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
  33 def frequencies(text):
  34     """Count the number of occurrences of each character in text
  35
  36     >>> sorted(frequencies('abcdefabc').items())
  37     [('a', 2), ('b', 2), ('c', 2), ('d', 1), ('e', 1), ('f', 1)]
  38     >>> sorted(frequencies('the quick brown fox jumped over the lazy ' \
  39          'dog').items()) # doctest: +NORMALIZE_WHITESPACE
  40     [(' ', 8), ('a', 1), ('b', 1), ('c', 1), ('d', 2), ('e', 4), ('f', 1),
  41      ('g', 1), ('h', 2), ('i', 1), ('j', 1), ('k', 1), ('l', 1), ('m', 1),
  42      ('n', 1), ('o', 4), ('p', 1), ('q', 1), ('r', 2), ('t', 2), ('u', 2),
  43      ('v', 1), ('w', 1), ('x', 1), ('y', 1), ('z', 1)]
  44     >>> sorted(frequencies('The Quick BROWN fox jumped! over... the ' \
  45          '(9lazy) DOG').items()) # doctest: +NORMALIZE_WHITESPACE
  46     [(' ', 8), ('!', 1), ('(', 1), (')', 1), ('.', 3), ('9', 1), ('B', 1),
  47      ('D', 1), ('G', 1), ('N', 1), ('O', 2), ('Q', 1), ('R', 1), ('T', 1),
  48      ('W', 1), ('a', 1), ('c', 1), ('d', 1), ('e', 4), ('f', 1), ('h', 2),
  49      ('i', 1), ('j', 1), ('k', 1), ('l', 1), ('m', 1), ('o', 2), ('p', 1),
  50      ('r', 1), ('t', 1), ('u', 2), ('v', 1), ('x', 1), ('y', 1), ('z', 1)]
  51     >>> sorted(frequencies(sanitise('The Quick BROWN fox jumped! over... '\
  52          'the (9lazy) DOG')).items()) # doctest: +NORMALIZE_WHITESPACE
  53     [('a', 1), ('b', 1), ('c', 1), ('d', 2), ('e', 4), ('f', 1), ('g', 1),
  54      ('h', 2), ('i', 1), ('j', 1), ('k', 1), ('l', 1), ('m', 1), ('n', 1),
  55      ('o', 4), ('p', 1), ('q', 1), ('r', 2), ('t', 2), ('u', 2), ('v', 1),
  56      ('w', 1), ('x', 1), ('y', 1), ('z', 1)]
  57     >>> frequencies('abcdefabcdef')['x']
  58     0
  59     """
  60     return collections.Counter(c for c in text)
  61
  62
  63 def caesar_break(message, fitness=Pletters):
  64     """Breaks a Caesar cipher using frequency analysis
  65
  66     >>> caesar_break('ibxcsyorsaqcheyklxivoexlevmrimwxsfiqevvmihrsasrxliwyrh' \
  67           'ecjsppsamrkwleppfmergefifvmhixscsymjcsyqeoixlm') # doctest: +ELLIPSIS
  68     (4, -130.849989015...)
  69     >>> caesar_break('wxwmaxdgheetgwuxztgptedbgznitgwwhpguxyhkxbmhvvtlbhgtee' \
  70           'raxlmhiixweblmxgxwmhmaxybkbgztgwztsxwbgmxgmert') # doctest: +ELLIPSIS
  71     (19, -128.82410410...)
  72     >>> caesar_break('yltbbqnqnzvguvaxurorgenafsbezqvagbnornfgsbevpnaabjurer' \
  73           'svaquvzyvxrnznazlybequrvfohgriraabjtbaruraprur') # doctest: +ELLIPSIS
  74     (13, -126.25403935...)
