Tweaks
[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 number_of_solutions=1, 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 >>> keyword_break_mp(keyword_encipher('this is a test message for the ' \
175 'keyword decipherment', 'elephant', KeywordWrapAlphabet.from_last), \
176 wordlist=['cat', 'elephant', 'kangaroo'], \
177 number_of_solutions=2) # doctest: +ELLIPSIS, +NORMALIZE_WHITESPACE
178 [(('elephant', <KeywordWrapAlphabet.from_last: 2>), -52.834575011...),
179 (('elephant', <KeywordWrapAlphabet.from_largest: 3>), -52.834575011...)]
180 """
181 with Pool() as pool:
182 helper_args = [(message, word, wrap, fitness)
183 for word in wordlist
184 for wrap in KeywordWrapAlphabet]
185 # Gotcha: the helper function here needs to be defined at the top level
186 # (limitation of Pool.starmap)
187 breaks = pool.starmap(keyword_break_worker, helper_args, chunksize)
188 if number_of_solutions == 1:
189 return max(breaks, key=lambda k: k[1])
190 else:
191 return sorted(breaks, key=lambda k: k[1], reverse=True)[:number_of_solutions]
192
193 def keyword_break_worker(message, keyword, wrap_alphabet, fitness):
194 plaintext = keyword_decipher(message, keyword, wrap_alphabet)
195 fit = fitness(plaintext)
196 logger.debug('Keyword break attempt using key {0} (wrap={1}) gives fit of '
197 '{2} and decrypt starting: {3}'.format(keyword,
198 wrap_alphabet, fit, sanitise(plaintext)[:50]))
199 return (keyword, wrap_alphabet), fit
200
201 def monoalphabetic_break_hillclimbing(message, max_iterations=10000000,
202 fitness=Pletters):
203 ciphertext = unaccent(message).lower()
204 alphabet = list(string.ascii_lowercase)
205 random.shuffle(alphabet)
206 alphabet = ''.join(alphabet)
207 return monoalphabetic_break_hillclimbing_worker(ciphertext, alphabet,
208 max_iterations, fitness)
209
210 def monoalphabetic_break_hillclimbing_mp(message, workers=10,
211 max_iterations = 10000000, fitness=Pletters, chunksize=1):
212 worker_args = []
213 ciphertext = unaccent(message).lower()
214 for i in range(workers):
215 alphabet = list(string.ascii_lowercase)
216 random.shuffle(alphabet)
217 alphabet = ''.join(alphabet)
218 worker_args.append((ciphertext, alphabet, max_iterations, fitness))
219 with Pool() as pool:
220 breaks = pool.starmap(monoalphabetic_break_hillclimbing_worker,
221 worker_args, chunksize)
222 return max(breaks, key=lambda k: k[1])
223
224 def monoalphabetic_break_hillclimbing_worker(message, alphabet,
225 max_iterations, fitness):
226 def swap(letters, i, j):
227 if i > j:
228 i, j = j, i
229 if i == j:
230 return letters
231 else:
232 return (letters[:i] + letters[j] + letters[i+1:j] + letters[i] +
233 letters[j+1:])
234 best_alphabet = alphabet
235 best_fitness = float('-inf')
236 for i in range(max_iterations):
237 alphabet = swap(alphabet, random.randrange(26), random.randrange(26))
238 cipher_translation = ''.maketrans(string.ascii_lowercase, alphabet)
239 plaintext = message.translate(cipher_translation)
240 if fitness(plaintext) > best_fitness:
241 best_fitness = fitness(plaintext)
242 best_alphabet = alphabet
243 print(i, best_alphabet, best_fitness, plaintext)
244 return best_alphabet, best_fitness
245
246
247 def column_transposition_break_mp(message, translist=transpositions,
248 fitness=Pbigrams, chunksize=500):
249 """Breaks a column transposition cipher using a dictionary and
250 n-gram frequency analysis
251
252 >>> column_transposition_break_mp(column_transposition_encipher(sanitise( \
253 "It is a truth universally acknowledged, that a single man in \
254 possession of a good fortune, must be in want of a wife. However \
255 little known the feelings or views of such a man may be on his \
256 first entering a neighbourhood, this truth is so well fixed in \
257 the minds of the surrounding families, that he is considered the \
258 rightful property of some one or other of their daughters."), \
259 'encipher'), \
260 translist={(2, 0, 5, 3, 1, 4, 6): ['encipher'], \
261 (5, 0, 6, 1, 3, 4, 2): ['fourteen'], \
262 (6, 1, 0, 4, 5, 3, 2): ['keyword']}) # doctest: +ELLIPSIS
263 (((2, 0, 5, 3, 1, 4, 6), False, False), -709.4646722...)
