Hillclimbing to solve monosubstitution ciphers
[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
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,
84 plaintext[:50]))
85 if fit > best_fit:
86 best_fit = fit
87 best_shift = shift
88 logger.info('Caesar break best fit: key {0} gives fit of {1} and '
89 'decrypt starting: {2}'.format(best_shift, best_fit,
90 caesar_decipher(sanitised_message, best_shift)[:50]))
91 return best_shift, best_fit
92
93 def affine_break(message, fitness=Pletters):
94 """Breaks an affine cipher using frequency analysis
95
96 >>> affine_break('lmyfu bkuusd dyfaxw claol psfaom jfasd snsfg jfaoe ls ' \
97 'omytd jlaxe mh jm bfmibj umis hfsul axubafkjamx. ls kffkxwsd jls ' \
98 'ofgbjmwfkiu olfmxmtmwaokttg jlsx ls kffkxwsd jlsi zg tsxwjl. jlsx ' \
99 'ls umfjsd jlsi zg hfsqysxog. ls dmmdtsd mx jls bats mh bkbsf. ls ' \
100 'bfmctsd kfmyxd jls lyj, mztanamyu xmc jm clm cku tmmeaxw kj lai ' \
101 'kxd clm ckuxj.') # doctest: +ELLIPSIS
102 ((15, 22, True), -340.601181913...)
103 """
104 sanitised_message = sanitise(message)
105 best_multiplier = 0
106 best_adder = 0
107 best_one_based = True
108 best_fit = float("-inf")
109 for one_based in [True, False]:
110 for multiplier in [x for x in range(1, 26, 2) if x != 13]:
111 for adder in range(26):
112 plaintext = affine_decipher(sanitised_message,
113 multiplier, adder, one_based)
114 fit = fitness(plaintext)
115 logger.debug('Affine break attempt using key {0}x+{1} ({2}) '
116 'gives fit of {3} and decrypt starting: {4}'.
117 format(multiplier, adder, one_based, fit,
118 plaintext[:50]))
119 if fit > best_fit:
120 best_fit = fit
121 best_multiplier = multiplier
122 best_adder = adder
123 best_one_based = one_based
124 logger.info('Affine break best fit with key {0}x+{1} ({2}) gives fit of '
125 '{3} and decrypt starting: {4}'.format(
126 best_multiplier, best_adder, best_one_based, best_fit,
127 affine_decipher(sanitised_message, best_multiplier,
128 best_adder, best_one_based)[:50]))
129 return (best_multiplier, best_adder, best_one_based), best_fit
130
131 def keyword_break(message, wordlist=keywords, fitness=Pletters):
132 """Breaks a keyword substitution cipher using a dictionary and
133 frequency analysis.
134
135 >>> keyword_break(keyword_encipher('this is a test message for the ' \
136 'keyword decipherment', 'elephant', KeywordWrapAlphabet.from_last), \
137 wordlist=['cat', 'elephant', 'kangaroo']) # doctest: +ELLIPSIS
138 (('elephant', <KeywordWrapAlphabet.from_last: 2>), -52.834575011...)
139 """
140 best_keyword = ''
141 best_wrap_alphabet = True
142 best_fit = float("-inf")
143 for wrap_alphabet in KeywordWrapAlphabet:
144 for keyword in wordlist:
145 plaintext = keyword_decipher(message, keyword, wrap_alphabet)
146 fit = fitness(plaintext)
147 logger.debug('Keyword break attempt using key {0} (wrap={1}) '
148 'gives fit of {2} and decrypt starting: {3}'.format(
149 keyword, wrap_alphabet, fit,
150 sanitise(plaintext)[:50]))
151 if fit > best_fit:
152 best_fit = fit
153 best_keyword = keyword
154 best_wrap_alphabet = wrap_alphabet
155 logger.info('Keyword break best fit with key {0} (wrap={1}) gives fit of '
156 '{2} and decrypt starting: {3}'.format(best_keyword,
157 best_wrap_alphabet, best_fit, sanitise(
158 keyword_decipher(message, best_keyword,
159 best_wrap_alphabet))[:50]))
160 return (best_keyword, best_wrap_alphabet), best_fit
161
162 def keyword_break_mp(message, wordlist=keywords, fitness=Pletters,
163 chunksize=500):
164 """Breaks a keyword substitution cipher using a dictionary and
165 frequency analysis
166
167 >>> keyword_break_mp(keyword_encipher('this is a test message for the ' \
168 'keyword decipherment', 'elephant', KeywordWrapAlphabet.from_last), \
169 wordlist=['cat', 'elephant', 'kangaroo']) # doctest: +ELLIPSIS
170 (('elephant', <KeywordWrapAlphabet.from_last: 2>), -52.834575011...)
