5 from itertools
import zip_longest
, cycle
, chain
7 from numpy
import matrix
8 from numpy
import linalg
9 from language_models
import *
12 modular_division_table
= [[0]*26 for _
in range(26)]
16 modular_division_table
[b
][c
] = a
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
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!']
33 split_text
= chunks(text
, n
, fillvalue
)
34 return [''.join(l
) for l
in zip_longest(*split_text
, fillvalue
=fillvalue
)]
36 def combine_every_nth(split_text
):
37 """Reforms a text split into every_nth strings
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'
46 return ''.join([''.join(l
)
47 for l
in zip_longest(*split_text
, fillvalue
='')])
49 def chunks(text
, n
, fillvalue
=None):
50 """Split a text into chunks of n characters
52 >>> chunks('abcdefghi', 3)
54 >>> chunks('abcdefghi', 4)
56 >>> chunks('abcdefghi', 4, fillvalue='!')
57 ['abcd', 'efgh', 'i!!!']
60 padding
= fillvalue
[0] * (n
- len(text
) % n
)
63 return [(text
+padding
)[i
:i
+n
] for i
in range(0, len(text
), n
)]
65 def transpose(items
, transposition
):
66 """Moves items around according to the given transposition
68 >>> transpose(['a', 'b', 'c', 'd'], (0,1,2,3))
70 >>> transpose(['a', 'b', 'c', 'd'], (3,1,2,0))
72 >>> transpose([10,11,12,13,14,15], (3,2,4,1,5,0))
73 [13, 12, 14, 11, 15, 10]
75 transposed
= [''] * len(transposition
)
76 for p
, t
in enumerate(transposition
):
77 transposed
[p
] = items
[t
]
80 def untranspose(items
, transposition
):
83 >>> untranspose(['a', 'b', 'c', 'd'], [0,1,2,3])
85 >>> untranspose(['d', 'b', 'c', 'a'], [3,1,2,0])
87 >>> untranspose([13, 12, 14, 11, 15, 10], [3,2,4,1,5,0])
88 [10, 11, 12, 13, 14, 15]
90 transposed
= [''] * len(transposition
)
91 for p
, t
in enumerate(transposition
):
92 transposed
[t
] = items
[p
]
95 def deduplicate(text
):
96 return list(collections
.OrderedDict
.fromkeys(text
))
99 def caesar_encipher_letter(accented_letter
, shift
):
100 """Encipher a letter, given a shift amount
102 >>> caesar_encipher_letter('a', 1)
104 >>> caesar_encipher_letter('a', 2)
106 >>> caesar_encipher_letter('b', 2)
108 >>> caesar_encipher_letter('x', 2)
110 >>> caesar_encipher_letter('y', 2)
112 >>> caesar_encipher_letter('z', 2)
114 >>> caesar_encipher_letter('z', -1)
116 >>> caesar_encipher_letter('a', -1)
118 >>> caesar_encipher_letter('A', 1)
120 >>> caesar_encipher_letter('é', 1)
123 letter
= unaccent(accented_letter
)
124 if letter
in string
.ascii_letters
:
125 if letter
in string
.ascii_uppercase
:
126 alphabet_start
= ord('A')
128 alphabet_start
= ord('a')
129 return chr(((ord(letter
) - alphabet_start
+ shift
) % 26) +
134 def caesar_decipher_letter(letter
, shift
):
135 """Decipher a letter, given a shift amount
137 >>> caesar_decipher_letter('b', 1)
139 >>> caesar_decipher_letter('b', 2)
142 return caesar_encipher_letter(letter
, -shift
)
144 def caesar_encipher(message
, shift
):
145 """Encipher a message with the Caesar cipher of given shift
147 >>> caesar_encipher('abc', 1)
149 >>> caesar_encipher('abc', 2)
151 >>> caesar_encipher('abcxyz', 2)
153 >>> caesar_encipher('ab cx yz', 2)
155 >>> caesar_encipher('Héllo World!', 2)
158 enciphered
= [caesar_encipher_letter(l
, shift
) for l
in message
]
159 return ''.join(enciphered
)
161 def caesar_decipher(message
, shift
):
162 """Decipher a message with the Caesar cipher of given shift
164 >>> caesar_decipher('bcd', 1)
166 >>> caesar_decipher('cde', 2)
168 >>> caesar_decipher('cd ez ab', 2)
170 >>> caesar_decipher('Jgnnq Yqtnf!', 2)
173 return caesar_encipher(message
, -shift
)
175 def affine_encipher_letter(accented_letter
, multiplier
=1, adder
=0, one_based
=True):
176 """Encipher a letter, given a multiplier and adder
