Pocket enigma only
[cipher-training.git] / cipherbreak.py
1 """A set of functions to break the ciphers give in ciphers.py.
2 """
3
4 import string
5 import collections
6 import norms
7 import logging
8 import random
9 import math
10 from itertools import starmap
11 from segment import segment
12 from multiprocessing import Pool
13
14 import matplotlib.pyplot as plt
15
16 logger = logging.getLogger(__name__)
17 logger.addHandler(logging.FileHandler('cipher.log'))
18 logger.setLevel(logging.WARNING)
19 #logger.setLevel(logging.INFO)
20 #logger.setLevel(logging.DEBUG)
21
22 from cipher import *
23 from language_models import *
24
25 # To time a run:
26 #
27 # import timeit
28 # c5a = open('2012/5a.ciphertext', 'r').read()
29 # timeit.timeit('keyword_break(c5a)', setup='gc.enable() ; from __main__ import c5a ; from cipher import keyword_break', number=1)
30 # 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)
31
32 transpositions = collections.defaultdict(list)
33 for word in keywords:
34 transpositions[transpositions_of(word)] += [word]
35
36 def frequencies(text):
37 """Count the number of occurrences of each character in text
38
39 >>> sorted(frequencies('abcdefabc').items())
40 [('a', 2), ('b', 2), ('c', 2), ('d', 1), ('e', 1), ('f', 1)]
41 >>> sorted(frequencies('the quick brown fox jumped over the lazy ' \
42 'dog').items()) # doctest: +NORMALIZE_WHITESPACE
43 [(' ', 8), ('a', 1), ('b', 1), ('c', 1), ('d', 2), ('e', 4), ('f', 1),
44 ('g', 1), ('h', 2), ('i', 1), ('j', 1), ('k', 1), ('l', 1), ('m', 1),
45 ('n', 1), ('o', 4), ('p', 1), ('q', 1), ('r', 2), ('t', 2), ('u', 2),
46 ('v', 1), ('w', 1), ('x', 1), ('y', 1), ('z', 1)]
47 >>> sorted(frequencies('The Quick BROWN fox jumped! over... the ' \
48 '(9lazy) DOG').items()) # doctest: +NORMALIZE_WHITESPACE
49 [(' ', 8), ('!', 1), ('(', 1), (')', 1), ('.', 3), ('9', 1), ('B', 1),
50 ('D', 1), ('G', 1), ('N', 1), ('O', 2), ('Q', 1), ('R', 1), ('T', 1),
51 ('W', 1), ('a', 1), ('c', 1), ('d', 1), ('e', 4), ('f', 1), ('h', 2),
52 ('i', 1), ('j', 1), ('k', 1), ('l', 1), ('m', 1), ('o', 2), ('p', 1),
53 ('r', 1), ('t', 1), ('u', 2), ('v', 1), ('x', 1), ('y', 1), ('z', 1)]
54 >>> sorted(frequencies(sanitise('The Quick BROWN fox jumped! over... '\
55 'the (9lazy) DOG')).items()) # doctest: +NORMALIZE_WHITESPACE
56 [('a', 1), ('b', 1), ('c', 1), ('d', 2), ('e', 4), ('f', 1), ('g', 1),
57 ('h', 2), ('i', 1), ('j', 1), ('k', 1), ('l', 1), ('m', 1), ('n', 1),
58 ('o', 4), ('p', 1), ('q', 1), ('r', 2), ('t', 2), ('u', 2), ('v', 1),
59 ('w', 1), ('x', 1), ('y', 1), ('z', 1)]
60 >>> frequencies('abcdefabcdef')['x']
61 0
62 """
63 return collections.Counter(c for c in text)
64
65
66 def caesar_break(message, fitness=Pletters):
67 """Breaks a Caesar cipher using frequency analysis
68
69 >>> caesar_break('ibxcsyorsaqcheyklxivoexlevmrimwxsfiqevvmihrsasrxliwyrh' \
70 'ecjsppsamrkwleppfmergefifvmhixscsymjcsyqeoixlm') # doctest: +ELLIPSIS
71 (4, -130.849989015...)
72 >>> caesar_break('wxwmaxdgheetgwuxztgptedbgznitgwwhpguxyhkxbmhvvtlbhgtee' \
73 'raxlmhiixweblmxgxwmhmaxybkbgztgwztsxwbgmxgmert') # doctest: +ELLIPSIS
74 (19, -128.82410410...)
