cipher.py

   1 import string
   2 import collections
   3 import math
   4 from enum import Enum
   5 from itertools import zip_longest, cycle, chain, count
   6 import numpy as np
   7 from numpy import matrix
   8 from numpy import linalg
   9 from language_models import *
  10
  11
  12 modular_division_table = [[0]*26 for _ in range(26)]
  13 for a in range(26):
  14     for b in range(26):
  15         c = (a * b) % 26
  16         modular_division_table[b][c] = a
  17
  18
  19 def every_nth(text, n, fillvalue=''):
  20     """Returns n strings, each of which consists of every nth character,
  21     starting with the 0th, 1st, 2nd, ... (n-1)th character
  22
  23     >>> every_nth(string.ascii_lowercase, 5)
  24     ['afkpuz', 'bglqv', 'chmrw', 'dinsx', 'ejoty']
  25     >>> every_nth(string.ascii_lowercase, 1)
  26     ['abcdefghijklmnopqrstuvwxyz']
  27     >>> every_nth(string.ascii_lowercase, 26) # doctest: +NORMALIZE_WHITESPACE
  28     ['a', 'b', 'c', 'd', 'e', 'f', 'g', 'h', 'i', 'j', 'k', 'l', 'm', 'n',
  29      'o', 'p', 'q', 'r', 's', 't', 'u', 'v', 'w', 'x', 'y', 'z']
  30     >>> every_nth(string.ascii_lowercase, 5, fillvalue='!')
  31     ['afkpuz', 'bglqv!', 'chmrw!', 'dinsx!', 'ejoty!']
  32     """
  33     split_text = chunks(text, n, fillvalue)
  34     return [''.join(l) for l in zip_longest(*split_text, fillvalue=fillvalue)]
  35
  36 def combine_every_nth(split_text):
  37     """Reforms a text split into every_nth strings
  38
  39     >>> combine_every_nth(every_nth(string.ascii_lowercase, 5))
  40     'abcdefghijklmnopqrstuvwxyz'
  41     >>> combine_every_nth(every_nth(string.ascii_lowercase, 1))
  42     'abcdefghijklmnopqrstuvwxyz'
  43     >>> combine_every_nth(every_nth(string.ascii_lowercase, 26))
  44     'abcdefghijklmnopqrstuvwxyz'
  45     """
  46     return ''.join([''.join(l)
  47                     for l in zip_longest(*split_text, fillvalue='')])
  48
  49 def chunks(text, n, fillvalue=None):
  50     """Split a text into chunks of n characters
  51
  52     >>> chunks('abcdefghi', 3)
  53     ['abc', 'def', 'ghi']
  54     >>> chunks('abcdefghi', 4)
  55     ['abcd', 'efgh', 'i']
  56     >>> chunks('abcdefghi', 4, fillvalue='!')
  57     ['abcd', 'efgh', 'i!!!']
  58     """
  59     if fillvalue:
  60         padding = fillvalue[0] * (n - len(text) % n)
  61     else:
  62         padding = ''
  63     return [(text+padding)[i:i+n] for i in range(0, len(text), n)]
  64
  65 def transpose(items, transposition):
  66     """Moves items around according to the given transposition
  67
  68     >>> transpose(['a', 'b', 'c', 'd'], (0,1,2,3))
  69     ['a', 'b', 'c', 'd']
  70     >>> transpose(['a', 'b', 'c', 'd'], (3,1,2,0))
  71     ['d', 'b', 'c', 'a']
  72     >>> transpose([10,11,12,13,14,15], (3,2,4,1,5,0))
  73     [13, 12, 14, 11, 15, 10]
  74     """
  75     transposed = [''] * len(transposition)
  76     for p, t in enumerate(transposition):
  77        transposed[p] = items[t]
  78     return transposed
  79
  80 def untranspose(items, transposition):
  81     """Undoes a transpose
  82
  83     >>> untranspose(['a', 'b', 'c', 'd'], [0,1,2,3])
  84     ['a', 'b', 'c', 'd']
  85     >>> untranspose(['d', 'b', 'c', 'a'], [3,1,2,0])
  86     ['a', 'b', 'c', 'd']
  87     >>> untranspose([13, 12, 14, 11, 15, 10], [3,2,4,1,5,0])
  88     [10, 11, 12, 13, 14, 15]
  89     """
  90     transposed = [''] * len(transposition)
  91     for p, t in enumerate(transposition):
  92        transposed[t] = items[p]
  93     return transposed
  94
  95 def deduplicate(text):
  96     return list(collections.OrderedDict.fromkeys(text))
  97
  98
  99 def caesar_encipher_letter(accented_letter, shift):
 100     """Encipher a letter, given a shift amount
 101
 102     >>> caesar_encipher_letter('a', 1)
 103     'b'
 104     >>> caesar_encipher_letter('a', 2)
 105     'c'
 106     >>> caesar_encipher_letter('b', 2)
 107     'd'
 108     >>> caesar_encipher_letter('x', 2)
 109     'z'
 110     >>> caesar_encipher_letter('y', 2)
 111     'a'
 112     >>> caesar_encipher_letter('z', 2)
 113     'b'
 114     >>> caesar_encipher_letter('z', -1)
 115     'y'
 116     >>> caesar_encipher_letter('a', -1)
 117     'z'
 118     >>> caesar_encipher_letter('A', 1)
 119     'B'
 120     >>> caesar_encipher_letter('é', 1)
 121     'f'
 122     """
 123     letter = unaccent(accented_letter)
 124     if letter in string.ascii_letters:
 125         if letter in string.ascii_uppercase:
 126             alphabet_start = ord('A')
 127         else:
 128             alphabet_start = ord('a')
 129         return chr(((ord(letter) - alphabet_start + shift) % 26) +
 130                    alphabet_start)
 131     else:
 132         return letter
 133
 134 def caesar_decipher_letter(letter, shift):
 135     """Decipher a letter, given a shift amount
 136
 137     >>> caesar_decipher_letter('b', 1)
 138     'a'
 139     >>> caesar_decipher_letter('b', 2)
 140     'z'
 141     """
 142     return caesar_encipher_letter(letter, -shift)
 143
 144 def caesar_encipher(message, shift):
 145     """Encipher a message with the Caesar cipher of given shift
 146
 147     >>> caesar_encipher('abc', 1)
 148     'bcd'
 149     >>> caesar_encipher('abc', 2)
 150     'cde'
 151     >>> caesar_encipher('abcxyz', 2)
 152     'cdezab'
 153     >>> caesar_encipher('ab cx yz', 2)
 154     'cd ez ab'
 155     >>> caesar_encipher('Héllo World!', 2)
 156     'Jgnnq Yqtnf!'