  75     """
  76     sanitised_message = sanitise(message)
  77     best_shift = 0
  78     best_fit = float('-inf')
  79     for shift in range(26):
  80         plaintext = caesar_decipher(sanitised_message, shift)
  81         fit = fitness(plaintext)
  82         logger.debug('Caesar break attempt using key {0} gives fit of {1} '
  83                      'and decrypt starting: {2}'.format(shift, fit,
  84                                                         plaintext[:50]))
  85         if fit > best_fit:
  86             best_fit = fit
  87             best_shift = shift
  88     logger.info('Caesar break best fit: key {0} gives fit of {1} and '
  89                 'decrypt starting: {2}'.format(best_shift, best_fit,
  90                     caesar_decipher(sanitised_message, best_shift)[:50]))
  91     return best_shift, best_fit
  92
  93 def affine_break(message, fitness=Pletters):
  94     """Breaks an affine cipher using frequency analysis
  95
  96     >>> affine_break('lmyfu bkuusd dyfaxw claol psfaom jfasd snsfg jfaoe ls ' \
  97           'omytd jlaxe mh jm bfmibj umis hfsul axubafkjamx. ls kffkxwsd jls ' \
  98           'ofgbjmwfkiu olfmxmtmwaokttg jlsx ls kffkxwsd jlsi zg tsxwjl. jlsx ' \
  99           'ls umfjsd jlsi zg hfsqysxog. ls dmmdtsd mx jls bats mh bkbsf. ls ' \
 100           'bfmctsd kfmyxd jls lyj, mztanamyu xmc jm clm cku tmmeaxw kj lai ' \
 101           'kxd clm ckuxj.') # doctest: +ELLIPSIS
 102     ((15, 22, True), -340.601181913...)
 103     """
 104     sanitised_message = sanitise(message)
 105     best_multiplier = 0
 106     best_adder = 0
 107     best_one_based = True
 108     best_fit = float("-inf")
 109     for one_based in [True, False]:
 110         for multiplier in [x for x in range(1, 26, 2) if x != 13]:
 111             for adder in range(26):
 112                 plaintext = affine_decipher(sanitised_message,
 113                                             multiplier, adder, one_based)
 114                 fit = fitness(plaintext)
 115                 logger.debug('Affine break attempt using key {0}x+{1} ({2}) '
 116                              'gives fit of {3} and decrypt starting: {4}'.
 117                              format(multiplier, adder, one_based, fit,
 118                                     plaintext[:50]))
 119                 if fit > best_fit:
 120                     best_fit = fit
 121                     best_multiplier = multiplier
 122                     best_adder = adder
 123                     best_one_based = one_based
 124     logger.info('Affine break best fit with key {0}x+{1} ({2}) gives fit of '
 125                 '{3} and decrypt starting: {4}'.format(
 126                     best_multiplier, best_adder, best_one_based, best_fit,
 127                     affine_decipher(sanitised_message, best_multiplier,
 128                                     best_adder, best_one_based)[:50]))
 129     return (best_multiplier, best_adder, best_one_based), best_fit
 130
 131 def keyword_break(message, wordlist=keywords, fitness=Pletters):
 132     """Breaks a keyword substitution cipher using a dictionary and
 133     frequency analysis.
 134
 135     >>> keyword_break(keyword_encipher('this is a test message for the ' \
 136           'keyword decipherment', 'elephant', KeywordWrapAlphabet.from_last), \
 137           wordlist=['cat', 'elephant', 'kangaroo']) # doctest: +ELLIPSIS
 138     (('elephant', <KeywordWrapAlphabet.from_last: 2>), -52.834575011...)
 139     """
 140     best_keyword = ''
 141     best_wrap_alphabet = True
 142     best_fit = float("-inf")
 143     for wrap_alphabet in KeywordWrapAlphabet:
 144         for keyword in wordlist:
 145             plaintext = keyword_decipher(message, keyword, wrap_alphabet)
 146             fit = fitness(plaintext)
 147             logger.debug('Keyword break attempt using key {0} (wrap={1}) '
 148                          'gives fit of {2} and decrypt starting: {3}'.format(
 149                              keyword, wrap_alphabet, fit,
 150                              sanitise(plaintext)[:50]))
 151             if fit > best_fit:
 152                 best_fit = fit
 153                 best_keyword = keyword
 154                 best_wrap_alphabet = wrap_alphabet
 155     logger.info('Keyword break best fit with key {0} (wrap={1}) gives fit of '
 156                 '{2} and decrypt starting: {3}'.format(best_keyword,
 157                     best_wrap_alphabet, best_fit, sanitise(
 158                         keyword_decipher(message, best_keyword,
 159                                          best_wrap_alphabet))[:50]))
 160     return (best_keyword, best_wrap_alphabet), best_fit
 161
 162 def keyword_break_mp(message, wordlist=keywords, fitness=Pletters,
 163                      chunksize=500):
 164     """Breaks a keyword substitution cipher using a dictionary and
 165     frequency analysis
 166
 167     >>> keyword_break_mp(keyword_encipher('this is a test message for the ' \
 168           'keyword decipherment', 'elephant', KeywordWrapAlphabet.from_last), \
 169           wordlist=['cat', 'elephant', 'kangaroo']) # doctest: +ELLIPSIS
 170     (('elephant', <KeywordWrapAlphabet.from_last: 2>), -52.834575011...)