75 >>> caesar_break('yltbbqnqnzvguvaxurorgenafsbezqvagbnornfgsbevpnaabjurer' \
76 'svaquvzyvxrnznazlybequrvfohgriraabjtbaruraprur') # doctest: +ELLIPSIS
77 (13, -126.25403935...)
78 """
79 sanitised_message = sanitise(message)
80 best_shift = 0
81 best_fit = float('-inf')
82 for shift in range(26):
83 plaintext = caesar_decipher(sanitised_message, shift)
84 fit = fitness(plaintext)
85 logger.debug('Caesar break attempt using key {0} gives fit of {1} '
86 'and decrypt starting: {2}'.format(shift, fit,
87 plaintext[:50]))
88 if fit > best_fit:
89 best_fit = fit
90 best_shift = shift
91 logger.info('Caesar break best fit: key {0} gives fit of {1} and '
92 'decrypt starting: {2}'.format(best_shift, best_fit,
93 caesar_decipher(sanitised_message, best_shift)[:50]))
94 return best_shift, best_fit
95
96 def affine_break(message, fitness=Pletters):
97 """Breaks an affine cipher using frequency analysis
98
99 >>> affine_break('lmyfu bkuusd dyfaxw claol psfaom jfasd snsfg jfaoe ls ' \
100 'omytd jlaxe mh jm bfmibj umis hfsul axubafkjamx. ls kffkxwsd jls ' \
101 'ofgbjmwfkiu olfmxmtmwaokttg jlsx ls kffkxwsd jlsi zg tsxwjl. jlsx ' \
102 'ls umfjsd jlsi zg hfsqysxog. ls dmmdtsd mx jls bats mh bkbsf. ls ' \
103 'bfmctsd kfmyxd jls lyj, mztanamyu xmc jm clm cku tmmeaxw kj lai ' \
104 'kxd clm ckuxj.') # doctest: +ELLIPSIS
105 ((15, 22, True), -340.601181913...)
106 """
107 sanitised_message = sanitise(message)
108 best_multiplier = 0
109 best_adder = 0
110 best_one_based = True
111 best_fit = float("-inf")
112 for one_based in [True, False]:
113 for multiplier in [x for x in range(1, 26, 2) if x != 13]:
114 for adder in range(26):
115 plaintext = affine_decipher(sanitised_message,
116 multiplier, adder, one_based)
117 fit = fitness(plaintext)
118 logger.debug('Affine break attempt using key {0}x+{1} ({2}) '
119 'gives fit of {3} and decrypt starting: {4}'.
120 format(multiplier, adder, one_based, fit,
121 plaintext[:50]))
122 if fit > best_fit:
123 best_fit = fit
124 best_multiplier = multiplier
125 best_adder = adder
126 best_one_based = one_based
127 logger.info('Affine break best fit with key {0}x+{1} ({2}) gives fit of '
128 '{3} and decrypt starting: {4}'.format(
129 best_multiplier, best_adder, best_one_based, best_fit,
130 affine_decipher(sanitised_message, best_multiplier,
131 best_adder, best_one_based)[:50]))
132 return (best_multiplier, best_adder, best_one_based), best_fit
133
134 def keyword_break(message, wordlist=keywords, fitness=Pletters):
135 """Breaks a keyword substitution cipher using a dictionary and
136 frequency analysis.
137
138 >>> keyword_break(keyword_encipher('this is a test message for the ' \
139 'keyword decipherment', 'elephant', KeywordWrapAlphabet.from_last), \
140 wordlist=['cat', 'elephant', 'kangaroo']) # doctest: +ELLIPSIS
141 (('elephant', <KeywordWrapAlphabet.from_last: 2>), -52.834575011...)
