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
 132 def plot_frequency_histogram(freqs, sort_key=None):
 133     x = range(len(freqs.keys()))
 134     y = [freqs[l] for l in sorted(freqs.keys(), key=sort_key)]
 135     f = plt.figure()
 136     ax = f.add_axes([0.1, 0.1, 0.9, 0.9])
 137     ax.bar(x, y, align='center')
 138     ax.set_xticks(x)
 139     ax.set_xticklabels(sorted(freqs.keys(), key=sort_key))
 140     f.show()
 141
 142
 143 if __name__ == "__main__":
 144     import doctest
 145     doctest.testmod()