 171     """
 172     with Pool() as pool:
 173         helper_args = [(message, word, wrap, fitness)
 174                        for word in wordlist
 175                        for wrap in KeywordWrapAlphabet]
 176         # Gotcha: the helper function here needs to be defined at the top level
 177         #   (limitation of Pool.starmap)
 178         breaks = pool.starmap(keyword_break_worker, helper_args, chunksize)
 179         return max(breaks, key=lambda k: k[1])
 180
 181 def keyword_break_worker(message, keyword, wrap_alphabet, fitness):
 182     plaintext = keyword_decipher(message, keyword, wrap_alphabet)
 183     fit = fitness(plaintext)
 184     logger.debug('Keyword break attempt using key {0} (wrap={1}) gives fit of '
 185                  '{2} and decrypt starting: {3}'.format(keyword,
 186                      wrap_alphabet, fit, sanitise(plaintext)[:50]))
 187     return (keyword, wrap_alphabet), fit
 188
 189 def monoalphabetic_break_hillclimbing(message, max_iterations=10000000,
 190         fitness=Pletters):
 191     ciphertext = unaccent(message).lower()
 192     alphabet = list(string.ascii_lowercase)
 193     random.shuffle(alphabet)
 194     alphabet = ''.join(alphabet)
 195     return monoalphabetic_break_hillclimbing_worker(ciphertext, alphabet,
 196                                                     max_iterations, fitness)
 197
 198 def monoalphabetic_break_hillclimbing_mp(message, workers=10,
 199         max_iterations = 10000000, fitness=Pletters, chunksize=1):
 200     worker_args = []
 201     ciphertext = unaccent(message).lower()
 202     for i in range(workers):
 203         alphabet = list(string.ascii_lowercase)
 204         random.shuffle(alphabet)
 205         alphabet = ''.join(alphabet)
 206         worker_args.append((ciphertext, alphabet, max_iterations, fitness))
 207     with Pool() as pool:
 208         breaks = pool.starmap(monoalphabetic_break_hillclimbing_worker,
 209                               worker_args, chunksize)
 210     return max(breaks, key=lambda k: k[1])
 211
 212 def monoalphabetic_break_hillclimbing_worker(message, alphabet,
 213         max_iterations, fitness):
 214     def swap(letters, i, j):
 215         if i > j:
 216             i, j = j, i
 217         if i == j:
 218             return letters
 219         else:
 220             return (letters[:i] + letters[j] + letters[i+1:j] + letters[i] +
 221                     letters[j+1:])
 222     best_alphabet = alphabet
 223     best_fitness = float('-inf')
 224     for i in range(max_iterations):
 225         alphabet = swap(alphabet, random.randrange(26), random.randrange(26))
 226         cipher_translation = ''.maketrans(string.ascii_lowercase, alphabet)
 227         plaintext = message.translate(cipher_translation)
 228         if fitness(plaintext) > best_fitness:
 229             best_fitness = fitness(plaintext)
 230             best_alphabet = alphabet
 231             print(i, best_alphabet, best_fitness, plaintext)
 232     return best_alphabet, best_fitness
 233
 234
 235 def vigenere_keyword_break_mp(message, wordlist=keywords, fitness=Pletters,
 236                               chunksize=500):
 237     """Breaks a vigenere cipher using a dictionary and frequency analysis.
 238
 239     >>> vigenere_keyword_break_mp(vigenere_encipher(sanitise('this is a test ' \
 240              'message for the vigenere decipherment'), 'cat'), \
 241              wordlist=['cat', 'elephant', 'kangaroo']) # doctest: +ELLIPSIS
 242     ('cat', -52.947271216...)