 157     """
 158     enciphered = [caesar_encipher_letter(l, shift) for l in message]
 159     return ''.join(enciphered)
 160
 161 def caesar_decipher(message, shift):
 162     """Decipher a message with the Caesar cipher of given shift
 163
 164     >>> caesar_decipher('bcd', 1)
 165     'abc'
 166     >>> caesar_decipher('cde', 2)
 167     'abc'
 168     >>> caesar_decipher('cd ez ab', 2)
 169     'ab cx yz'
 170     >>> caesar_decipher('Jgnnq Yqtnf!', 2)
 171     'Hello World!'
 172     """
 173     return caesar_encipher(message, -shift)
 174
 175 def affine_encipher_letter(accented_letter, multiplier=1, adder=0, one_based=True):
 176     """Encipher a letter, given a multiplier and adder
 177
 178     >>> ''.join([affine_encipher_letter(l, 3, 5, True) \
 179             for l in string.ascii_uppercase])
 180     'HKNQTWZCFILORUXADGJMPSVYBE'
 181     >>> ''.join([affine_encipher_letter(l, 3, 5, False) \
 182             for l in string.ascii_uppercase])
 183     'FILORUXADGJMPSVYBEHKNQTWZC'
 184     """
 185     letter = unaccent(accented_letter)
 186     if letter in string.ascii_letters:
 187         if letter in string.ascii_uppercase:
 188             alphabet_start = ord('A')
 189         else:
 190             alphabet_start = ord('a')
 191         letter_number = ord(letter) - alphabet_start
 192         if one_based: letter_number += 1
 193         cipher_number = (letter_number * multiplier + adder) % 26
 194         if one_based: cipher_number -= 1
 195         return chr(cipher_number % 26 + alphabet_start)
 196     else:
 197         return letter
 198
 199 def affine_decipher_letter(letter, multiplier=1, adder=0, one_based=True):
 200     """Encipher a letter, given a multiplier and adder
 201
 202     >>> ''.join([affine_decipher_letter(l, 3, 5, True) \
 203             for l in 'HKNQTWZCFILORUXADGJMPSVYBE'])
 204     'ABCDEFGHIJKLMNOPQRSTUVWXYZ'
 205     >>> ''.join([affine_decipher_letter(l, 3, 5, False) \
 206             for l in 'FILORUXADGJMPSVYBEHKNQTWZC'])
 207     'ABCDEFGHIJKLMNOPQRSTUVWXYZ'
 208     """
 209     if letter in string.ascii_letters:
 210         if letter in string.ascii_uppercase:
 211             alphabet_start = ord('A')
 212         else:
 213             alphabet_start = ord('a')
 214         cipher_number = ord(letter) - alphabet_start
 215         if one_based: cipher_number += 1
 216         plaintext_number = (
 217             modular_division_table[multiplier]
 218                                   [(cipher_number - adder) % 26])
 219         if one_based: plaintext_number -= 1
 220         return chr(plaintext_number % 26 + alphabet_start)
 221     else:
 222         return letter
 223
 224 def affine_encipher(message, multiplier=1, adder=0, one_based=True):
 225     """Encipher a message
 226
 227     >>> affine_encipher('hours passed during which jerico tried every ' \
 228            'trick he could think of', 15, 22, True)
 229     'lmyfu bkuusd dyfaxw claol psfaom jfasd snsfg jfaoe ls omytd jlaxe mh'
 230     """
 231     enciphered = [affine_encipher_letter(l, multiplier, adder, one_based)
 232                   for l in message]
 233     return ''.join(enciphered)
 234
 235 def affine_decipher(message, multiplier=1, adder=0, one_based=True):
 236     """Decipher a message
 237
 238     >>> affine_decipher('lmyfu bkuusd dyfaxw claol psfaom jfasd snsfg ' \
 239            'jfaoe ls omytd jlaxe mh', 15, 22, True)
 240     'hours passed during which jerico tried every trick he could think of'
 241     """
 242     enciphered = [affine_decipher_letter(l, multiplier, adder, one_based)
 243                   for l in message]
 244     return ''.join(enciphered)
 245
 246
 247 class KeywordWrapAlphabet(Enum):
 248     from_a = 1
 249     from_last = 2
 250     from_largest = 3
 251
 252
 253 def keyword_cipher_alphabet_of(keyword, wrap_alphabet=KeywordWrapAlphabet.from_a):
 254     """Find the cipher alphabet given a keyword.
 255     wrap_alphabet controls how the rest of the alphabet is added
 256     after the keyword.
 257
 258     >>> keyword_cipher_alphabet_of('bayes')
 259     'bayescdfghijklmnopqrtuvwxz'
 260     >>> keyword_cipher_alphabet_of('bayes', KeywordWrapAlphabet.from_a)
 261     'bayescdfghijklmnopqrtuvwxz'
 262     >>> keyword_cipher_alphabet_of('bayes', KeywordWrapAlphabet.from_last)
 263     'bayestuvwxzcdfghijklmnopqr'
 264     >>> keyword_cipher_alphabet_of('bayes', KeywordWrapAlphabet.from_largest)
 265     'bayeszcdfghijklmnopqrtuvwx'
 266     """
 267     if wrap_alphabet == KeywordWrapAlphabet.from_a:
 268         cipher_alphabet = ''.join(deduplicate(sanitise(keyword) +
 269                                               string.ascii_lowercase))
 270     else:
 271         if wrap_alphabet == KeywordWrapAlphabet.from_last:
 272             last_keyword_letter = deduplicate(sanitise(keyword))[-1]
 273         else:
 274             last_keyword_letter = sorted(sanitise(keyword))[-1]
 275         last_keyword_position = string.ascii_lowercase.find(
 276             last_keyword_letter) + 1
 277         cipher_alphabet = ''.join(
 278             deduplicate(sanitise(keyword) +
 279                         string.ascii_lowercase[last_keyword_position:] +
 280                         string.ascii_lowercase))
 281     return cipher_alphabet
 282
 283
 284 def keyword_encipher(message, keyword, wrap_alphabet=KeywordWrapAlphabet.from_a):
 285     """Enciphers a message with a keyword substitution cipher.
 286     wrap_alphabet controls how the rest of the alphabet is added
 287     after the keyword.