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'
185 letter
= unaccent(accented_letter
)
186 if letter
in string
.ascii_letters
:
187 if letter
in string
.ascii_uppercase
:
188 alphabet_start
= ord('A')
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
)
199 def affine_decipher_letter(letter
, multiplier
=1, adder
=0, one_based
=True):
200 """Encipher a letter, given a multiplier and adder
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'
209 if letter
in string
.ascii_letters
:
210 if letter
in string
.ascii_uppercase
:
211 alphabet_start
= ord('A')
213 alphabet_start
= ord('a')
214 cipher_number
= ord(letter
) - alphabet_start
215 if one_based
: cipher_number
+= 1
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
)
224 def affine_encipher(message
, multiplier
=1, adder
=0, one_based
=True):
225 """Encipher a message
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'
231 enciphered
= [affine_encipher_letter(l
, multiplier
, adder
, one_based
)
233 return ''.join(enciphered
)
235 def affine_decipher(message
, multiplier
=1, adder
=0, one_based
=True):
236 """Decipher a message
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'
242 enciphered
= [affine_decipher_letter(l
, multiplier
, adder
, one_based
)
244 return ''.join(enciphered
)
247 class KeywordWrapAlphabet(Enum
):
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
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'
267 if wrap_alphabet
== KeywordWrapAlphabet
.from_a
:
268 cipher_alphabet
= ''.join(deduplicate(sanitise(keyword
) +
269 string
.ascii_lowercase
))
271 if wrap_alphabet
== KeywordWrapAlphabet
.from_last
:
272 last_keyword_letter
= deduplicate(sanitise(keyword
))[-1]
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
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
289 1 : from the last letter in the sanitised keyword
290 2 : from the largest letter in the sanitised keyword
292 >>> keyword_encipher('test message', 'bayes')
294 >>> keyword_encipher('test message', 'bayes', KeywordWrapAlphabet.from_a)
296 >>> keyword_encipher('test message', 'bayes', KeywordWrapAlphabet.from_last)
298 >>> keyword_encipher('test message', 'bayes', KeywordWrapAlphabet.from_largest)
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
)
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
310 1 : from the last letter in the sanitised keyword
311 2 : from the largest letter in the sanitised keyword
313 >>> keyword_decipher('rsqr ksqqbds', 'bayes')
315 >>> keyword_decipher('rsqr ksqqbds', 'bayes', KeywordWrapAlphabet.from_a)
317 >>> keyword_decipher('lskl dskkbus', 'bayes', KeywordWrapAlphabet.from_last)
319 >>> keyword_decipher('qspq jsppbcs', 'bayes', KeywordWrapAlphabet.from_largest)
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
)
327 def vigenere_encipher(message
, keyword
):
330 >>> vigenere_encipher('hello', 'abc')
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
])
337 def vigenere_decipher(message
, keyword
):
340 >>> vigenere_decipher('hfnlp', 'abc')
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
])
347 beaufort_encipher
=vigenere_decipher
348 beaufort_decipher
=vigenere_encipher
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,
357 If passed a tuple, assume it's already a transposition and just return it.
359 >>> transpositions_of('clever')
361 >>> transpositions_of('fred')
363 >>> transpositions_of((3, 2, 0, 1))
366 if isinstance(keyword
, tuple):
369 key
= deduplicate(keyword
)
370 transpositions
= tuple(key
.index(l
) for l
in sorted(key
))
371 return transpositions
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
377 for i
in range(padding_length
):
378 if callable(fillvalue
):
379 padding
+= fillvalue()
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.