264 >>> column_transposition_break_mp(column_transposition_encipher(sanitise( \
265 "It is a truth universally acknowledged, that a single man in \
266 possession of a good fortune, must be in want of a wife. However \
267 little known the feelings or views of such a man may be on his \
268 first entering a neighbourhood, this truth is so well fixed in \
269 the minds of the surrounding families, that he is considered the \
270 rightful property of some one or other of their daughters."), \
271 'encipher'), \
272 translist={(2, 0, 5, 3, 1, 4, 6): ['encipher'], \
273 (5, 0, 6, 1, 3, 4, 2): ['fourteen'], \
274 (6, 1, 0, 4, 5, 3, 2): ['keyword']}, \
275 fitness=Ptrigrams) # doctest: +ELLIPSIS
276 (((2, 0, 5, 3, 1, 4, 6), False, False), -997.0129085...)
277 """
278 with Pool() as pool:
279 helper_args = [(message, trans, fillcolumnwise, emptycolumnwise,
280 fitness)
281 for trans in translist.keys()
282 for fillcolumnwise in [True, False]
283 for emptycolumnwise in [True, False]]
284 # Gotcha: the helper function here needs to be defined at the top level
285 # (limitation of Pool.starmap)
286 breaks = pool.starmap(column_transposition_break_worker,
287 helper_args, chunksize)
288 return max(breaks, key=lambda k: k[1])
289 column_transposition_break = column_transposition_break_mp
290
291 def column_transposition_break_worker(message, transposition,
292 fillcolumnwise, emptycolumnwise, fitness):
293 plaintext = column_transposition_decipher(message, transposition,
294 fillcolumnwise=fillcolumnwise, emptycolumnwise=emptycolumnwise)
295 fit = fitness(sanitise(plaintext))
296 logger.debug('Column transposition break attempt using key {0} '
297 'gives fit of {1} and decrypt starting: {2}'.format(
298 transposition, fit,
299 sanitise(plaintext)[:50]))
300 return (transposition, fillcolumnwise, emptycolumnwise), fit
301
302
303 def scytale_break_mp(message, max_key_length=20,
304 fitness=Pbigrams, chunksize=500):
305 """Breaks a scytale cipher using a range of lengths and
306 n-gram frequency analysis
307
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)) # doctest: +ELLIPSIS
316 (5, -709.4646722...)
317 >>> scytale_break_mp(scytale_encipher(sanitise( \
318 "It is a truth universally acknowledged, that a single man in \
319 possession of a good fortune, must be in want of a wife. However \
320 little known the feelings or views of such a man may be on his \
321 first entering a neighbourhood, this truth is so well fixed in \
322 the minds of the surrounding families, that he is considered the \
323 rightful property of some one or other of their daughters."), \
324 5), \
325 fitness=Ptrigrams) # doctest: +ELLIPSIS
326 (5, -997.0129085...)
327 """
328 with Pool() as pool:
329 helper_args = [(message, trans, False, True, fitness)
330 for trans in
331 [[col for col in range(math.ceil(len(message)/rows))]
332 for rows in range(1,max_key_length+1)]]
333 # Gotcha: the helper function here needs to be defined at the top level
334 # (limitation of Pool.starmap)
335 breaks = pool.starmap(column_transposition_break_worker,
336 helper_args, chunksize)
337 best = max(breaks, key=lambda k: k[1])
338 return math.trunc(len(message) / len(best[0][0])), best[1]
339 scytale_break = scytale_break_mp
340
341
342 def vigenere_keyword_break_mp(message, wordlist=keywords, fitness=Pletters,
343 chunksize=500):
344 """Breaks a vigenere cipher using a dictionary and frequency analysis.
345
346 >>> vigenere_keyword_break_mp(vigenere_encipher(sanitise('this is a test ' \
347 'message for the vigenere decipherment'), 'cat'), \
348 wordlist=['cat', 'elephant', 'kangaroo']) # doctest: +ELLIPSIS
349 ('cat', -52.947271216...)