 288     0 : from 'a'
 289     1 : from the last letter in the sanitised keyword
 290     2 : from the largest letter in the sanitised keyword
 291
 292     >>> keyword_encipher('test message', 'bayes')
 293     'rsqr ksqqbds'
 294     >>> keyword_encipher('test message', 'bayes', KeywordWrapAlphabet.from_a)
 295     'rsqr ksqqbds'
 296     >>> keyword_encipher('test message', 'bayes', KeywordWrapAlphabet.from_last)
 297     'lskl dskkbus'
 298     >>> keyword_encipher('test message', 'bayes', KeywordWrapAlphabet.from_largest)
 299     'qspq jsppbcs'
 300     """
 301     cipher_alphabet = keyword_cipher_alphabet_of(keyword, wrap_alphabet)
 302     cipher_translation = ''.maketrans(string.ascii_lowercase, cipher_alphabet)
 303     return unaccent(message).lower().translate(cipher_translation)
 304
 305 def keyword_decipher(message, keyword, wrap_alphabet=KeywordWrapAlphabet.from_a):
 306     """Deciphers a message with a keyword substitution cipher.
 307     wrap_alphabet controls how the rest of the alphabet is added
 308     after the keyword.
 309     0 : from 'a'
 310     1 : from the last letter in the sanitised keyword
 311     2 : from the largest letter in the sanitised keyword
 312
 313     >>> keyword_decipher('rsqr ksqqbds', 'bayes')
 314     'test message'
 315     >>> keyword_decipher('rsqr ksqqbds', 'bayes', KeywordWrapAlphabet.from_a)
 316     'test message'
 317     >>> keyword_decipher('lskl dskkbus', 'bayes', KeywordWrapAlphabet.from_last)
 318     'test message'
 319     >>> keyword_decipher('qspq jsppbcs', 'bayes', KeywordWrapAlphabet.from_largest)
 320     'test message'
 321     """
 322     cipher_alphabet = keyword_cipher_alphabet_of(keyword, wrap_alphabet)
 323     cipher_translation = ''.maketrans(cipher_alphabet, string.ascii_lowercase)
 324     return message.lower().translate(cipher_translation)
 325
 326
 327 def vigenere_encipher(message, keyword):
 328     """Vigenere encipher
 329
 330     >>> vigenere_encipher('hello', 'abc')
 331     'hfnlp'
 332     """
 333     shifts = [ord(l) - ord('a') for l in sanitise(keyword)]
 334     pairs = zip(message, cycle(shifts))
 335     return ''.join([caesar_encipher_letter(l, k) for l, k in pairs])
 336
 337 def vigenere_decipher(message, keyword):
 338     """Vigenere decipher
 339
 340     >>> vigenere_decipher('hfnlp', 'abc')
 341     'hello'
 342     """
 343     shifts = [ord(l) - ord('a') for l in sanitise(keyword)]
 344     pairs = zip(message, cycle(shifts))
 345     return ''.join([caesar_decipher_letter(l, k) for l, k in pairs])
 346
 347 beaufort_encipher=vigenere_decipher
 348 beaufort_decipher=vigenere_encipher
 349
 350
 351 def transpositions_of(keyword):
 352     """Finds the transpostions given by a keyword. For instance, the keyword
 353     'clever' rearranges to 'celrv', so the first column (0) stays first, the
 354     second column (1) moves to third, the third column (2) moves to second,
 355     and so on.
 356
 357     If passed a tuple, assume it's already a transposition and just return it.
 358
 359     >>> transpositions_of('clever')
 360     (0, 2, 1, 4, 3)
 361     >>> transpositions_of('fred')
 362     (3, 2, 0, 1)
 363     >>> transpositions_of((3, 2, 0, 1))
 364     (3, 2, 0, 1)
 365     """
 366     if isinstance(keyword, tuple):
 367         return keyword
 368     else:
 369         key = deduplicate(keyword)
 370         transpositions = tuple(key.index(l) for l in sorted(key))
 371         return transpositions
 372
 373 def pad(message_len, group_len, fillvalue):
 374     padding_length = group_len - message_len % group_len
 375     if padding_length == group_len: padding_length = 0
 376     padding = ''
 377     for i in range(padding_length):
 378         if callable(fillvalue):
 379             padding += fillvalue()
 380         else:
 381             padding += fillvalue
 382     return padding
 383
 384 def column_transposition_encipher(message, keyword, fillvalue=' ',
 385       fillcolumnwise=False,
 386       emptycolumnwise=False):
 387     """Enciphers using the column transposition cipher.
 388     Message is padded to allow all rows to be the same length.
 389
 390     >>> column_transposition_encipher('hellothere', 'abcdef', fillcolumnwise=True)
 391     'hlohr eltee '
 392     >>> column_transposition_encipher('hellothere', 'abcdef', fillcolumnwise=True, emptycolumnwise=True)
 393     'hellothere  '
 394     >>> column_transposition_encipher('hellothere', 'abcdef')
 395     'hellothere  '
 396     >>> column_transposition_encipher('hellothere', 'abcde')
 397     'hellothere'
 398     >>> column_transposition_encipher('hellothere', 'abcde', fillcolumnwise=True, emptycolumnwise=True)
 399     'hellothere'
 400     >>> column_transposition_encipher('hellothere', 'abcde', fillcolumnwise=True, emptycolumnwise=False)
 401     'hlohreltee'
 402     >>> column_transposition_encipher('hellothere', 'abcde', fillcolumnwise=False, emptycolumnwise=True)
 403     'htehlelroe'
 404     >>> column_transposition_encipher('hellothere', 'abcde', fillcolumnwise=False, emptycolumnwise=False)
 405     'hellothere'
 406     >>> column_transposition_encipher('hellothere', 'clever', fillcolumnwise=True, emptycolumnwise=True)
 407     'heotllrehe'
 408     >>> column_transposition_encipher('hellothere', 'clever', fillcolumnwise=True, emptycolumnwise=False)
 409     'holrhetlee'
 410     >>> column_transposition_encipher('hellothere', 'clever', fillcolumnwise=False, emptycolumnwise=True)
 411     'htleehoelr'
 412     >>> column_transposition_encipher('hellothere', 'clever', fillcolumnwise=False, emptycolumnwise=False)
 413     'hleolteher'
 414     >>> column_transposition_encipher('hellothere', 'cleverly')
 415     'hleolthre e '
 416     >>> column_transposition_encipher('hellothere', 'cleverly', fillvalue='!')
 417     'hleolthre!e!'
