eae56cfc3c8560ae50f33c60b8b8d8a9e95f622f
[cipher-training.git] / cipherbreak.py
1 import string
2 import collections
3 import norms
4 import logging
5 import random
6 from itertools import zip_longest, cycle, permutations, starmap
7 from segment import segment
8 from multiprocessing import Pool
9 from math import log10
10
11 import matplotlib.pyplot as plt
12
13 logger = logging.getLogger(__name__)
14 logger.addHandler(logging.FileHandler('cipher.log'))
15 logger.setLevel(logging.WARNING)
16 #logger.setLevel(logging.INFO)
17 #logger.setLevel(logging.DEBUG)
18
19 from cipher import *
20 from language_models import *
21
22 # To time a run:
23 #
24 # import timeit
25 # c5a = open('2012/5a.ciphertext', 'r').read()
26 # timeit.timeit('keyword_break(c5a)', setup='gc.enable() ; from __main__ import c5a ; from cipher import keyword_break', number=1)
27 # timeit.repeat('keyword_break_mp(c5a, chunksize=500)', setup='gc.enable() ; from __main__ import c5a ; from cipher import keyword_break_mp', repeat=5, number=1)
28
29 transpositions = collections.defaultdict(list)
30 for word in keywords:
31 transpositions[transpositions_of(word)] += [word]
32
33 def frequencies(text):
34 """Count the number of occurrences of each character in text
35
36 >>> sorted(frequencies('abcdefabc').items())
37 [('a', 2), ('b', 2), ('c', 2), ('d', 1), ('e', 1), ('f', 1)]
38 >>> sorted(frequencies('the quick brown fox jumped over the lazy ' \
39 'dog').items()) # doctest: +NORMALIZE_WHITESPACE
40 [(' ', 8), ('a', 1), ('b', 1), ('c', 1), ('d', 2), ('e', 4), ('f', 1),
41 ('g', 1), ('h', 2), ('i', 1), ('j', 1), ('k', 1), ('l', 1), ('m', 1),
42 ('n', 1), ('o', 4), ('p', 1), ('q', 1), ('r', 2), ('t', 2), ('u', 2),
43 ('v', 1), ('w', 1), ('x', 1), ('y', 1), ('z', 1)]
44 >>> sorted(frequencies('The Quick BROWN fox jumped! over... the ' \
45 '(9lazy) DOG').items()) # doctest: +NORMALIZE_WHITESPACE
46 [(' ', 8), ('!', 1), ('(', 1), (')', 1), ('.', 3), ('9', 1), ('B', 1),
47 ('D', 1), ('G', 1), ('N', 1), ('O', 2), ('Q', 1), ('R', 1), ('T', 1),
48 ('W', 1), ('a', 1), ('c', 1), ('d', 1), ('e', 4), ('f', 1), ('h', 2),
49 ('i', 1), ('j', 1), ('k', 1), ('l', 1), ('m', 1), ('o', 2), ('p', 1),
50 ('r', 1), ('t', 1), ('u', 2), ('v', 1), ('x', 1), ('y', 1), ('z', 1)]
51 >>> sorted(frequencies(sanitise('The Quick BROWN fox jumped! over... ' \
52 'the (9lazy) DOG')).items()) # doctest: +NORMALIZE_WHITESPACE
53 [('a', 1), ('b', 1), ('c', 1), ('d', 2), ('e', 4), ('f', 1), ('g', 1),
54 ('h', 2), ('i', 1), ('j', 1), ('k', 1), ('l', 1), ('m', 1), ('n', 1),
55 ('o', 4), ('p', 1), ('q', 1), ('r', 2), ('t', 2), ('u', 2), ('v', 1),
56 ('w', 1), ('x', 1), ('y', 1), ('z', 1)]
57 >>> frequencies('abcdefabcdef')['x']
58 0
59 """
60 return collections.Counter(c for c in text)
61
62
63 def caesar_break(message, fitness=Pletters):
64 """Breaks a Caesar cipher using frequency analysis
65
66 >>> caesar_break('ibxcsyorsaqcheyklxivoexlevmrimwxsfiqevvmihrsasrxliwyrh' \
67 'ecjsppsamrkwleppfmergefifvmhixscsymjcsyqeoixlm') # doctest: +ELLIPSIS
68 (4, -130.849989015...)
