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