cipher/affine.py

   1 from support.utilities import *
   2 from support.language_models import *
   3 from logger import logger
   4
   5
   6 # modular_division_table = [[0]*26 for _ in range(26)]
   7 # for a in range(26):
   8 #     for b in range(26):
   9 #         c = (a * b) % 26
  10 #         modular_division_table[b][c] = a
  11
  12
  13 modular_division_table = {
  14     (multiplier, (multiplier * plaintext) % 26): plaintext
  15     for plaintext in range(26)
  16     for multiplier in range(26)
  17     }
  18
  19
  20
  21 def affine_encipher_letter(accented_letter, multiplier=1, adder=0, one_based=True):
  22     """Encipher a letter, given a multiplier and adder
  23
  24     >>> cat(affine_encipher_letter(l, 3, 5, True) \
  25             for l in string.ascii_letters)
  26     'hknqtwzcfiloruxadgjmpsvybeHKNQTWZCFILORUXADGJMPSVYBE'
  27     >>> cat(affine_encipher_letter(l, 3, 5, False) \
  28             for l in string.ascii_letters)
  29     'filoruxadgjmpsvybehknqtwzcFILORUXADGJMPSVYBEHKNQTWZC'
  30     """
  31     # letter = unaccent(accented_letter)
  32     # if letter in string.ascii_letters:
  33     #     if letter in string.ascii_uppercase:
  34     #         alphabet_start = ord('A')
  35     #     else:
  36     #         alphabet_start = ord('a')
  37     #     letter_number = ord(letter) - alphabet_start
  38     #     if one_based: letter_number += 1
  39     #     cipher_number = (letter_number * multiplier + adder) % 26
  40     #     if one_based: cipher_number -= 1
  41     #     return chr(cipher_number % 26 + alphabet_start)
  42     # else:
  43     #     return letter
  44     letter = unaccent(accented_letter)
  45     if letter in string.ascii_letters:
  46         letter_number = pos(letter)
  47         if one_based: letter_number += 1
  48         cipher_number = (letter_number * multiplier + adder) % 26
  49         if one_based: cipher_number -= 1
  50         if letter in string.ascii_uppercase:
  51             return unpos(cipher_number).upper()
  52         else:
  53             return unpos(cipher_number)
  54     else:
  55         return letter
  56
  57 def affine_decipher_letter(letter, multiplier=1, adder=0, one_based=True):
  58     """Encipher a letter, given a multiplier and adder
  59
  60     >>> cat(affine_decipher_letter(l, 3, 5, True) \
  61             for l in 'hknqtwzcfiloruxadgjmpsvybeHKNQTWZCFILORUXADGJMPSVYBE')
  62     'abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ'
  63     >>> cat(affine_decipher_letter(l, 3, 5, False) \
  64             for l in 'filoruxadgjmpsvybehknqtwzcFILORUXADGJMPSVYBEHKNQTWZC')
  65     'abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ'
  66     """
  67     # if letter in string.ascii_letters:
  68     #     if letter in string.ascii_uppercase:
  69     #         alphabet_start = ord('A')
  70     #     else:
  71     #         alphabet_start = ord('a')
  72     #     cipher_number = ord(letter) - alphabet_start
  73     #     if one_based: cipher_number += 1
  74     #     plaintext_number = (
  75     #         modular_division_table[multiplier]
  76     #                               [(cipher_number - adder) % 26])
  77     #     if one_based: plaintext_number -= 1
  78     #     return chr(plaintext_number % 26 + alphabet_start)
  79     # else:
  80     #     return letter
  81     if letter in string.ascii_letters:
  82         cipher_number = pos(letter)
  83         if one_based: cipher_number += 1
  84         # plaintext_number = (
  85         #     modular_division_table[multiplier]
  86         #                           [(cipher_number - adder) % 26])
  87         plaintext_number = (
  88             modular_division_table[multiplier, (cipher_number - adder) % 26]
  89             )
  90         if one_based: plaintext_number -= 1
  91         if letter in string.ascii_uppercase:
  92             return unpos(plaintext_number).upper()
  93         else:
  94             return unpos(plaintext_number)
  95     else:
  96         return letter
  97
  98 def affine_encipher(message, multiplier=1, adder=0, one_based=True):
  99     """Encipher a message
 100
 101     >>> affine_encipher('hours passed during which jerico tried every ' \
 102            'trick he could think of', 15, 22, True)
 103     'lmyfu bkuusd dyfaxw claol psfaom jfasd snsfg jfaoe ls omytd jlaxe mh'
 104     """
 105     enciphered = [affine_encipher_letter(l, multiplier, adder, one_based)
 106                   for l in message]
 107     return cat(enciphered)
 108
 109 def affine_decipher(message, multiplier=1, adder=0, one_based=True):
 110     """Decipher a message
 111
 112     >>> affine_decipher('lmyfu bkuusd dyfaxw claol psfaom jfasd snsfg ' \
 113            'jfaoe ls omytd jlaxe mh', 15, 22, True)
 114     'hours passed during which jerico tried every trick he could think of'
 115     """
 116     enciphered = [affine_decipher_letter(l, multiplier, adder, one_based)
 117                   for l in message]
 118     return cat(enciphered)
 119
 120
 121
 122 def affine_break(message, fitness=Pletters):
 123     """Breaks an affine cipher using frequency analysis
 124
 125     >>> affine_break('lmyfu bkuusd dyfaxw claol psfaom jfasd snsfg jfaoe ls ' \
 126           'omytd jlaxe mh jm bfmibj umis hfsul axubafkjamx. ls kffkxwsd jls ' \
 127           'ofgbjmwfkiu olfmxmtmwaokttg jlsx ls kffkxwsd jlsi zg tsxwjl. jlsx ' \
 128           'ls umfjsd jlsi zg hfsqysxog. ls dmmdtsd mx jls bats mh bkbsf. ls ' \
 129           'bfmctsd kfmyxd jls lyj, mztanamyu xmc jm clm cku tmmeaxw kj lai ' \
 130           'kxd clm ckuxj.') # doctest: +ELLIPSIS
 131     ((15, 22, True), -340.601181913...)
 132     """
 133     sanitised_message = sanitise(message)
 134     best_multiplier = 0
 135     best_adder = 0
 136     best_one_based = True
 137     best_fit = float("-inf")
 138     for one_based in [True, False]:
 139         for multiplier in [x for x in range(1, 26, 2) if x != 13]:
 140             for adder in range(26):
 141                 plaintext = affine_decipher(sanitised_message,
 142                                             multiplier, adder, one_based)
 143                 fit = fitness(plaintext)
 144                 logger.debug('Affine break attempt using key {0}x+{1} ({2}) '
 145                              'gives fit of {3} and decrypt starting: {4}'.
 146                              format(multiplier, adder, one_based, fit,
 147                                     plaintext[:50]))
 148                 if fit > best_fit:
 149                     best_fit = fit
 150                     best_multiplier = multiplier
 151                     best_adder = adder
 152                     best_one_based = one_based
 153     logger.info('Affine break best fit with key {0}x+{1} ({2}) gives fit of '
 154                 '{3} and decrypt starting: {4}'.format(
 155                     best_multiplier, best_adder, best_one_based, best_fit,
 156                     affine_decipher(sanitised_message, best_multiplier,
 157                                     best_adder, best_one_based)[:50]))
 158     return (best_multiplier, best_adder, best_one_based), best_fit