171 """
172 with Pool() as pool:
173 helper_args = [(message, word, wrap, fitness)
174 for word in wordlist
175 for wrap in KeywordWrapAlphabet]
176 # Gotcha: the helper function here needs to be defined at the top level
177 # (limitation of Pool.starmap)
178 breaks = pool.starmap(keyword_break_worker, helper_args, chunksize)
179 return max(breaks, key=lambda k: k[1])
180
181 def keyword_break_worker(message, keyword, wrap_alphabet, fitness):
182 plaintext = keyword_decipher(message, keyword, wrap_alphabet)
183 fit = fitness(plaintext)
184 logger.debug('Keyword break attempt using key {0} (wrap={1}) gives fit of '
185 '{2} and decrypt starting: {3}'.format(keyword,
186 wrap_alphabet, fit, sanitise(plaintext)[:50]))
187 return (keyword, wrap_alphabet), fit
188
189 def monoalphabetic_break_hillclimbing(message, max_iterations=10000000,
190 fitness=Pletters):
191 ciphertext = unaccent(message).lower()
192 alphabet = list(string.ascii_lowercase)
193 random.shuffle(alphabet)
194 alphabet = ''.join(alphabet)
195 return monoalphabetic_break_hillclimbing_worker(ciphertext, alphabet,
196 max_iterations, fitness)
197
198 def monoalphabetic_break_hillclimbing_mp(message, workers=10,
199 max_iterations = 10000000, fitness=Pletters, chunksize=1):
200 worker_args = []
201 ciphertext = unaccent(message).lower()
202 for i in range(workers):
203 alphabet = list(string.ascii_lowercase)
204 random.shuffle(alphabet)
205 alphabet = ''.join(alphabet)
206 worker_args.append((ciphertext, alphabet, max_iterations, fitness))
207 with Pool() as pool:
208 breaks = pool.starmap(monoalphabetic_break_hillclimbing_worker,
209 worker_args, chunksize)
210 return max(breaks, key=lambda k: k[1])
211
212 def monoalphabetic_break_hillclimbing_worker(message, alphabet,
213 max_iterations, fitness):
214 def swap(letters, i, j):
215 if i > j:
216 i, j = j, i
217 if i == j:
218 return letters
219 else:
220 return (letters[:i] + letters[j] + letters[i+1:j] + letters[i] +
221 letters[j+1:])
222 best_alphabet = alphabet
223 best_fitness = float('-inf')
224 for i in range(max_iterations):
225 alphabet = swap(alphabet, random.randrange(26), random.randrange(26))
226 cipher_translation = ''.maketrans(string.ascii_lowercase, alphabet)
227 plaintext = message.translate(cipher_translation)
228 if fitness(plaintext) > best_fitness:
229 best_fitness = fitness(plaintext)
230 best_alphabet = alphabet
231 print(i, best_alphabet, best_fitness, plaintext)
232 return best_alphabet, best_fitness
233
234
235 def vigenere_keyword_break_mp(message, wordlist=keywords, fitness=Pletters,
236 chunksize=500):
237 """Breaks a vigenere cipher using a dictionary and frequency analysis.
238
239 >>> vigenere_keyword_break_mp(vigenere_encipher(sanitise('this is a test ' \
240 'message for the vigenere decipherment'), 'cat'), \
241 wordlist=['cat', 'elephant', 'kangaroo']) # doctest: +ELLIPSIS
242 ('cat', -52.947271216...)