 418     >>> column_transposition_encipher('hellothere', 'cleverly', fillvalue=lambda: '*')
 419     'hleolthre*e*'
 420     """
 421     transpositions = transpositions_of(keyword)
 422     message += pad(len(message), len(transpositions), fillvalue)
 423     if fillcolumnwise:
 424         rows = every_nth(message, len(message) // len(transpositions))
 425     else:
 426         rows = chunks(message, len(transpositions))
 427     transposed = [transpose(r, transpositions) for r in rows]
 428     if emptycolumnwise:
 429         return combine_every_nth(transposed)
 430     else:
 431         return ''.join(chain(*transposed))
 432
 433 def column_transposition_decipher(message, keyword, fillvalue=' ',
 434       fillcolumnwise=False,
 435       emptycolumnwise=False):
 436     """Deciphers using the column transposition cipher.
 437     Message is padded to allow all rows to be the same length.
 438
 439     >>> column_transposition_decipher('hellothere', 'abcde', fillcolumnwise=True, emptycolumnwise=True)
 440     'hellothere'
 441     >>> column_transposition_decipher('hlohreltee', 'abcde', fillcolumnwise=True, emptycolumnwise=False)
 442     'hellothere'
 443     >>> column_transposition_decipher('htehlelroe', 'abcde', fillcolumnwise=False, emptycolumnwise=True)
 444     'hellothere'
 445     >>> column_transposition_decipher('hellothere', 'abcde', fillcolumnwise=False, emptycolumnwise=False)
 446     'hellothere'
 447     >>> column_transposition_decipher('heotllrehe', 'clever', fillcolumnwise=True, emptycolumnwise=True)
 448     'hellothere'
 449     >>> column_transposition_decipher('holrhetlee', 'clever', fillcolumnwise=True, emptycolumnwise=False)
 450     'hellothere'
 451     >>> column_transposition_decipher('htleehoelr', 'clever', fillcolumnwise=False, emptycolumnwise=True)
 452     'hellothere'
 453     >>> column_transposition_decipher('hleolteher', 'clever', fillcolumnwise=False, emptycolumnwise=False)
 454     'hellothere'
 455     """
 456     transpositions = transpositions_of(keyword)
 457     message += pad(len(message), len(transpositions), fillvalue)
 458     if emptycolumnwise:
 459         rows = every_nth(message, len(message) // len(transpositions))
 460     else:
 461         rows = chunks(message, len(transpositions))
 462     untransposed = [untranspose(r, transpositions) for r in rows]
 463     if fillcolumnwise:
 464         return combine_every_nth(untransposed)
 465     else:
 466         return ''.join(chain(*untransposed))
 467
 468 def scytale_encipher(message, rows, fillvalue=' '):
 469     """Enciphers using the scytale transposition cipher.
 470     Message is padded with spaces to allow all rows to be the same length.
 471
 472     >>> scytale_encipher('thequickbrownfox', 3)
 473     'tcnhkfeboqrxuo iw '
 474     >>> scytale_encipher('thequickbrownfox', 4)
 475     'tubnhirfecooqkwx'
 476     >>> scytale_encipher('thequickbrownfox', 5)
 477     'tubn hirf ecoo qkwx '
 478     >>> scytale_encipher('thequickbrownfox', 6)
 479     'tqcrnxhukof eibwo '
 480     >>> scytale_encipher('thequickbrownfox', 7)
 481     'tqcrnx hukof  eibwo  '
 482     """
 483     # transpositions = [i for i in range(math.ceil(len(message) / rows))]
 484     # return column_transposition_encipher(message, transpositions,
 485     #     fillvalue=fillvalue, fillcolumnwise=False, emptycolumnwise=True)
 486     transpositions = [i for i in range(rows)]
 487     return column_transposition_encipher(message, transpositions,
 488         fillvalue=fillvalue, fillcolumnwise=True, emptycolumnwise=False)
 489
 490 def scytale_decipher(message, rows):
 491     """Deciphers using the scytale transposition cipher.
 492     Assumes the message is padded so that all rows are the same length.
 493
 494     >>> scytale_decipher('tcnhkfeboqrxuo iw ', 3)
 495     'thequickbrownfox  '
 496     >>> scytale_decipher('tubnhirfecooqkwx', 4)
 497     'thequickbrownfox'
 498     >>> scytale_decipher('tubn hirf ecoo qkwx ', 5)
 499     'thequickbrownfox    '
 500     >>> scytale_decipher('tqcrnxhukof eibwo ', 6)
 501     'thequickbrownfox  '
 502     >>> scytale_decipher('tqcrnx hukof  eibwo  ', 7)
 503     'thequickbrownfox     '
 504     """
 505     # transpositions = [i for i in range(math.ceil(len(message) / rows))]
 506     # return column_transposition_decipher(message, transpositions,
 507     #     fillcolumnwise=False, emptycolumnwise=True)
 508     transpositions = [i for i in range(rows)]
 509     return column_transposition_decipher(message, transpositions,
 510         fillcolumnwise=True, emptycolumnwise=False)
 511
 512
 513 def railfence_encipher(message, height, fillvalue=''):
 514     """Railfence cipher.
 515     Works by splitting the text into sections, then reading across them to
 516     generate the rows in the cipher. The rows are then combined to form the
 517     ciphertext.
 518
 519     Example: the plaintext "hellotherefriends", with a height of four, written
 520     out in the railfence as
 521        h h i
 522        etere*
 523        lorfns
 524        l e d
 525     (with the * showing the one character to finish the last section).
 526     Each 'section' is two columns, but unfolded. In the example, the first
 527     section is 'hellot'.
 528
 529     >>> railfence_encipher('hellothereavastmeheartiesthisisalongpieceoftextfortestingrailfenceciphers', 2, fillvalue='!')
 530     'hlohraateerishsslnpeefetotsigaleccpeselteevsmhatetiiaogicotxfretnrifneihr!'
 531     >>> railfence_encipher('hellothereavastmeheartiesthisisalongpieceoftextfortestingrailfenceciphers', 3, fillvalue='!')
 532     'horaersslpeeosglcpselteevsmhatetiiaogicotxfretnrifneihr!!lhateihsnefttiaece!'
 533     >>> railfence_encipher('hellothereavastmeheartiesthisisalongpieceoftextfortestingrailfenceciphers', 5, fillvalue='!')
 534     'hresleogcseeemhetaocofrnrner!!lhateihsnefttiaece!!ltvsatiigitxetifih!!oarspeslp!'
 535     >>> railfence_encipher('hellothereavastmeheartiesthisisalongpieceoftextfortestingrailfenceciphers', 10, fillvalue='!')
 536     'hepisehagitnr!!lernesge!!lmtocerh!!otiletap!!tseaorii!!hassfolc!!evtitffe!!rahsetec!!eixn!'