69 >>> caesar_break('wxwmaxdgheetgwuxztgptedbgznitgwwhpguxyhkxbmhvvtlbhgtee' \
70 'raxlmhiixweblmxgxwmhmaxybkbgztgwztsxwbgmxgmert') # doctest: +ELLIPSIS
71 (19, -128.82410410...)
72 >>> caesar_break('yltbbqnqnzvguvaxurorgenafsbezqvagbnornfgsbevpnaabjurer' \
73 'svaquvzyvxrnznazlybequrvfohgriraabjtbaruraprur') # doctest: +ELLIPSIS
74 (13, -126.25403935...)
75 """
76 sanitised_message = sanitise(message)
77 best_shift = 0
78 best_fit = float('-inf')
79 for shift in range(26):
80 plaintext = caesar_decipher(sanitised_message, shift)
81 fit = fitness(plaintext)
82 logger.debug('Caesar break attempt using key {0} gives fit of {1} '
83 'and decrypt starting: {2}'.format(shift, fit, plaintext[:50]))
84 if fit > best_fit:
85 best_fit = fit
86 best_shift = shift
87 logger.info('Caesar break best fit: key {0} gives fit of {1} and '
88 'decrypt starting: {2}'.format(best_shift, best_fit,
89 caesar_decipher(sanitised_message, best_shift)[:50]))
90 return best_shift, best_fit
91
92 def affine_break(message, fitness=Pletters):
93 """Breaks an affine cipher using frequency analysis
94
95 >>> affine_break('lmyfu bkuusd dyfaxw claol psfaom jfasd snsfg jfaoe ls ' \
96 'omytd jlaxe mh jm bfmibj umis hfsul axubafkjamx. ls kffkxwsd jls ' \
97 'ofgbjmwfkiu olfmxmtmwaokttg jlsx ls kffkxwsd jlsi zg tsxwjl. jlsx ' \
98 'ls umfjsd jlsi zg hfsqysxog. ls dmmdtsd mx jls bats mh bkbsf. ls ' \
99 'bfmctsd kfmyxd jls lyj, mztanamyu xmc jm clm cku tmmeaxw kj lai ' \
100 'kxd clm ckuxj.') # doctest: +ELLIPSIS
101 ((15, 22, True), -340.601181913...)
102 """
103 sanitised_message = sanitise(message)
104 best_multiplier = 0
105 best_adder = 0
106 best_one_based = True
107 best_fit = float("-inf")
108 for one_based in [True, False]:
109 for multiplier in [x for x in range(1, 26, 2) if x != 13]:
110 for adder in range(26):
111 plaintext = affine_decipher(sanitised_message,
112 multiplier, adder, one_based)
113 fit = fitness(plaintext)
114 logger.debug('Affine break attempt using key {0}x+{1} ({2}) '
115 'gives fit of {3} and decrypt starting: {4}'.
116 format(multiplier, adder, one_based, fit,
117 plaintext[:50]))
118 if fit > best_fit:
119 best_fit = fit
120 best_multiplier = multiplier
121 best_adder = adder
122 best_one_based = one_based
123 logger.info('Affine break best fit with key {0}x+{1} ({2}) gives fit of {3} '
124 'and decrypt starting: {4}'.format(
125 best_multiplier, best_adder, best_one_based, best_fit,
126 affine_decipher(sanitised_message, best_multiplier,
127 best_adder, best_one_based)[:50]))
128 return (best_multiplier, best_adder, best_one_based), best_fit
129
130 def keyword_break(message, wordlist=keywords, fitness=Pletters):
131 """Breaks a keyword substitution cipher using a dictionary and
132 frequency analysis
133
134 >>> keyword_break(keyword_encipher('this is a test message for the ' \
135 'keyword decipherment', 'elephant', Keyword_wrap_alphabet.from_last), \
136 wordlist=['cat', 'elephant', 'kangaroo']) # doctest: +ELLIPSIS
137 (('elephant', <Keyword_wrap_alphabet.from_last: 2>), -52.834575011...)
