)])
 577     return max(results, key=lambda k: k[1])
 578
 579
 580 def railfence_break(message, max_key_length=20,
 581                      fitness=Pbigrams, chunksize=500):
 582     """Breaks a railfence cipher using a range of lengths and
 583     n-gram frequency analysis
 584
 585     >>> railfence_break(railfence_encipher(sanitise( \
 586             "It is a truth universally acknowledged, that a single man in \
 587              possession of a good fortune, must be in want of a wife. However \
 588              little known the feelings or views of such a man may be on his \
 589              first entering a neighbourhood, this truth is so well fixed in \
 590              the minds of the surrounding families, that he is considered the \
 591              rightful property of some one or other of their daughters."), \
 592         7)) # doctest: +ELLIPSIS
 593     (7, -709.46467226...)
 594     >>> railfence_break(railfence_encipher(sanitise( \
 595             "It is a truth universally acknowledged, that a single man in \
 596              possession of a good fortune, must be in want of a wife. However \
 597              little known the feelings or views of such a man may be on his \
 598              first entering a neighbourhood, this truth is so well fixed in \
 599              the minds of the surrounding families, that he is considered the \
 600              rightful property of some one or other of their daughters."), \
 601         7), \
 602         fitness=Ptrigrams) # doctest: +ELLIPSIS
 603     (7, -997.0129085...)
 604     """
 605     def worker(message, height, fitness):
 606         plaintext = railfence_decipher(message, height)
 607         fit = fitness(plaintext)
 608         return height, fit
 609
 610     sanitised_message = sanitise(message)
 611     results = starmap(worker, [(sanitised_message, i, fitness)
 612                                for i in range(2, max_key_length+1)])
 613     return max(results, key=lambda k: k[1])
 614
 615 def amsco_break(message, translist=transpositions, patterns = [(1, 2), (2, 1)],
 616                                   fillstyles = [AmscoFillStyle.continuous,
 617                                                 AmscoFillStyle.same_each_row,
 618                                                 AmscoFillStyle.reverse_each_row],
 619                                   fitness=Pbigrams,
 620                                   chunksize=500):
 621     """Breaks an AMSCO transposition cipher using a dictionary and
 622     n-gram frequency analysis
 623
 624     >>> amsco_break(amsco_transposition_encipher(sanitise( \
 625             "It is a truth universally acknowledged, that a single man in \
 626              possession of a good fortune, must be in want of a wife. However \
 627              little known the feelings or views of such a man may be on his \
 628              first entering a neighbourhood, this truth is so well fixed in \
 629              the minds of the surrounding families, that he is considered the \
 630              rightful property of some one or other of their daughters."), \
 631         'encipher'), \
 632         translist={(2, 0, 5, 3, 1, 4, 6): ['encipher'], \
 633                    (5, 0, 6, 1, 3, 4, 2): ['fourteen'], \
 634                    (6, 1, 0, 4, 5, 3, 2): ['keyword']}, \
 635         patterns=[(1, 2)]) # doctest: +ELLIPSIS
 636     (((2, 0, 5, 3, 1, 4, 6), (1, 2), <AmscoFillStyle.continuous: 1>), -709.4646722...)
 637     >>> amsco_break(amsco_transposition_encipher(sanitise( \
 638             "It is a truth universally acknowledged, that a single man in \
 639              possession of a good fortune, must be in want of a wife. However \
 640              little known the feelings or views of such a man may be on his \
 641              first entering a neighbourhood, this truth is so well fixed in \
 642              the minds of the surrounding families, that he is considered the \
 643              rightful property of some one or other of their daughters."), \
 644         'encipher', fillpattern=(2, 1)), \
 645         translist={(2, 0, 5, 3, 1, 4, 6): ['encipher'], \
 646                    (5, 0, 6, 1, 3, 4, 2): ['fourteen'], \
 647                    (6, 1, 0, 4, 5, 3, 2): ['keyword']}, \
 648         patterns=[(1, 2), (2, 1)], fitness=Ptrigrams) # doctest: +ELLIPSIS
 649     (((2, 0, 5, 3, 1, 4, 6), (2, 1), <AmscoFillStyle.continuous: 1>), -997.0129085...)