142 """
143 best_keyword = ''
144 best_wrap_alphabet = True
145 best_fit = float("-inf")
146 for wrap_alphabet in KeywordWrapAlphabet:
147 for keyword in wordlist:
148 plaintext = keyword_decipher(message, keyword, wrap_alphabet)
149 fit = fitness(plaintext)
150 logger.debug('Keyword break attempt using key {0} (wrap={1}) '
151 'gives fit of {2} and decrypt starting: {3}'.format(
152 keyword, wrap_alphabet, fit,
153 sanitise(plaintext)[:50]))
154 if fit > best_fit:
155 best_fit = fit
156 best_keyword = keyword
157 best_wrap_alphabet = wrap_alphabet
158 logger.info('Keyword break best fit with key {0} (wrap={1}) gives fit of '
159 '{2} and decrypt starting: {3}'.format(best_keyword,
160 best_wrap_alphabet, best_fit, sanitise(
161 keyword_decipher(message, best_keyword,
162 best_wrap_alphabet))[:50]))
163 return (best_keyword, best_wrap_alphabet), best_fit
164
165 def keyword_break_mp(message, wordlist=keywords, fitness=Pletters,
166 chunksize=500):
167 """Breaks a keyword substitution cipher using a dictionary and
168 frequency analysis
169
170 >>> keyword_break_mp(keyword_encipher('this is a test message for the ' \
171 'keyword decipherment', 'elephant', KeywordWrapAlphabet.from_last), \
172 wordlist=['cat', 'elephant', 'kangaroo']) # doctest: +ELLIPSIS
173 (('elephant', <KeywordWrapAlphabet.from_last: 2>), -52.834575011...)
174 """
175 with Pool() as pool:
176 helper_args = [(message, word, wrap, fitness)
177 for word in wordlist
178 for wrap in KeywordWrapAlphabet]
179 # Gotcha: the helper function here needs to be defined at the top level
180 # (limitation of Pool.starmap)
181 breaks = pool.starmap(keyword_break_worker, helper_args, chunksize)
182 return max(breaks, key=lambda k: k[1])
183
184 def keyword_break_worker(message, keyword, wrap_alphabet, fitness):
185 plaintext = keyword_decipher(message, keyword, wrap_alphabet)
186 fit = fitness(plaintext)
187 logger.debug('Keyword break attempt using key {0} (wrap={1}) gives fit of '
188 '{2} and decrypt starting: {3}'.format(keyword,
189 wrap_alphabet, fit, sanitise(plaintext)[:50]))
190 return (keyword, wrap_alphabet), fit
191
192 def monoalphabetic_break_hillclimbing(message, max_iterations=10000000,
193 fitness=Pletters):
194 ciphertext = unaccent(message).lower()
195 alphabet = list(string.ascii_lowercase)
196 random.shuffle(alphabet)
197 alphabet = ''.join(alphabet)
198 return monoalphabetic_break_hillclimbing_worker(ciphertext, alphabet,
199 max_iterations, fitness)
200
201 def monoalphabetic_break_hillclimbing_mp(message, workers=10,
202 max_iterations = 10000000, fitness=Pletters, chunksize=1):
203 worker_args = []
204 ciphertext = unaccent(message).lower()
205 for i in range(workers):
206 alphabet = list(string.ascii_lowercase)
207 random.shuffle(alphabet)
208 alphabet = ''.join(alphabet)
209 worker_args.append((ciphertext, alphabet, max_iterations, fitness))
210 with Pool() as pool:
211 breaks = pool.starmap(monoalphabetic_break_hillclimbing_worker,
212 worker_args, chunksize)
213 return max(breaks, key=lambda k: k[1])
214
215 def monoalphabetic_break_hillclimbing_worker(message, alphabet,
216 max_iterations, fitness):
217 def swap(letters, i, j):
218 if i > j:
219 i, j = j, i
220 if i == j:
221 return letters
222 else:
223 return (letters[:i] + letters[j] + letters[i+1:j] + letters[i] +
224 letters[j+1:])
225 best_alphabet = alphabet
226 best_fitness = float('-inf')
227 for i in range(max_iterations):
228 alphabet = swap(alphabet, random.randrange(26), random.randrange(26))
229 cipher_translation = ''.maketrans(string.ascii_lowercase, alphabet)
230 plaintext = message.translate(cipher_translation)
231 if fitness(plaintext) > best_fitness:
232 best_fitness = fitness(plaintext)
233 best_alphabet = alphabet
234 print(i, best_alphabet, best_fitness, plaintext)
235 return best_alphabet, best_fitness
236
237
238 def column_transposition_break_mp(message, translist=transpositions,
239 fitness=Pbigrams, chunksize=500):
240 """Breaks a column transposition cipher using a dictionary and
241 n-gram frequency analysis
242
243 >>> column_transposition_break_mp(column_transposition_encipher(sanitise( \
244 "It is a truth universally acknowledged, that a single man in \
245 possession of a good fortune, must be in want of a wife. However \
246 little known the feelings or views of such a man may be on his \
247 first entering a neighbourhood, this truth is so well fixed in \
248 the minds of the surrounding families, that he is considered the \
249 rightful property of some one or other of their daughters."), \
250 'encipher'), \
251 translist={(2, 0, 5, 3, 1, 4, 6): ['encipher'], \
252 (5, 0, 6, 1, 3, 4, 2): ['fourteen'], \
253 (6, 1, 0, 4, 5, 3, 2): ['keyword']}) # doctest: +ELLIPSIS
254 (((2, 0, 5, 3, 1, 4, 6), False, False), -709.4646722...)