243 """
244 with Pool() as pool:
245 helper_args = [(message, word, fitness)
246 for word in wordlist]
247 # Gotcha: the helper function here needs to be defined at the top level
248 # (limitation of Pool.starmap)
249 breaks = pool.starmap(vigenere_keyword_break_worker, helper_args,
250 chunksize)
251 return max(breaks, key=lambda k: k[1])
252 vigenere_keyword_break = vigenere_keyword_break_mp
253
254 def vigenere_keyword_break_worker(message, keyword, fitness):
255 plaintext = vigenere_decipher(message, keyword)
256 fit = fitness(plaintext)
257 logger.debug('Vigenere keyword break attempt using key {0} gives fit of '
258 '{1} and decrypt starting: {2}'.format(keyword,
259 fit, sanitise(plaintext)[:50]))
260 return keyword, fit
261
262
263 def vigenere_frequency_break(message, max_key_length=20, fitness=Pletters):
264 """Breaks a Vigenere cipher with frequency analysis
265
266 >>> vigenere_frequency_break(vigenere_encipher(sanitise("It is time to " \
267 "run. She is ready and so am I. I stole Daniel's pocketbook this " \
268 "afternoon when he left his jacket hanging on the easel in the " \
269 "attic. I jump every time I hear a footstep on the stairs, " \
270 "certain that the theft has been discovered and that I will " \
271 "be caught. The SS officer visits less often now that he is " \
272 "sure"), 'florence')) # doctest: +ELLIPSIS
273 ('florence', -307.5473096791...)
274 """
275 def worker(message, key_length, fitness):
276 splits = every_nth(sanitised_message, key_length)
277 key = ''.join([chr(caesar_break(s)[0] + ord('a')) for s in splits])
278 plaintext = vigenere_decipher(message, key)
279 fit = fitness(plaintext)
280 return key, fit
281 sanitised_message = sanitise(message)
282 results = starmap(worker, [(sanitised_message, i, fitness)
283 for i in range(1, max_key_length+1)])
284 return max(results, key=lambda k: k[1])
285
286
287 def beaufort_frequency_break(message, max_key_length=20, fitness=Pletters):
288 """Breaks a Beaufort cipher with frequency analysis
289
290 >>> beaufort_frequency_break(beaufort_encipher(sanitise("It is time to " \
291 "run. She is ready and so am I. I stole Daniel's pocketbook this " \
292 "afternoon when he left his jacket hanging on the easel in the " \
293 "attic. I jump every time I hear a footstep on the stairs, " \
294 "certain that the theft has been discovered and that I will " \
295 "be caught. The SS officer visits less often now " \
296 "that he is sure"), 'florence')) # doctest: +ELLIPSIS
297 ('florence', -307.5473096791...)
298 """
299 def worker(message, key_length, fitness):
300 splits = every_nth(sanitised_message, key_length)
301 key = ''.join([chr(-caesar_break(s)[0] % 26 + ord('a'))
302 for s in splits])
303 plaintext = beaufort_decipher(message, key)
304 fit = fitness(plaintext)
305 return key, fit
306 sanitised_message = sanitise(message)
307 results = starmap(worker, [(sanitised_message, i, fitness)
308 for i in range(1, max_key_length+1)])
309 return max(results, key=lambda k: k[1])
310
311 def plot_frequency_histogram(freqs, sort_key=None):
312 x = range(len(freqs.keys()))
313 y = [freqs[l] for l in sorted(freqs.keys(), key=sort_key)]
314 f = plt.figure()
315 ax = f.add_axes([0.1, 0.1, 0.9, 0.9])
316 ax.bar(x, y, align='center')
317 ax.set_xticks(x)
318 ax.set_xticklabels(sorted(freqs.keys(), key=sort_key))
319 f.show()
320
321
322 if __name__ == "__main__":
323 import doctest
324 doctest.testmod()