 650     """
 651     with Pool() as pool:
 652         helper_args = [(message, trans, pattern, fillstyle, fitness)
 653                        for trans in translist
 654                        for pattern in patterns
 655                        for fillstyle in fillstyles]
 656         # Gotcha: the helper function here needs to be defined at the top level
 657         #   (limitation of Pool.starmap)
 658         breaks = pool.starmap(amsco_break_worker, helper_args, chunksize)
 659         return max(breaks, key=lambda k: k[1])
 660
 661 def amsco_break_worker(message, transposition,
 662         pattern, fillstyle, fitness):
 663     plaintext = amsco_transposition_decipher(message, transposition,
 664         fillpattern=pattern, fillstyle=fillstyle)
 665     fit = fitness(sanitise(plaintext))
 666     logger.debug('AMSCO transposition break attempt using key {0} and pattern'
 667                          '{1} ({2}) gives fit of {3} and decrypt starting: '
 668                          '{4}'.format(
 669                              transposition, pattern, fillstyle, fit,
 670                              sanitise(plaintext)[:50]))
 671     return (transposition, pattern, fillstyle), fit
 672
 673
 674 def hill_break(message, matrix_size=2, fitness=Pletters,
 675     number_of_solutions=1, chunksize=500):
 676
 677     all_matrices = [np.matrix(list(m))
 678         for m in itertools.product([list(r)
 679             for r in itertools.product(range(26), repeat=matrix_size)],
 680         repeat=matrix_size)]
 681     valid_matrices = [m for m, d in
 682         zip(all_matrices, (int(round(linalg.det(m))) for m in all_matrices))
 683                   if d != 0
 684                   if d % 2 != 0
 685                   if d % 13 != 0 ]
 686     with Pool() as pool:
 687         helper_args = [(message, matrix, fitness)
 688                        for matrix in valid_matrices]
 689         # Gotcha: the helper function here needs to be defined at the top level
 690         #   (limitation of Pool.starmap)
 691         breaks = pool.starmap(hill_break_worker, helper_args, chunksize)
 692         if number_of_solutions == 1:
 693             return max(breaks, key=lambda k: k[1])
 694         else:
 695             return sorted(breaks, key=lambda k: k[1], reverse=True)[:number_of_solutions]
 696
 697 def hill_break_worker(message, matrix, fitness):
 698     plaintext = hill_decipher(matrix, message)
 699     fit = fitness(plaintext)
 700     logger.debug('Hill cipher break attempt using key {0} gives fit of '
 701                  '{1} and decrypt starting: {2}'.format(matrix,
 702                      fit, sanitise(plaintext)[:50]))
 703     return matrix, fit
 704
 705 def bifid_break_mp(message, wordlist=keywords, fitness=Pletters, max_period=10,
 706                      number_of_solutions=1, chunksize=500):
 707     """Breaks a keyword substitution cipher using a dictionary and
 708     frequency analysis
 709
 710     >>> bifid_break_mp(bifid_encipher('this is a test message for the ' \
 711           'keyword decipherment', 'elephant', wrap_alphabet=KeywordWrapAlphabet.from_last), \
 712           wordlist=['cat', 'elephant', 'kangaroo']) # doctest: +ELLIPSIS
 713     (('elephant', <KeywordWrapAlphabet.from_last: 2>, 0), -52.834575011...)
 714     >>> bifid_break_mp(bifid_encipher('this is a test message for the ' \
 715           'keyword decipherment', 'elephant', wrap_alphabet=KeywordWrapAlphabet.from_last), \
 716           wordlist=['cat', 'elephant', 'kangaroo'], \
 717           number_of_solutions=2) # doctest: +ELLIPSIS, +NORMALIZE_WHITESPACE
 718     [(('elephant', <KeywordWrapAlphabet.from_last: 2>, 0), -52.834575011...),
 719     (('elephant', <KeywordWrapAlphabet.from_largest: 3>, 0), -52.834575011...)]
 720     """
 721     with Pool() as pool:
 722         helper_args = [(message, word, wrap, period, fitness)
 723                        for word in wordlist
 724                        for wrap in KeywordWrapAlphabet
 725                        for period in range(max_period+1)]
 726         # Gotcha: the helper function here needs to be defined at the top level
 727         #   (limitation of Pool.starmap)
 728         breaks = pool.starmap(bifid_break_worker, helper_args, chunksize)
 729         if number_of_solutions == 1:
 730             return max(breaks, key=lambda k: k[1])
 731         else:
 732             return sorted(breaks, key=lambda k: k[1], reverse=True)[:number_of_solutions]
 733
 734 def bifid_break_worker(message, keyword, wrap_alphabet, period, fitness):
 735     plaintext = bifid_decipher(message, keyword, wrap_alphabet, period=period)
 736     fit = fitness(plaintext)
 737     logger.debug('Keyword break attempt using key {0} (wrap={1}) gives fit of '
 738                  '{2} and decrypt starting: {3}'.format(keyword,
 739                      wrap_alphabet, fit, sanitise(plaintext)[:50]))
 740     return (keyword, wrap_alphabet, period), fit
 741
 742
 743 def pocket_enigma_break_by_crib(message, wheel_spec, crib, crib_position):
 744     """Break a pocket enigma using a crib (some plaintext that's expected to
 745     be in a certain position). Returns a list of possible starting wheel
 746     positions that could produce the crib.
 747
 748     >>> pocket_enigma_break_by_crib('kzpjlzmoga', 1, 'h', 0)
 749     ['a', 'f', 'q']
 750     >>> pocket_enigma_break_by_crib('kzpjlzmoga', 1, 'he', 0)
 751     ['a']
 752     >>> pocket_enigma_break_by_crib('kzpjlzmoga', 1, 'll', 2)
 753     ['a']
 754     >>> pocket_enigma_break_by_crib('kzpjlzmoga', 1, 'l', 2)
 755     ['a']
 756     >>> pocket_enigma_break_by_crib('kzpjlzmoga', 1, 'l', 3)
 757     ['a', 'j', 'n']
 758     >>> pocket_enigma_break_by_crib('aaaaa', 1, 'l', 3)
 759     []
 760     """
 761     pe = PocketEnigma(wheel=wheel_spec)
 762     possible_positions = []
 763     for p in string.ascii_lowercase:
 764         pe.set_position(p)
 765         plaintext = pe.decipher(message)
 766         if plaintext[crib_position:crib_position+len(crib)] == crib:
 767             possible_positions += [p]
 768     return possible_positions
 769
 770
 771 def plot_frequency_histogram(freqs, sort_key=None):
 772     x = range(len(freqs))
 773     y = [freqs[l] for l in sorted(freqs, key=sort_key)]
 774     f = plt.figure()
 775     ax = f.add_axes([0.1, 0.1, 0.9, 0.9])
 776     ax.bar(x, y, align='center')
 777     ax.set_xticks(x)
 778     ax.set_xticklabels(sorted(freqs, key=sort_key))
 779     f.show()
 780
 781
 782 if __name__ == "__main__":
 783     import doctest
 784     doctest.testmod()