255 >>> column_transposition_break_mp(column_transposition_encipher(sanitise( \
256 "It is a truth universally acknowledged, that a single man in \
257 possession of a good fortune, must be in want of a wife. However \
258 little known the feelings or views of such a man may be on his \
259 first entering a neighbourhood, this truth is so well fixed in \
260 the minds of the surrounding families, that he is considered the \
261 rightful property of some one or other of their daughters."), \
262 'encipher'), \
263 translist={(2, 0, 5, 3, 1, 4, 6): ['encipher'], \
264 (5, 0, 6, 1, 3, 4, 2): ['fourteen'], \
265 (6, 1, 0, 4, 5, 3, 2): ['keyword']}, \
266 fitness=Ptrigrams) # doctest: +ELLIPSIS
267 (((2, 0, 5, 3, 1, 4, 6), False, False), -997.0129085...)
268 """
269 with Pool() as pool:
270 helper_args = [(message, trans, fillcolumnwise, emptycolumnwise,
271 fitness)
272 for trans in translist.keys()
273 for fillcolumnwise in [True, False]
274 for emptycolumnwise in [True, False]]
275 # Gotcha: the helper function here needs to be defined at the top level
276 # (limitation of Pool.starmap)
277 breaks = pool.starmap(column_transposition_break_worker,
278 helper_args, chunksize)
279 return max(breaks, key=lambda k: k[1])
280 column_transposition_break = column_transposition_break_mp
281
282 def column_transposition_break_worker(message, transposition,
283 fillcolumnwise, emptycolumnwise, fitness):
284 plaintext = column_transposition_decipher(message, transposition,
285 fillcolumnwise=fillcolumnwise, emptycolumnwise=emptycolumnwise)
286 fit = fitness(sanitise(plaintext))
287 logger.debug('Column transposition break attempt using key {0} '
288 'gives fit of {1} and decrypt starting: {2}'.format(
289 transposition, fit,
290 sanitise(plaintext)[:50]))
291 return (transposition, fillcolumnwise, emptycolumnwise), fit
292
293
294 def scytale_break_mp(message, max_key_length=20,
295 fitness=Pbigrams, chunksize=500):
296 """Breaks a scytale cipher using a range of lengths and
297 n-gram frequency analysis
298
299 >>> scytale_break_mp(scytale_encipher(sanitise( \
300 "It is a truth universally acknowledged, that a single man in \
301 possession of a good fortune, must be in want of a wife. However \
302 little known the feelings or views of such a man may be on his \
303 first entering a neighbourhood, this truth is so well fixed in \
304 the minds of the surrounding families, that he is considered the \
305 rightful property of some one or other of their daughters."), \
306 5)) # doctest: +ELLIPSIS
307 (5, -709.4646722...)
308 >>> scytale_break_mp(scytale_encipher(sanitise( \
309 "It is a truth universally acknowledged, that a single man in \
310 possession of a good fortune, must be in want of a wife. However \
311 little known the feelings or views of such a man may be on his \
312 first entering a neighbourhood, this truth is so well fixed in \
313 the minds of the surrounding families, that he is considered the \
314 rightful property of some one or other of their daughters."), \
315 5), \
316 fitness=Ptrigrams) # doctest: +ELLIPSIS
317 (5, -997.0129085...)
318 """
319 with Pool() as pool:
320 helper_args = [(message, trans, False, True, fitness)
321 for trans in
322 [[col for col in range(math.ceil(len(message)/rows))]
323 for rows in range(1,max_key_length+1)]]
324 # Gotcha: the helper function here needs to be defined at the top level
325 # (limitation of Pool.starmap)
326 breaks = pool.starmap(column_transposition_break_worker,
327 helper_args, chunksize)
328 best = max(breaks, key=lambda k: k[1])
329 return math.trunc(len(message) / len(best[0][0])), best[1]
330 scytale_break = scytale_break_mp
331
332
333 def vigenere_keyword_break_mp(message, wordlist=keywords, fitness=Pletters,
334 chunksize=500):
335 """Breaks a vigenere cipher using a dictionary and frequency analysis.