350 """
351 with Pool() as pool:
352 helper_args = [(message, word, fitness)
353 for word in wordlist]
354 # Gotcha: the helper function here needs to be defined at the top level
355 # (limitation of Pool.starmap)
356 breaks = pool.starmap(vigenere_keyword_break_worker, helper_args,
357 chunksize)
358 return max(breaks, key=lambda k: k[1])
359 vigenere_keyword_break = vigenere_keyword_break_mp
360
361 def vigenere_keyword_break_worker(message, keyword, fitness):
362 plaintext = vigenere_decipher(message, keyword)
363 fit = fitness(plaintext)
364 logger.debug('Vigenere keyword break attempt using key {0} gives fit of '
365 '{1} and decrypt starting: {2}'.format(keyword,
366 fit, sanitise(plaintext)[:50]))
367 return keyword, fit
368
369
370
371 def vigenere_frequency_break(message, max_key_length=20, fitness=Pletters):
372 """Breaks a Vigenere cipher with frequency analysis
373
374 >>> vigenere_frequency_break(vigenere_encipher(sanitise("It is time to " \
375 "run. She is ready and so am I. I stole Daniel's pocketbook this " \
376 "afternoon when he left his jacket hanging on the easel in the " \
377 "attic. I jump every time I hear a footstep on the stairs, " \
378 "certain that the theft has been discovered and that I will " \
379 "be caught. The SS officer visits less often now that he is " \
380 "sure"), 'florence')) # doctest: +ELLIPSIS
381 ('florence', -307.5473096791...)
382 """
383 def worker(message, key_length, fitness):
384 splits = every_nth(sanitised_message, key_length)
385 key = ''.join([chr(caesar_break(s)[0] + ord('a')) for s in splits])
386 plaintext = vigenere_decipher(message, key)
387 fit = fitness(plaintext)
388 return key, fit
389 sanitised_message = sanitise(message)
390 results = starmap(worker, [(sanitised_message, i, fitness)
391 for i in range(1, max_key_length+1)])
392 return max(results, key=lambda k: k[1])
393
394
395 def beaufort_frequency_break(message, max_key_length=20, fitness=Pletters):
396 """Breaks a Beaufort cipher with frequency analysis
397
398 >>> beaufort_frequency_break(beaufort_encipher(sanitise("It is time to " \
399 "run. She is ready and so am I. I stole Daniel's pocketbook this " \
400 "afternoon when he left his jacket hanging on the easel in the " \
401 "attic. I jump every time I hear a footstep on the stairs, " \
402 "certain that the theft has been discovered and that I will " \
403 "be caught. The SS officer visits less often now " \
404 "that he is sure"), 'florence')) # doctest: +ELLIPSIS
405 ('florence', -307.5473096791...)
406 """
407 def worker(message, key_length, fitness):
408 splits = every_nth(sanitised_message, key_length)
409 key = ''.join([chr(-caesar_break(s)[0] % 26 + ord('a'))
410 for s in splits])
411 plaintext = beaufort_decipher(message, key)
412 fit = fitness(plaintext)
413 return key, fit
414 sanitised_message = sanitise(message)
415 results = starmap(worker, [(sanitised_message, i, fitness)
416 for i in range(1, max_key_length+1)])
417 return max(results, key=lambda k: k[1])
418
419
420 def pocket_enigma_break_by_crib(message, wheel_spec, crib, crib_position):
421 """Break a pocket enigma using a crib (some plaintext that's expected to
422 be in a certain position). Returns a list of possible starting wheel
423 positions that could produce the crib.
424
425 >>> pocket_enigma_break_by_crib('kzpjlzmoga', 1, 'h', 0)
426 ['a', 'f', 'q']
427 >>> pocket_enigma_break_by_crib('kzpjlzmoga', 1, 'he', 0)
428 ['a']
429 >>> pocket_enigma_break_by_crib('kzpjlzmoga', 1, 'll', 2)
430 ['a']
431 >>> pocket_enigma_break_by_crib('kzpjlzmoga', 1, 'l', 2)
432 ['a']
433 >>> pocket_enigma_break_by_crib('kzpjlzmoga', 1, 'l', 3)
434 ['a', 'j', 'n']
435 >>> pocket_enigma_break_by_crib('aaaaa', 1, 'l', 3)
436 []
437 """
438 pe = PocketEnigma(wheel=wheel_spec)
439 possible_positions = []
440 for p in string.ascii_lowercase:
441 pe.set_position(p)
442 plaintext = pe.decipher(message)
443 if plaintext[crib_position:crib_position+len(crib)] == crib:
444 possible_positions += [p]
445 return possible_positions
446
447
448 def plot_frequency_histogram(freqs, sort_key=None):
449 x = range(len(freqs.keys()))
450 y = [freqs[l] for l in sorted(freqs.keys(), key=sort_key)]
451 f = plt.figure()
452 ax = f.add_axes([0.1, 0.1, 0.9, 0.9])
453 ax.bar(x, y, align='center')
454 ax.set_xticks(x)
455 ax.set_xticklabels(sorted(freqs.keys(), key=sort_key))
456 f.show()
457
458
459 if __name__ == "__main__":
460 import doctest
461 doctest.testmod()