 537     >>> railfence_encipher('hellothereavastmeheartiesthisisalongpieceoftextfortestingrailfenceciphers', 3)
 538     'horaersslpeeosglcpselteevsmhatetiiaogicotxfretnrifneihrlhateihsnefttiaece'
 539     >>> railfence_encipher('hellothereavastmeheartiesthisisalongpieceoftextfortestingrailfenceciphers', 5)
 540     'hresleogcseeemhetaocofrnrnerlhateihsnefttiaeceltvsatiigitxetifihoarspeslp'
 541     >>> railfence_encipher('hellothereavastmeheartiesthisisalongpieceoftextfortestingrailfenceciphers', 7)
 542     'haspolsevsetgifrifrlatihnettaeelemtiocxernhorersleesgcptehaiaottneihesfic'
 543     """
 544     sections = chunks(message, (height - 1) * 2, fillvalue=fillvalue)
 545     n_sections = len(sections)
 546     # Add the top row
 547     rows = [''.join([s[0] for s in sections])]
 548     # process the middle rows of the grid
 549     for r in range(1, height-1):
 550         rows += [''.join([s[r:r+1] + s[height*2-r-2:height*2-r-1] for s in sections])]
 551     # process the bottom row
 552     rows += [''.join([s[height - 1:height] for s in sections])]
 553     # rows += [' '.join([s[height - 1] for s in sections])]
 554     return ''.join(rows)
 555
 556 def railfence_decipher(message, height, fillvalue=''):
 557     """Railfence decipher.
 558     Works by reconstructing the grid used to generate the ciphertext, then
 559     unfolding the sections so the text can be concatenated together.
 560
 561     Example: given the ciphertext 'hhieterelorfnsled' and a height of 4, first
 562     work out that the second row has a character missing, find the rows of the
 563     grid, then split the section into its two columns.
 564
 565     'hhieterelorfnsled' is split into
 566         h h i
 567         etere
 568         lorfns
 569         l e d
 570     (spaces added for clarity), which is stored in 'rows'. This is then split
 571     into 'down_rows' and 'up_rows':
 572
 573     down_rows:
 574        hhi
 575        eee
 576        lrn
 577        led
 578
 579     up_rows:
 580        tr
 581        ofs
 582
 583     These are then zipped together (after the up_rows are reversed) to recover
 584     the plaintext.
 585
 586     Most of the procedure is about finding the correct lengths for each row then
 587     splitting the ciphertext into those rows.
 588
 589     >>> railfence_decipher('hlohraateerishsslnpeefetotsigaleccpeselteevsmhatetiiaogicotxfretnrifneihr!', 2).strip('!')
 590     'hellothereavastmeheartiesthisisalongpieceoftextfortestingrailfenceciphers'
 591     >>> railfence_decipher('horaersslpeeosglcpselteevsmhatetiiaogicotxfretnrifneihr!!lhateihsnefttiaece!', 3).strip('!')
 592     'hellothereavastmeheartiesthisisalongpieceoftextfortestingrailfenceciphers'
 593     >>> railfence_decipher('hresleogcseeemhetaocofrnrner!!lhateihsnefttiaece!!ltvsatiigitxetifih!!oarspeslp!', 5).strip('!')
 594     'hellothereavastmeheartiesthisisalongpieceoftextfortestingrailfenceciphers'
 595     >>> railfence_decipher('hepisehagitnr!!lernesge!!lmtocerh!!otiletap!!tseaorii!!hassfolc!!evtitffe!!rahsetec!!eixn!', 10).strip('!')
 596     'hellothereavastmeheartiesthisisalongpieceoftextfortestingrailfenceciphers'
 597     >>> railfence_decipher('horaersslpeeosglcpselteevsmhatetiiaogicotxfretnrifneihrlhateihsnefttiaece', 3)
 598     'hellothereavastmeheartiesthisisalongpieceoftextfortestingrailfenceciphers'
 599     >>> railfence_decipher('hresleogcseeemhetaocofrnrnerlhateihsnefttiaeceltvsatiigitxetifihoarspeslp', 5)
 600     'hellothereavastmeheartiesthisisalongpieceoftextfortestingrailfenceciphers'
 601     >>> railfence_decipher('haspolsevsetgifrifrlatihnettaeelemtiocxernhorersleesgcptehaiaottneihesfic', 7)
 602     'hellothereavastmeheartiesthisisalongpieceoftextfortestingrailfenceciphers'
 603     """
 604     # find the number and size of the sections, including how many characters
 605     #   are missing for a full grid
 606     n_sections = math.ceil(len(message) / ((height - 1) * 2))
 607     padding_to_add = n_sections * (height - 1) * 2 - len(message)
 608     # row_lengths are for the both up rows and down rows
 609     row_lengths = [n_sections] * (height - 1) * 2
 610     for i in range((height - 1) * 2 - 1, (height - 1) * 2 - (padding_to_add + 1), -1):
 611         row_lengths[i] -= 1
 612     # folded_rows are the combined row lengths in the middle of the railfence
 613     folded_row_lengths = [row_lengths[0]]
 614     for i in range(1, height-1):
 615         folded_row_lengths += [row_lengths[i] + row_lengths[-i]]
 616     folded_row_lengths += [row_lengths[height - 1]]
 617     # find the rows that form the railfence grid
 618     rows = []
 619     row_start = 0
 620     for i in folded_row_lengths:
 621         rows += [message[row_start:row_start + i]]
 622         row_start += i
 623     # split the rows into the 'down_rows' (those that form the first column of
 624     #   a section) and the 'up_rows' (those that ofrm the second column of a
 625     #   section).