390 >>> column_transposition_encipher('hellothere', 'abcdef', fillcolumnwise=True)
392 >>> column_transposition_encipher('hellothere', 'abcdef', fillcolumnwise=True, emptycolumnwise=True)
394 >>> column_transposition_encipher('hellothere', 'abcdef')
396 >>> column_transposition_encipher('hellothere', 'abcde')
398 >>> column_transposition_encipher('hellothere', 'abcde', fillcolumnwise=True, emptycolumnwise=True)
400 >>> column_transposition_encipher('hellothere', 'abcde', fillcolumnwise=True, emptycolumnwise=False)
402 >>> column_transposition_encipher('hellothere', 'abcde', fillcolumnwise=False, emptycolumnwise=True)
404 >>> column_transposition_encipher('hellothere', 'abcde', fillcolumnwise=False, emptycolumnwise=False)
406 >>> column_transposition_encipher('hellothere', 'clever', fillcolumnwise=True, emptycolumnwise=True)
408 >>> column_transposition_encipher('hellothere', 'clever', fillcolumnwise=True, emptycolumnwise=False)
410 >>> column_transposition_encipher('hellothere', 'clever', fillcolumnwise=False, emptycolumnwise=True)
412 >>> column_transposition_encipher('hellothere', 'clever', fillcolumnwise=False, emptycolumnwise=False)
414 >>> column_transposition_encipher('hellothere', 'cleverly')
416 >>> column_transposition_encipher('hellothere', 'cleverly', fillvalue='!')
418 >>> column_transposition_encipher('hellothere', 'cleverly', fillvalue=lambda: '*')
421 transpositions
= transpositions_of(keyword
)
422 message
+= pad(len(message
), len(transpositions
), fillvalue
)
424 rows
= every_nth(message
, len(message
) // len(transpositions
))
426 rows
= chunks(message
, len(transpositions
))
427 transposed
= [transpose(r
, transpositions
) for r
in rows
]
429 return combine_every_nth(transposed
)
431 return ''.join(chain(*transposed
))
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.
439 >>> column_transposition_decipher('hellothere', 'abcde', fillcolumnwise=True, emptycolumnwise=True)
441 >>> column_transposition_decipher('hlohreltee', 'abcde', fillcolumnwise=True, emptycolumnwise=False)
443 >>> column_transposition_decipher('htehlelroe', 'abcde', fillcolumnwise=False, emptycolumnwise=True)
445 >>> column_transposition_decipher('hellothere', 'abcde', fillcolumnwise=False, emptycolumnwise=False)
447 >>> column_transposition_decipher('heotllrehe', 'clever', fillcolumnwise=True, emptycolumnwise=True)
449 >>> column_transposition_decipher('holrhetlee', 'clever', fillcolumnwise=True, emptycolumnwise=False)
451 >>> column_transposition_decipher('htleehoelr', 'clever', fillcolumnwise=False, emptycolumnwise=True)
453 >>> column_transposition_decipher('hleolteher', 'clever', fillcolumnwise=False, emptycolumnwise=False)
456 transpositions
= transpositions_of(keyword
)
457 message
+= pad(len(message
), len(transpositions
), fillvalue
)
459 rows
= every_nth(message
, len(message
) // len(transpositions
))
461 rows
= chunks(message
, len(transpositions
))
462 untransposed
= [untranspose(r
, transpositions
) for r
in rows
]
464 return combine_every_nth(untransposed
)
466 return ''.join(chain(*untransposed
))
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.
472 >>> scytale_encipher('thequickbrownfox', 3)
474 >>> scytale_encipher('thequickbrownfox', 4)
476 >>> scytale_encipher('thequickbrownfox', 5)
477 'tubn hirf ecoo qkwx '
478 >>> scytale_encipher('thequickbrownfox', 6)
480 >>> scytale_encipher('thequickbrownfox', 7)
481 'tqcrnx hukof eibwo '
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)
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.
494 >>> scytale_decipher('tcnhkfeboqrxuo iw ', 3)
496 >>> scytale_decipher('tubnhirfecooqkwx', 4)
498 >>> scytale_decipher('tubn hirf ecoo qkwx ', 5)
500 >>> scytale_decipher('tqcrnxhukof eibwo ', 6)
502 >>> scytale_decipher('tqcrnx hukof eibwo ', 7)
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)
513 def railfence_encipher(message
, height
, fillvalue
=''):
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
519 Example: the plaintext "hellotherefriends", with a height of four, written
520 out in the railfence as
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
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'
544 sections
= chunks(message
, (height
- 1) * 2, fillvalue
=fillvalue
)
545 n_sections
= len(sections
)
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])]
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.
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.
565 'hhieterelorfnsled' is split into
570 (spaces added for clarity), which is stored in 'rows'. This is then split
571 into 'down_rows' and 'up_rows':
583 These are then zipped together (after the up_rows are reversed) to recover
586 Most of the procedure is about finding the correct lengths for each row then
587 splitting the ciphertext into those rows.