336
337 >>> vigenere_keyword_break_mp(vigenere_encipher(sanitise('this is a test ' \
338 'message for the vigenere decipherment'), 'cat'), \
339 wordlist=['cat', 'elephant', 'kangaroo']) # doctest: +ELLIPSIS
340 ('cat', -52.947271216...)
341 """
342 with Pool() as pool:
343 helper_args = [(message, word, fitness)
344 for word in wordlist]
345 # Gotcha: the helper function here needs to be defined at the top level
346 # (limitation of Pool.starmap)
347 breaks = pool.starmap(vigenere_keyword_break_worker, helper_args,
348 chunksize)
349 return max(breaks, key=lambda k: k[1])
350 vigenere_keyword_break = vigenere_keyword_break_mp
351
352 def vigenere_keyword_break_worker(message, keyword, fitness):
353 plaintext = vigenere_decipher(message, keyword)
354 fit = fitness(plaintext)
355 logger.debug('Vigenere keyword break attempt using key {0} gives fit of '
356 '{1} and decrypt starting: {2}'.format(keyword,
357 fit, sanitise(plaintext)[:50]))
358 return keyword, fit
359
360
361
362 def vigenere_frequency_break(message, max_key_length=20, fitness=Pletters):
363 """Breaks a Vigenere cipher with frequency analysis
364
365 >>> vigenere_frequency_break(vigenere_encipher(sanitise("It is time to " \
366 "run. She is ready and so am I. I stole Daniel's pocketbook this " \
367 "afternoon when he left his jacket hanging on the easel in the " \
368 "attic. I jump every time I hear a footstep on the stairs, " \
369 "certain that the theft has been discovered and that I will " \
370 "be caught. The SS officer visits less often now that he is " \
371 "sure"), 'florence')) # doctest: +ELLIPSIS
372 ('florence', -307.5473096791...)
373 """
374 def worker(message, key_length, fitness):
375 splits = every_nth(sanitised_message, key_length)
376 key = ''.join([chr(caesar_break(s)[0] + ord('a')) for s in splits])
377 plaintext = vigenere_decipher(message, key)
378 fit = fitness(plaintext)
379 return key, fit
380 sanitised_message = sanitise(message)
381 results = starmap(worker, [(sanitised_message, i, fitness)
382 for i in range(1, max_key_length+1)])
383 return max(results, key=lambda k: k[1])
384
385
386 def beaufort_frequency_break(message, max_key_length=20, fitness=Pletters):
387 """Breaks a Beaufort cipher with frequency analysis
388
389 >>> beaufort_frequency_break(beaufort_encipher(sanitise("It is time to " \
390 "run. She is ready and so am I. I stole Daniel's pocketbook this " \
391 "afternoon when he left his jacket hanging on the easel in the " \
392 "attic. I jump every time I hear a footstep on the stairs, " \
393 "certain that the theft has been discovered and that I will " \
394 "be caught. The SS officer visits less often now " \
395 "that he is sure"), 'florence')) # doctest: +ELLIPSIS
396 ('florence', -307.5473096791...)
397 """
398 def worker(message, key_length, fitness):
399 splits = every_nth(sanitised_message, key_length)
400 key = ''.join([chr(-caesar_break(s)[0] % 26 + ord('a'))
401 for s in splits])
402 plaintext = beaufort_decipher(message, key)
403 fit = fitness(plaintext)
404 return key, fit
405 sanitised_message = sanitise(message)
406 results = starmap(worker, [(sanitised_message, i, fitness)
407 for i in range(1, max_key_length+1)])
408 return max(results, key=lambda k: k[1])
409
410 def plot_frequency_histogram(freqs, sort_key=None):
411 x = range(len(freqs.keys()))
412 y = [freqs[l] for l in sorted(freqs.keys(), key=sort_key)]
413 f = plt.figure()
414 ax = f.add_axes([0.1, 0.1, 0.9, 0.9])
415 ax.bar(x, y, align='center')
416 ax.set_xticks(x)
417 ax.set_xticklabels(sorted(freqs.keys(), key=sort_key))
418 f.show()
419
420
421 if __name__ == "__main__":
422 import doctest
423 doctest.testmod()