 626     down_rows = [rows[0]]
 627     up_rows = []
 628     for i in range(1, height-1):
 629         down_rows += [''.join([c for n, c in enumerate(rows[i]) if n % 2 == 0])]
 630         up_rows += [''.join([c for n, c in enumerate(rows[i]) if n % 2 == 1])]
 631     down_rows += [rows[-1]]
 632     up_rows.reverse()
 633     return ''.join(c for r in zip_longest(*(down_rows + up_rows), fillvalue='') for c in r)
 634
 635 def make_cadenus_keycolumn(doubled_letters = 'vw', start='a', reverse=False):
 636     """Makes the key column for a Cadenus cipher (the column down between the
 637         rows of letters)
 638
 639     >>> make_cadenus_keycolumn()['a']
 640     0
 641     >>> make_cadenus_keycolumn()['b']
 642     1
 643     >>> make_cadenus_keycolumn()['c']
 644     2
 645     >>> make_cadenus_keycolumn()['v']
 646     21
 647     >>> make_cadenus_keycolumn()['w']
 648     21
 649     >>> make_cadenus_keycolumn()['z']
 650     24
 651     >>> make_cadenus_keycolumn(doubled_letters='ij', start='b', reverse=True)['a']
 652     1
 653     >>> make_cadenus_keycolumn(doubled_letters='ij', start='b', reverse=True)['b']
 654     0
 655     >>> make_cadenus_keycolumn(doubled_letters='ij', start='b', reverse=True)['c']
 656     24
 657     >>> make_cadenus_keycolumn(doubled_letters='ij', start='b', reverse=True)['i']
 658     18
 659     >>> make_cadenus_keycolumn(doubled_letters='ij', start='b', reverse=True)['j']
 660     18
 661     >>> make_cadenus_keycolumn(doubled_letters='ij', start='b', reverse=True)['v']
 662     6
 663     >>> make_cadenus_keycolumn(doubled_letters='ij', start='b', reverse=True)['z']
 664     2
 665     """
 666     index_to_remove = string.ascii_lowercase.find(doubled_letters[0])
 667     short_alphabet = string.ascii_lowercase[:index_to_remove] + string.ascii_lowercase[index_to_remove+1:]
 668     if reverse:
 669         short_alphabet = ''.join(reversed(short_alphabet))
 670     start_pos = short_alphabet.find(start)
 671     rotated_alphabet = short_alphabet[start_pos:] + short_alphabet[:start_pos]
 672     keycolumn = {l: i for i, l in enumerate(rotated_alphabet)}
 673     keycolumn[doubled_letters[0]] = keycolumn[doubled_letters[1]]
 674     return keycolumn
 675
 676 def cadenus_encipher(message, keyword, keycolumn, fillvalue='a'):
 677     """Encipher with the Cadenus cipher
 678
 679     >>> cadenus_encipher(sanitise('Whoever has made a voyage up the Hudson ' \
 680                                   'must remember the Kaatskill mountains. ' \
 681                                   'They are a dismembered branch of the great'), \
 682                 'wink', \
 683                 make_cadenus_keycolumn(doubled_letters='vw', start='a', reverse=True))
 684     'antodeleeeuhrsidrbhmhdrrhnimefmthgeaetakseomehetyaasuvoyegrastmmuuaeenabbtpchehtarorikswosmvaleatned'
 685     >>> cadenus_encipher(sanitise('a severe limitation on the usefulness of ' \
 686                                   'the cadenus is that every message must be ' \
 687                                   'a multiple of twenty-five letters long'), \
 688                 'easy', \
 689                 make_cadenus_keycolumn(doubled_letters='vw', start='a', reverse=True))
 690     'systretomtattlusoatleeesfiyheasdfnmschbhneuvsnpmtofarenuseieeieltarlmentieetogevesitfaisltngeeuvowul'
 691     """
 692     rows = chunks(message, len(message) // 25, fillvalue=fillvalue)
 693     columns = zip(*rows)
 694     rotated_columns = [col[start:] + col[:start] for start, col in zip([keycolumn[l] for l in keyword], columns)]
 695     rotated_rows = zip(*rotated_columns)
 696     transpositions = transpositions_of(keyword)
 697     transposed = [transpose(r, transpositions) for r in rotated_rows]
 698     return ''.join(chain(*transposed))
 699
 700 def cadenus_decipher(message, keyword, keycolumn, fillvalue='a'):
 701     """
 702     >>> cadenus_decipher('antodeleeeuhrsidrbhmhdrrhnimefmthgeaetakseomehetyaa' \
 703                          'suvoyegrastmmuuaeenabbtpchehtarorikswosmvaleatned', \
 704                  'wink', \
 705                  make_cadenus_keycolumn(reverse=True))
 706     'whoeverhasmadeavoyageupthehudsonmustrememberthekaatskillmountainstheyareadismemberedbranchofthegreat'
 707     >>> cadenus_decipher('systretomtattlusoatleeesfiyheasdfnmschbhneuvsnpmtof' \
 708                         'arenuseieeieltarlmentieetogevesitfaisltngeeuvowul', \
 709                  'easy', \
 710                  make_cadenus_keycolumn(reverse=True))
 711     'aseverelimitationontheusefulnessofthecadenusisthateverymessagemustbeamultipleoftwentyfiveletterslong'
 712     """
 713     rows = chunks(message, len(message) // 25, fillvalue=fillvalue)
 714     transpositions = transpositions_of(keyword)
 715     untransposed_rows = [untranspose(r, transpositions) for r in rows]
 716     columns = zip(*untransposed_rows)
 717     rotated_columns = [col[-start:] + col[:-start] for start, col in zip([keycolumn[l] for l in keyword], columns)]
 718     rotated_rows = zip(*rotated_columns)
 719     # return rotated_columns
 720     return ''.join(chain(*rotated_rows))
 721
 722
 723 def hill_encipher(matrix, message_letters, fillvalue='a'):
 724     """Hill cipher
 725
 726     >>> hill_encipher(np.matrix([[7,8], [11,11]]), 'hellothere')
 727     'drjiqzdrvx'
 728     >>> hill_encipher(np.matrix([[6, 24, 1], [13, 16, 10], [20, 17, 15]]), \
 729         'hello there')
 730     'tfjflpznvyac'
 731     """
 732     n = len(matrix)
 733     sanitised_message = sanitise(message_letters)
 734     if len(sanitised_message) % n != 0:
 735         padding = fillvalue[0] * (n - len(sanitised_message) % n)
 736     else:
 737         padding = ''
 738     message = [ord(c) - ord('a') for c in sanitised_message + padding]
 739     message_chunks = [message[i:i+n] for i in range(0, len(message), n)]
 740     # message_chunks = chunks(message, len(matrix), fillvalue=None)
 741     enciphered_chunks = [((matrix * np.matrix(c).T).T).tolist()[0]
 742             for c in message_chunks]
 743     return ''.join([chr(int(round(l)) % 26 + ord('a'))
 744             for l in sum(enciphered_chunks, [])])
 745
 746 def hill_decipher(matrix, message, fillvalue='a'):
 747     """Hill cipher
 748
 749     >>> hill_decipher(np.matrix([[7,8], [11,11]]), 'drjiqzdrvx')
 750     'hellothere'
 751     >>> hill_decipher(np.matrix([[6, 24, 1], [13, 16, 10], [20, 17, 15]]), \
 752         'tfjflpznvyac')
 753     'hellothereaa'
 754     """
 755     adjoint = linalg.det(matrix)*linalg.inv(matrix)
 756     inverse_determinant = modular_division_table[int(round(linalg.det(matrix))) % 26][1]
 757     inverse_matrix = (inverse_determinant * adjoint) % 26
 758     return hill_encipher(inverse_matrix, message, fillvalue)
 759
 760
 761 # Where each piece of text ends up in the AMSCO transpositon cipher.