138 """
139 best_keyword = ''
140 best_wrap_alphabet = True
141 best_fit = float("-inf")
142 for wrap_alphabet in Keyword_wrap_alphabet:
143 for keyword in wordlist:
144 plaintext = keyword_decipher(message, keyword, wrap_alphabet)
145 fit = fitness(plaintext)
146 logger.debug('Keyword break attempt using key {0} (wrap={1}) '
147 'gives fit of {2} and decrypt starting: {3}'.format(
148 keyword, wrap_alphabet, fit,
149 sanitise(plaintext)[:50]))
150 if fit > best_fit:
151 best_fit = fit
152 best_keyword = keyword
153 best_wrap_alphabet = wrap_alphabet
154 logger.info('Keyword break best fit with key {0} (wrap={1}) gives fit of '
155 '{2} and decrypt starting: {3}'.format(best_keyword,
156 best_wrap_alphabet, best_fit, sanitise(
157 keyword_decipher(message, best_keyword,
158 best_wrap_alphabet))[:50]))
159 return (best_keyword, best_wrap_alphabet), best_fit
160
161 def keyword_break_mp(message, wordlist=keywords, fitness=Pletters, chunksize=500):
162 """Breaks a keyword substitution cipher using a dictionary and
163 frequency analysis
164
165 >>> keyword_break_mp(keyword_encipher('this is a test message for the ' \
166 'keyword decipherment', 'elephant', Keyword_wrap_alphabet.from_last), \
167 wordlist=['cat', 'elephant', 'kangaroo']) # doctest: +ELLIPSIS
168 (('elephant', <Keyword_wrap_alphabet.from_last: 2>), -52.834575011...)
169 """
170 with Pool() as pool:
171 helper_args = [(message, word, wrap, fitness)
172 for word in wordlist
173 for wrap in Keyword_wrap_alphabet]
174 # Gotcha: the helper function here needs to be defined at the top level
175 # (limitation of Pool.starmap)
176 breaks = pool.starmap(keyword_break_worker, helper_args, chunksize)
177 return max(breaks, key=lambda k: k[1])
178
179 def keyword_break_worker(message, keyword, wrap_alphabet, fitness):
180 plaintext = keyword_decipher(message, keyword, wrap_alphabet)
181 fit = fitness(plaintext)
182 logger.debug('Keyword break attempt using key {0} (wrap={1}) gives fit of '
183 '{2} and decrypt starting: {3}'.format(keyword,
184 wrap_alphabet, fit, sanitise(plaintext)[:50]))
185 return (keyword, wrap_alphabet), fit
186
187
188 def column_transposition_break_mp(message, translist=transpositions,
189 fitness=Pbigrams, chunksize=500):
190 """Breaks a column transposition cipher using a dictionary and
191 n-gram frequency analysis
192
193 >>> column_transposition_break_mp(column_transposition_encipher(sanitise( \
194 "It is a truth universally acknowledged, that a single man in \
195 possession of a good fortune, must be in want of a wife. However \
196 little known the feelings or views of such a man may be on his \
197 first entering a neighbourhood, this truth is so well fixed in the \
198 minds of the surrounding families, that he is considered the \
199 rightful property of some one or other of their daughters."), \
200 'encipher'), \
201 translist={(2, 0, 5, 3, 1, 4, 6): ['encipher'], \
202 (5, 0, 6, 1, 3, 4, 2): ['fourteen'], \
203 (6, 1, 0, 4, 5, 3, 2): ['keyword']}) # doctest: +ELLIPSIS
204 (((2, 0, 5, 3, 1, 4, 6), False, False), -709.4646722...)
205 >>> column_transposition_break_mp(column_transposition_encipher(sanitise( \
206 "It is a truth universally acknowledged, that a single man in \
207 possession of a good fortune, must be in want of a wife. However \
208 little known the feelings or views of such a man may be on his \
209 first entering a neighbourhood, this truth is so well fixed in the \
210 minds of the surrounding families, that he is considered the \
211 rightful property of some one or other of their daughters."), \
212 'encipher'), \
213 translist={(2, 0, 5, 3, 1, 4, 6): ['encipher'], \
214 (5, 0, 6, 1, 3, 4, 2): ['fourteen'], \
215 (6, 1, 0, 4, 5, 3, 2): ['keyword']}, \
216 fitness=Ptrigrams) # doctest: +ELLIPSIS
217 (((2, 0, 5, 3, 1, 4, 6), False, False), -997.0129085...)
