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