Breaking hill ciphers done, challenge 6 done.
[cipher-training.git] / cipher.py
1 import string
2 import collections
3 import math
4 from enum import Enum
5 from itertools import zip_longest, cycle, chain
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
636 def hill_encipher(matrix, message_letters, fillvalue='a'):
637 """Hill cipher
638
639 >>> hill_encipher(np.matrix([[7,8], [11,11]]), 'hellothere')
640 'drjiqzdrvx'
641 >>> hill_encipher(np.matrix([[6, 24, 1], [13, 16, 10], [20, 17, 15]]), \
642 'hello there')
643 'tfjflpznvyac'
644 """
645 n = len(matrix)
646 sanitised_message = sanitise(message_letters)
647 if len(sanitised_message) % n != 0:
648 padding = fillvalue[0] * (n - len(sanitised_message) % n)
649 else:
650 padding = ''
651 message = [ord(c) - ord('a') for c in sanitised_message + padding]
652 message_chunks = [message[i:i+n] for i in range(0, len(message), n)]
653 # message_chunks = chunks(message, len(matrix), fillvalue=None)
654 enciphered_chunks = [((matrix * np.matrix(c).T).T).tolist()[0]
655 for c in message_chunks]
656 return ''.join([chr(int(round(l)) % 26 + ord('a'))
657 for l in sum(enciphered_chunks, [])])
658
659 def hill_decipher(matrix, message, fillvalue='a'):
660 """Hill cipher
661
662 >>> hill_decipher(np.matrix([[7,8], [11,11]]), 'drjiqzdrvx')
663 'hellothere'
664 >>> hill_decipher(np.matrix([[6, 24, 1], [13, 16, 10], [20, 17, 15]]), \
665 'tfjflpznvyac')
666 'hellothereaa'
667 """
668 adjoint = linalg.det(matrix)*linalg.inv(matrix)
669 inverse_determinant = modular_division_table[int(round(linalg.det(matrix))) % 26][1]
670 inverse_matrix = (inverse_determinant * adjoint) % 26
671 return hill_encipher(inverse_matrix, message, fillvalue)
672
673
674 class PocketEnigma(object):
675 """A pocket enigma machine
676 The wheel is internally represented as a 26-element list self.wheel_map,
677 where wheel_map[i] == j shows that the position i places on from the arrow
678 maps to the position j places on.
679 """
680 def __init__(self, wheel=1, position='a'):
681 """initialise the pocket enigma, including which wheel to use and the
682 starting position of the wheel.
683
684 The wheel is either 1 or 2 (the predefined wheels) or a list of letter
685 pairs.
686
687 The position is the letter pointed to by the arrow on the wheel.
688
689 >>> pe.wheel_map
690 [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]
691 >>> pe.position
692 0
693 """
694 self.wheel1 = [('a', 'z'), ('b', 'e'), ('c', 'x'), ('d', 'k'),
695 ('f', 'h'), ('g', 'j'), ('i', 'm'), ('l', 'r'), ('n', 'o'),
696 ('p', 'v'), ('q', 't'), ('s', 'u'), ('w', 'y')]
697 self.wheel2 = [('a', 'c'), ('b', 'd'), ('e', 'w'), ('f', 'i'),
698 ('g', 'p'), ('h', 'm'), ('j', 'k'), ('l', 'n'), ('o', 'q'),
699 ('r', 'z'), ('s', 'u'), ('t', 'v'), ('x', 'y')]
700 if wheel == 1:
701 self.make_wheel_map(self.wheel1)
702 elif wheel == 2:
703 self.make_wheel_map(self.wheel2)
704 else:
705 self.validate_wheel_spec(wheel)
706 self.make_wheel_map(wheel)
707 if position in string.ascii_lowercase:
708 self.position = ord(position) - ord('a')
709 else:
710 self.position = position
711
712 def make_wheel_map(self, wheel_spec):
713 """Expands a wheel specification from a list of letter-letter pairs
714 into a full wheel_map.