 762 # 'index' shows where the slice appears in the plaintext, with the slice
 763 # from 'start' to 'end'
 764 AmscoSlice = collections.namedtuple('AmscoSlice', ['index', 'start', 'end'])
 765
 766 class AmscoFillStyle(Enum):
 767     continuous = 1
 768     same_each_row = 2
 769     reverse_each_row = 3
 770
 771 def amsco_transposition_positions(message, keyword,
 772       fillpattern=(1, 2),
 773       fillstyle=AmscoFillStyle.continuous,
 774       fillcolumnwise=False,
 775       emptycolumnwise=True):
 776     """Creates the grid for the AMSCO transposition cipher. Each element in the
 777     grid shows the index of that slice and the start and end positions of the
 778     plaintext that go to make it up.
 779
 780     >>> amsco_transposition_positions(string.ascii_lowercase, 'freddy', \
 781         fillpattern=(1, 2)) # doctest:  +NORMALIZE_WHITESPACE
 782     [[AmscoSlice(index=3, start=4, end=6),
 783      AmscoSlice(index=2, start=3, end=4),
 784      AmscoSlice(index=0, start=0, end=1),
 785      AmscoSlice(index=1, start=1, end=3),
 786      AmscoSlice(index=4, start=6, end=7)],
 787     [AmscoSlice(index=8, start=12, end=13),
 788      AmscoSlice(index=7, start=10, end=12),
 789      AmscoSlice(index=5, start=7, end=9),
 790      AmscoSlice(index=6, start=9, end=10),
 791      AmscoSlice(index=9, start=13, end=15)],
 792     [AmscoSlice(index=13, start=19, end=21),
 793      AmscoSlice(index=12, start=18, end=19),
 794      AmscoSlice(index=10, start=15, end=16),
 795      AmscoSlice(index=11, start=16, end=18),
 796      AmscoSlice(index=14, start=21, end=22)],
 797     [AmscoSlice(index=18, start=27, end=28),
 798      AmscoSlice(index=17, start=25, end=27),
 799      AmscoSlice(index=15, start=22, end=24),
 800      AmscoSlice(index=16, start=24, end=25),
 801      AmscoSlice(index=19, start=28, end=30)]]
 802     """
 803     transpositions = transpositions_of(keyword)
 804     fill_iterator = cycle(fillpattern)
 805     indices = count()
 806     message_length = len(message)
 807
 808     current_position = 0
 809     grid = []
 810     current_fillpattern = fillpattern
 811     while current_position < message_length:
 812         row = []
 813         if fillstyle == AmscoFillStyle.same_each_row:
 814             fill_iterator = cycle(fillpattern)
 815         if fillstyle == AmscoFillStyle.reverse_each_row:
 816             fill_iterator = cycle(current_fillpattern)
 817         for _ in range(len(transpositions)):
 818             index = next(indices)
 819             gap = next(fill_iterator)
 820             row += [AmscoSlice(index, current_position, current_position + gap)]
 821             current_position += gap
 822         grid += [row]
 823         if fillstyle == AmscoFillStyle.reverse_each_row:
 824             current_fillpattern = list(reversed(current_fillpattern))
 825     return [transpose(r, transpositions) for r in grid]
 826
 827 def amsco_transposition_encipher(message, keyword,
 828     fillpattern=(1,2), fillstyle=AmscoFillStyle.reverse_each_row):
 829     """AMSCO transposition encipher.
 830
 831     >>> amsco_transposition_encipher('hellothere', 'abc', fillpattern=(1, 2))
 832     'hoteelhler'
 833     >>> amsco_transposition_encipher('hellothere', 'abc', fillpattern=(2, 1))
 834     'hetelhelor'
 835     >>> amsco_transposition_encipher('hellothere', 'acb', fillpattern=(1, 2))
 836     'hotelerelh'
 837     >>> amsco_transposition_encipher('hellothere', 'acb', fillpattern=(2, 1))
 838     'hetelorlhe'
 839     >>> amsco_transposition_encipher('hereissometexttoencipher', 'cipher', fillpattern=(1, 2))
 840     'hecsoisttererteipexhomen'
 841     >>> amsco_transposition_encipher('hereissometexttoencipher', 'cipher', fillpattern=(2, 1))
 842     'heetcisooestrrepeixthemn'
 843     >>> amsco_transposition_encipher('hereissometexttoencipher', 'cipher', fillpattern=(1, 3, 2))
 844     'hxomeiphscerettoisenteer'
 845     """
 846     grid = amsco_transposition_positions(message, keyword,
 847         fillpattern=fillpattern, fillstyle=fillstyle)
 848     ct_as_grid = [[message[s.start:s.end] for s in r] for r in grid]
 849     return combine_every_nth(ct_as_grid)
 850
 851
 852 def amsco_transposition_decipher(message, keyword,
 853     fillpattern=(1,2), fillstyle=AmscoFillStyle.reverse_each_row):
 854     """AMSCO transposition decipher
 855
 856     >>> amsco_transposition_decipher('hoteelhler', 'abc', fillpattern=(1, 2))
 857     'hellothere'
 858     >>> amsco_transposition_decipher('hetelhelor', 'abc', fillpattern=(2, 1))
 859     'hellothere'
 860     >>> amsco_transposition_decipher('hotelerelh', 'acb', fillpattern=(1, 2))
 861     'hellothere'
 862     >>> amsco_transposition_decipher('hetelorlhe', 'acb', fillpattern=(2, 1))
 863     'hellothere'
 864     >>> amsco_transposition_decipher('hecsoisttererteipexhomen', 'cipher', fillpattern=(1, 2))
 865     'hereissometexttoencipher'
 866     >>> amsco_transposition_decipher('heetcisooestrrepeixthemn', 'cipher', fillpattern=(2, 1))
 867     'hereissometexttoencipher'
 868     >>> amsco_transposition_decipher('hxomeiphscerettoisenteer', 'cipher', fillpattern=(1, 3, 2))
 869     'hereissometexttoencipher'
 870     """
 871
 872     grid = amsco_transposition_positions(message, keyword,
 873         fillpattern=fillpattern, fillstyle=fillstyle)
 874     transposed_sections = [s for c in [l for l in zip(*grid)] for s in c]
 875     plaintext_list = [''] * len(transposed_sections)
 876     current_pos = 0
 877     for slice in transposed_sections:
 878         plaintext_list[slice.index] = message[current_pos:current_pos-slice.start+slice.end][:len(message[slice.start:slice.end])]
 879         current_pos += len(message[slice.start:slice.end])
 880     return ''.join(plaintext_list)
 881
 882
 883 class PocketEnigma(object):
 884     """A pocket enigma machine
 885     The wheel is internally represented as a 26-element list self.wheel_map,
 886     where wheel_map[i] == j shows that the position i places on from the arrow
 887     maps to the position j places on.