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'
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):
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
620 for i
in folded_row_lengths
:
621 rows
+= [message
[row_start
: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
626 down_rows
= [rows
[0]]
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]]
633 return ''.join(c
for r
in zip_longest(*(down_rows
+ up_rows
), fillvalue
='') for c
in r
)
636 def hill_encipher(matrix
, message_letters
, fillvalue
='a'):
639 >>> hill_encipher(np.matrix([[7,8], [11,11]]), 'hellothere')
641 >>> hill_encipher(np.matrix([[6, 24, 1], [13, 16, 10], [20, 17, 15]]), \
646 sanitised_message
= sanitise(message_letters
)
647 if len(sanitised_message
) % n
!= 0:
648 padding
= fillvalue
[0] * (n
- len(sanitised_message
) % n
)
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
, [])])
660 def hill_decipher(matrix
, message
, fillvalue
='a'):
663 >>> hill_decipher(np.matrix([[7,8], [11,11]]), 'drjiqzdrvx')
665 >>> hill_decipher(np.matrix([[6, 24, 1], [13, 16, 10], [20, 17, 15]]), \
669 adjoint
= linalg
.det(matrix
)*linalg
.inv(matrix
)
670 inverse_determinant
= modular_division_table
[int(round(linalg
.det(matrix
))) % 26][1]
671 inverse_matrix
= (inverse_determinant
* adjoint
) % 26
672 return hill_encipher(inverse_matrix
, message
, fillvalue
)
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.
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.
684 The wheel is either 1 or 2 (the predefined wheels) or a list of letter
687 The position is the letter pointed to by the arrow on the wheel.
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]
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')]
701 self
.make_wheel_map(self
.wheel1
)
703 self
.make_wheel_map(self
.wheel2
)
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')
710 self
.position
= position
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.
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]
719 self
.validate_wheel_spec(wheel_spec
)
720 self
.wheel_map
= [0] * 26
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
726 def validate_wheel_spec(self
, wheel_spec
):
727 """Validates that a wheel specificaiton will turn into a valid wheel
730 >>> pe.validate_wheel_spec([])
731 Traceback (most recent call last):
733 ValueError: Wheel specification has 0 pairs, requires 13
734 >>> pe.validate_wheel_spec([('a', 'b', 'c')]*13)
735 Traceback (most recent call last):
737 ValueError: Not all mappings in wheel specificationhave two elements
738 >>> pe.validate_wheel_spec([('a', 'b')]*13)
739 Traceback (most recent call last):
741 ValueError: Wheel specification does not contain 26 letters
743 if len(wheel_spec
) != 13:
744 raise ValueError("Wheel specification has {} pairs, requires 13".
745 format(len(wheel_spec
)))
748 raise ValueError("Not all mappings in wheel specification"
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")
754 def encipher_letter(self
, letter
):
755 """Enciphers a single letter, by advancing the wheel before looking up
756 the letter on the wheel.
758 >>> pe.set_position('f')
760 >>> pe.encipher_letter('k')
764 return self
.lookup(letter
)
765 decipher_letter
= encipher_letter
767 def lookup(self
, letter
):
768 """Look up what a letter enciphers to, without turning the wheel.
770 >>> pe.set_position('f')
772 >>> ''.join([pe.lookup(l) for l in string.ascii_lowercase])
773 'udhbfejcpgmokrliwntsayqzvx'
777 if letter
in string
.ascii_lowercase
:
779 (self
.wheel_map
[(ord(letter
) - ord('a') - self
.position
) % 26] +
780 self
.position
) % 26 +
786 """Advances the wheel one position.
788 >>> pe.set_position('f')
793 self
.position
= (self
.position
+ 1) % 26
796 def encipher(self
, message
, starting_position
=None):
797 """Enciphers a whole message.
799 >>> pe.set_position('f')
801 >>> pe.encipher('helloworld')
803 >>> pe.set_position('f')
805 >>> pe.encipher('kjsglcjoqc')
807 >>> pe.encipher('helloworld', starting_position = 'x')
810 if starting_position
:
811 self
.set_position(starting_position
)
814 transformed
+= self
.encipher_letter(l
)
818 def set_position(self
, position
):
819 """Sets the position of the wheel, by specifying the letter the arrow
822 >>> pe.set_position('a')
824 >>> pe.set_position('m')
826 >>> pe.set_position('z')
829 self
.position
= ord(position
) - ord('a')
833 if __name__
== "__main__":
835 doctest
.testmod(extraglobs
={'pe': PocketEnigma(1, 'a')})