 243     """
 244     with Pool() as pool:
 245         helper_args = [(message, word, fitness)
 246                        for word in wordlist]
 247         # Gotcha: the helper function here needs to be defined at the top level
 248         #   (limitation of Pool.starmap)
 249         breaks = pool.starmap(vigenere_keyword_break_worker, helper_args,
 250                               chunksize)
 251         return max(breaks, key=lambda k: k[1])
 252 vigenere_keyword_break = vigenere_keyword_break_mp
 253
 254 def vigenere_keyword_break_worker(message, keyword, fitness):
 255     plaintext = vigenere_decipher(message, keyword)
 256     fit = fitness(plaintext)
 257     logger.debug('Vigenere keyword break attempt using key {0} gives fit of '
 258                  '{1} and decrypt starting: {2}'.format(keyword,
 259                      fit, sanitise(plaintext)[:50]))
 260     return keyword, fit
 261
 262
 263 def vigenere_frequency_break(message, max_key_length=20, fitness=Pletters):
 264     """Breaks a Vigenere cipher with frequency analysis
 265
 266     >>> vigenere_frequency_break(vigenere_encipher(sanitise("It is time to " \
 267             "run. She is ready and so am I. I stole Daniel's pocketbook this " \
 268             "afternoon when he left his jacket hanging on the easel in the " \
 269             "attic. I jump every time I hear a footstep on the stairs, " \
 270             "certain that the theft has been discovered and that I will " \
 271             "be caught. The SS officer visits less often now that he is " \
 272             "sure"), 'florence')) # doctest: +ELLIPSIS
 273     ('florence', -307.5473096791...)
 274     """
 275     def worker(message, key_length, fitness):
 276         splits = every_nth(sanitised_message, key_length)
 277         key = ''.join([chr(caesar_break(s)[0] + ord('a')) for s in splits])
 278         plaintext = vigenere_decipher(message, key)
 279         fit = fitness(plaintext)
 280         return key, fit
 281     sanitised_message = sanitise(message)
 282     results = starmap(worker, [(sanitised_message, i, fitness)
 283                                for i in range(1, max_key_length+1)])
 284     return max(results, key=lambda k: k[1])
 285
 286
 287 def beaufort_frequency_break(message, max_key_length=20, fitness=Pletters):
 288     """Breaks a Beaufort cipher with frequency analysis
 289
 290     >>> beaufort_frequency_break(beaufort_encipher(sanitise("It is time to " \
 291             "run. She is ready and so am I. I stole Daniel's pocketbook this " \
 292             "afternoon when he left his jacket hanging on the easel in the " \
 293             "attic. I jump every time I hear a footstep on the stairs, " \
 294             "certain that the theft has been discovered and that I will " \
 295             "be caught. The SS officer visits less often now " \
 296             "that he is sure"), 'florence')) # doctest: +ELLIPSIS
 297     ('florence', -307.5473096791...)
 298     """
 299     def worker(message, key_length, fitness):
 300         splits = every_nth(sanitised_message, key_length)
 301         key = ''.join([chr(-caesar_break(s)[0] % 26 + ord('a'))
 302                        for s in splits])
 303         plaintext = beaufort_decipher(message, key)
 304         fit = fitness(plaintext)
 305         return key, fit
 306     sanitised_message = sanitise(message)
 307     results = starmap(worker, [(sanitised_message, i, fitness)
 308                                for i in range(1, max_key_length+1)])
 309     return max(results, key=lambda k: k[1])
 310
 311 def plot_frequency_histogram(freqs, sort_key=None):
 312     x = range(len(freqs.keys()))
 313     y = [freqs[l] for l in sorted(freqs.keys(), key=sort_key)]
 314     f = plt.figure()
 315     ax = f.add_axes([0.1, 0.1, 0.9, 0.9])
 316     ax.bar(x, y, align='center')
 317     ax.set_xticks(x)
 318     ax.set_xticklabels(sorted(freqs.keys(), key=sort_key))
 319     f.show()
 320
 321
 322 if __name__ == "__main__":
 323     import doctest
 324     doctest.testmod()