715
716 >>> pe.make_wheel_map(pe.wheel2)
717 [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]
718 """
719 self.validate_wheel_spec(wheel_spec)
720 self.wheel_map = [0] * 26
721 for p in wheel_spec:
722 self.wheel_map[ord(p[0]) - ord('a')] = ord(p[1]) - ord('a')
723 self.wheel_map[ord(p[1]) - ord('a')] = ord(p[0]) - ord('a')
724 return self.wheel_map
725
726 def validate_wheel_spec(self, wheel_spec):
727 """Validates that a wheel specificaiton will turn into a valid wheel
728 map.
729
730 >>> pe.validate_wheel_spec([])
731 Traceback (most recent call last):
732 ...
733 ValueError: Wheel specification has 0 pairs, requires 13
734 >>> pe.validate_wheel_spec([('a', 'b', 'c')]*13)
735 Traceback (most recent call last):
736 ...
737 ValueError: Not all mappings in wheel specificationhave two elements
738 >>> pe.validate_wheel_spec([('a', 'b')]*13)
739 Traceback (most recent call last):
740 ...
741 ValueError: Wheel specification does not contain 26 letters
742 """
743 if len(wheel_spec) != 13:
744 raise ValueError("Wheel specification has {} pairs, requires 13".
745 format(len(wheel_spec)))
746 for p in wheel_spec:
747 if len(p) != 2:
748 raise ValueError("Not all mappings in wheel specification"
749 "have two elements")
750 if len(set([p[0] for p in wheel_spec] +
751 [p[1] for p in wheel_spec])) != 26:
752 raise ValueError("Wheel specification does not contain 26 letters")
753
754 def encipher_letter(self, letter):
755 """Enciphers a single letter, by advancing the wheel before looking up
756 the letter on the wheel.
757
758 >>> pe.set_position('f')
759 5
760 >>> pe.encipher_letter('k')
761 'h'
762 """
763 self.advance()
764 return self.lookup(letter)
765 decipher_letter = encipher_letter
766
767 def lookup(self, letter):
768 """Look up what a letter enciphers to, without turning the wheel.
769
770 >>> pe.set_position('f')
771 5
772 >>> ''.join([pe.lookup(l) for l in string.ascii_lowercase])
773 'udhbfejcpgmokrliwntsayqzvx'
774 >>> pe.lookup('A')
775 ''
776 """
777 if letter in string.ascii_lowercase:
778 return chr(
779 (self.wheel_map[(ord(letter) - ord('a') - self.position) % 26] +
780 self.position) % 26 +
781 ord('a'))
782 else:
783 return ''
784
785 def advance(self):
786 """Advances the wheel one position.
787
788 >>> pe.set_position('f')
789 5
790 >>> pe.advance()
791 6
792 """
793 self.position = (self.position + 1) % 26
794 return self.position
795
796 def encipher(self, message, starting_position=None):
797 """Enciphers a whole message.
798
799 >>> pe.set_position('f')
800 5
801 >>> pe.encipher('helloworld')
802 'kjsglcjoqc'
803 >>> pe.set_position('f')
804 5
805 >>> pe.encipher('kjsglcjoqc')
806 'helloworld'
807 >>> pe.encipher('helloworld', starting_position = 'x')
808 'egrekthnnf'
809 """
810 if starting_position:
811 self.set_position(starting_position)
812 transformed = ''
813 for l in message:
814 transformed += self.encipher_letter(l)
815 return transformed
816 decipher = encipher
817
818 def set_position(self, position):
819 """Sets the position of the wheel, by specifying the letter the arrow
820 points to.
821
822 >>> pe.set_position('a')
823 0
824 >>> pe.set_position('m')
825 12
826 >>> pe.set_position('z')
827 25
828 """
829 self.position = ord(position) - ord('a')
830 return self.position
831
832
833 if __name__ == "__main__":
834 import doctest
835 doctest.testmod(extraglobs={'pe': PocketEnigma(1, 'a')})