218 """
219 with Pool() as pool:
220 helper_args = [(message, trans, fillcolumnwise, emptycolumnwise,
221 fitness)
222 for trans in translist.keys()
223 for fillcolumnwise in [True, False]
224 for emptycolumnwise in [True, False]]
225 # Gotcha: the helper function here needs to be defined at the top level
226 # (limitation of Pool.starmap)
227 breaks = pool.starmap(column_transposition_break_worker,
228 helper_args, chunksize)
229 return max(breaks, key=lambda k: k[1])
230 column_transposition_break = column_transposition_break_mp
231
232 def monoalphabetic_break_hillclimbing(message, max_iterations = 10000000,
233 fitness=Pletters):
234 ciphertext = unaccent(message).lower()
235 alphabet = list(string.ascii_lowercase)
236 random.shuffle(alphabet)
237 alphabet = ''.join(alphabet)
238 return monoalphabetic_break_hillclimbing_worker(ciphertext, alphabet,
239 max_iterations, fitness)
240
241 def monoalphabetic_break_hillclimbing_mp(message, workers=100,
242 max_iterations = 10000000, fitness=Pletters, chunksize=1):
243 worker_args = []
244 ciphertext = unaccent(message).lower()
245 for i in range(workers):
246 alphabet = list(string.ascii_lowercase)
247 random.shuffle(alphabet)
248 alphabet = ''.join(alphabet)
249 worker_args.append((ciphertext, alphabet, max_iterations, fitness))
250 with Pool() as pool:
251 breaks = pool.starmap(monoalphabetic_break_hillclimbing_worker,
252 worker_args, chunksize)
253 return max(breaks, key=lambda k: k[1])
254
255 def monoalphabetic_break_hillclimbing_worker(message, alphabet,
256 max_iterations, fitness):
257 def swap(letters, i, j):
258 if i > j:
259 i, j = j, i
260 if i == j:
261 return letters
262 else:
263 return letters[:i] + letters[j] + letters[i+1:j] + letters[i] + letters[j+1:]
264 best_alphabet = alphabet
265 best_fitness = float('-inf')
266 for i in range(max_iterations):
267 alphabet = swap(alphabet, random.randrange(26), random.randrange(26))
268 cipher_translation = ''.maketrans(string.ascii_lowercase, alphabet)
269 plaintext = message.translate(cipher_translation)
270 if fitness(plaintext) > best_fitness:
271 best_fitness = fitness(plaintext)
272 best_alphabet = alphabet
273 print(i, best_alphabet, best_fitness, plaintext)
274 return best_alphabet, best_fitness
275
276
277 def column_transposition_break_worker(message, transposition,
278 fillcolumnwise, emptycolumnwise, fitness):
279 plaintext = column_transposition_decipher(message, transposition,
280 fillcolumnwise=fillcolumnwise, emptycolumnwise=emptycolumnwise)
281 fit = fitness(sanitise(plaintext))
282 logger.debug('Column transposition break attempt using key {0} '
283 'gives fit of {1} and decrypt starting: {2}'.format(
284 transposition, fit,
285 sanitise(plaintext)[:50]))
286 return (transposition, fillcolumnwise, emptycolumnwise), fit
287
288
289 def scytale_break_mp(message, max_key_length=20,
290 fitness=Pbigrams, chunksize=500):
291 """Breaks a scytale cipher using a range of lengths and
292 n-gram frequency analysis
293
294 >>> scytale_break_mp(scytale_encipher(sanitise( \
295 "It is a truth universally acknowledged, that a single man in \
296 possession of a good fortune, must be in want of a wife. However \
297 little known the feelings or views of such a man may be on his \
298 first entering a neighbourhood, this truth is so well fixed in the \
299 minds of the surrounding families, that he is considered the \
300 rightful property of some one or other of their daughters."), \
301 5)) # doctest: +ELLIPSIS
302 (5, -709.4646722...)
303 >>> scytale_break_mp(scytale_encipher(sanitise( \
304 "It is a truth universally acknowledged, that a single man in \
305 possession of a good fortune, must be in want of a wife. However \
306 little known the feelings or views of such a man may be on his \
307 first entering a neighbourhood, this truth is so well fixed in the \
308 minds of the surrounding families, that he is considered the \
309 rightful property of some one or other of their daughters."), \
310 5), \
311 fitness=Ptrigrams) # doctest: +ELLIPSIS
312 (5, -997.0129085...)