 888     """
 889     def __init__(self, wheel=1, position='a'):
 890         """initialise the pocket enigma, including which wheel to use and the
 891         starting position of the wheel.
 892
 893         The wheel is either 1 or 2 (the predefined wheels) or a list of letter
 894         pairs.
 895
 896         The position is the letter pointed to by the arrow on the wheel.
 897
 898         >>> pe.wheel_map
 899         [25, 4, 23, 10, 1, 7, 9, 5, 12, 6, 3, 17, 8, 14, 13, 21, 19, 11, 20, 16, 18, 15, 24, 2, 22, 0]
 900         >>> pe.position
 901         0
 902         """
 903         self.wheel1 = [('a', 'z'), ('b', 'e'), ('c', 'x'), ('d', 'k'),
 904             ('f', 'h'), ('g', 'j'), ('i', 'm'), ('l', 'r'), ('n', 'o'),
 905             ('p', 'v'), ('q', 't'), ('s', 'u'), ('w', 'y')]
 906         self.wheel2 = [('a', 'c'), ('b', 'd'), ('e', 'w'), ('f', 'i'),
 907             ('g', 'p'), ('h', 'm'), ('j', 'k'), ('l', 'n'), ('o', 'q'),
 908             ('r', 'z'), ('s', 'u'), ('t', 'v'), ('x', 'y')]
 909         if wheel == 1:
 910             self.make_wheel_map(self.wheel1)
 911         elif wheel == 2:
 912             self.make_wheel_map(self.wheel2)
 913         else:
 914             self.validate_wheel_spec(wheel)
 915             self.make_wheel_map(wheel)
 916         if position in string.ascii_lowercase:
 917             self.position = ord(position) - ord('a')
 918         else:
 919             self.position = position
 920
 921     def make_wheel_map(self, wheel_spec):
 922         """Expands a wheel specification from a list of letter-letter pairs
 923         into a full wheel_map.
 924
 925         >>> pe.make_wheel_map(pe.wheel2)
 926         [2, 3, 0, 1, 22, 8, 15, 12, 5, 10, 9, 13, 7, 11, 16, 6, 14, 25, 20, 21, 18, 19, 4, 24, 23, 17]
 927         """
 928         self.validate_wheel_spec(wheel_spec)
 929         self.wheel_map = [0] * 26
 930         for p in wheel_spec:
 931             self.wheel_map[ord(p[0]) - ord('a')] = ord(p[1]) - ord('a')
 932             self.wheel_map[ord(p[1]) - ord('a')] = ord(p[0]) - ord('a')
 933         return self.wheel_map
 934
 935     def validate_wheel_spec(self, wheel_spec):
 936         """Validates that a wheel specificaiton will turn into a valid wheel
 937         map.
 938
 939         >>> pe.validate_wheel_spec([])
 940         Traceback (most recent call last):
 941             ...
 942         ValueError: Wheel specification has 0 pairs, requires 13
 943         >>> pe.validate_wheel_spec([('a', 'b', 'c')]*13)
 944         Traceback (most recent call last):
 945             ...
 946         ValueError: Not all mappings in wheel specificationhave two elements
 947         >>> pe.validate_wheel_spec([('a', 'b')]*13)
 948         Traceback (most recent call last):
 949             ...
 950         ValueError: Wheel specification does not contain 26 letters
 951         """
 952         if len(wheel_spec) != 13:
 953             raise ValueError("Wheel specification has {} pairs, requires 13".
 954                 format(len(wheel_spec)))
 955         for p in wheel_spec:
 956             if len(p) != 2:
 957                 raise ValueError("Not all mappings in wheel specification"
 958                     "have two elements")
 959         if len(set([p[0] for p in wheel_spec] +
 960                     [p[1] for p in wheel_spec])) != 26:
 961             raise ValueError("Wheel specification does not contain 26 letters")
 962
 963     def encipher_letter(self, letter):
 964         """Enciphers a single letter, by advancing the wheel before looking up
 965         the letter on the wheel.
 966
 967         >>> pe.set_position('f')
 968         5
 969         >>> pe.encipher_letter('k')
 970         'h'
 971         """
 972         self.advance()
 973         return self.lookup(letter)
 974     decipher_letter = encipher_letter
 975
 976     def lookup(self, letter):
 977         """Look up what a letter enciphers to, without turning the wheel.
 978
 979         >>> pe.set_position('f')
 980         5
 981         >>> ''.join([pe.lookup(l) for l in string.ascii_lowercase])
 982         'udhbfejcpgmokrliwntsayqzvx'
 983         >>> pe.lookup('A')
 984         ''
 985         """
 986         if letter in string.ascii_lowercase:
 987             return chr(
 988                 (self.wheel_map[(ord(letter) - ord('a') - self.position) % 26] +
 989                     self.position) % 26 +
 990                 ord('a'))
 991         else:
 992             return ''
 993
 994     def advance(self):
 995         """Advances the wheel one position.
 996
 997         >>> pe.set_position('f')
 998         5
 999         >>> pe.advance()
1000         6
1001         """
1002         self.position = (self.position + 1) % 26
1003         return self.position
1004
1005     def encipher(self, message, starting_position=None):
1006         """Enciphers a whole message.
1007
1008         >>> pe.set_position('f')
1009         5
1010         >>> pe.encipher('helloworld')
1011         'kjsglcjoqc'
1012         >>> pe.set_position('f')
1013         5
1014         >>> pe.encipher('kjsglcjoqc')
1015         'helloworld'
1016         >>> pe.encipher('helloworld', starting_position = 'x')
1017         'egrekthnnf'
1018         """
1019         if starting_position:
1020             self.set_position(starting_position)
1021         transformed = ''
1022         for l in message:
1023             transformed += self.encipher_letter(l)
1024         return transformed
1025     decipher = encipher
1026
1027     def set_position(self, position):
1028         """Sets the position of the wheel, by specifying the letter the arrow
1029         points to.
1030
1031         >>> pe.set_position('a')
1032         0
1033         >>> pe.set_position('m')
1034         12
1035         >>> pe.set_position('z')
1036         25
1037         """
1038         self.position = ord(position) - ord('a')
1039         return self.position
1040
1041
1042 if __name__ == "__main__":
1043     import doctest
1044     doctest.testmod(extraglobs={'pe': PocketEnigma(1, 'a')})