313 """
314 with Pool() as pool:
315 helper_args = [(message, trans, False, True, fitness)
316 for trans in
317 [[col for col in range(math.ceil(len(message)/rows))]
318 for rows in range(1,max_key_length+1)]]
319 # Gotcha: the helper function here needs to be defined at the top level
320 # (limitation of Pool.starmap)
321 breaks = pool.starmap(column_transposition_break_worker,
322 helper_args, chunksize)
323 best = max(breaks, key=lambda k: k[1])
324 return math.trunc(len(message) / len(best[0][0])), best[1]
325 scytale_break = scytale_break_mp
326
327
328 def vigenere_keyword_break_mp(message, wordlist=keywords, fitness=Pletters,
329 chunksize=500):
330 """Breaks a vigenere cipher using a dictionary and
331 frequency analysis
332
333 >>> vigenere_keyword_break_mp(vigenere_encipher(sanitise('this is a test ' \
334 'message for the vigenere decipherment'), 'cat'), \
335 wordlist=['cat', 'elephant', 'kangaroo']) # doctest: +ELLIPSIS
336 ('cat', -52.947271216...)
337 """
338 with Pool() as pool:
339 helper_args = [(message, word, fitness)
340 for word in wordlist]
341 # Gotcha: the helper function here needs to be defined at the top level
342 # (limitation of Pool.starmap)
343 breaks = pool.starmap(vigenere_keyword_break_worker, helper_args, chunksize)
344 return max(breaks, key=lambda k: k[1])
345 vigenere_keyword_break = vigenere_keyword_break_mp
346
347 def vigenere_keyword_break_worker(message, keyword, fitness):
348 plaintext = vigenere_decipher(message, keyword)
349 fit = fitness(plaintext)
350 logger.debug('Vigenere keyword break attempt using key {0} gives fit of '
351 '{1} and decrypt starting: {2}'.format(keyword,
352 fit, sanitise(plaintext)[:50]))
353 return keyword, fit
354
355
356
357 def vigenere_frequency_break(message, max_key_length=20, fitness=Pletters):
358 """Breaks a Vigenere cipher with frequency analysis
359
360 >>> vigenere_frequency_break(vigenere_encipher(sanitise("It is time to " \
361 "run. She is ready and so am I. I stole Daniel's pocketbook this " \
362 "afternoon when he left his jacket hanging on the easel in the " \
363 "attic. I jump every time I hear a footstep on the stairs, " \
364 "certain that the theft has been discovered and that I will " \
365 "be caught. The SS officer visits less often now that he is " \
366 "sure"), 'florence')) # doctest: +ELLIPSIS
367 ('florence', -307.5473096791...)
368 """
369 def worker(message, key_length, fitness):
370 splits = every_nth(sanitised_message, key_length)
371 key = ''.join([chr(caesar_break(s)[0] + ord('a')) for s in splits])
372 plaintext = vigenere_decipher(message, key)
373 fit = fitness(plaintext)
374 return key, fit
375 sanitised_message = sanitise(message)
376 results = starmap(worker, [(sanitised_message, i, fitness)
377 for i in range(1, max_key_length+1)])
378 return max(results, key=lambda k: k[1])
379
380
381 def beaufort_frequency_break(message, max_key_length=20, fitness=Pletters):
382 """Breaks a Beaufort cipher with frequency analysis
383
384 >>> beaufort_frequency_break(beaufort_encipher(sanitise("It is time to " \
385 "run. She is ready and so am I. I stole Daniel's pocketbook this " \
386 "afternoon when he left his jacket hanging on the easel in the " \
387 "attic. I jump every time I hear a footstep on the stairs, " \
388 "certain that the theft has been discovered and that I will " \
389 "be caught. The SS officer visits less often now " \
390 "that he is sure"), 'florence')) # doctest: +ELLIPSIS
391 ('florence', -307.5473096791...)
392 """
393 def worker(message, key_length, fitness):
394 splits = every_nth(sanitised_message, key_length)
395 key = ''.join([chr(-caesar_break(s)[0] % 26 + ord('a')) for s in splits])
396 plaintext = beaufort_decipher(message, key)
397 fit = fitness(plaintext)
398 return key, fit
399 sanitised_message = sanitise(message)
400 results = starmap(worker, [(sanitised_message, i, fitness)
401 for i in range(1, max_key_length+1)])
402 return max(results, key=lambda k: k[1])
403
404
405 def plot_frequency_histogram(freqs, sort_key=None):
406 x = range(len(freqs.keys()))
407 y = [freqs[l] for l in sorted(freqs.keys(), key=sort_key)]
408 f = plt.figure()
409 ax = f.add_axes([0.1, 0.1, 0.9, 0.9])
410 ax.bar(x, y, align='center')
411 ax.set_xticks(x)
412 ax.set_xticklabels(sorted(freqs.keys(), key=sort_key))
413 f.show()
414
415
416 if __name__ == "__main__":
417 import doctest
418 doctest.testmod()
419