+import string
+import collections
+import norms
+import logging
+from itertools import zip_longest, cycle, permutations
+from segment import segment
+from multiprocessing import Pool
+from math import log10
+
+import matplotlib.pyplot as plt
+
+from cipher import *
+from language_models import *
+
+# To time a run:
+#
+# import timeit
+# c5a = open('2012/5a.ciphertext', 'r').read()
+# timeit.timeit('keyword_break(c5a)', setup='gc.enable() ; from __main__ import c5a ; from cipher import keyword_break', number=1)
+# 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)
+
+transpositions = collections.defaultdict(list)
+for word in keywords:
+ transpositions[transpositions_of(word)] += [word]
+
+def frequencies(text):
+ """Count the number of occurrences of each character in text
+
+ >>> sorted(frequencies('abcdefabc').items())
+ [('a', 2), ('b', 2), ('c', 2), ('d', 1), ('e', 1), ('f', 1)]
+ >>> sorted(frequencies('the quick brown fox jumped over the lazy ' \
+ 'dog').items()) # doctest: +NORMALIZE_WHITESPACE
+ [(' ', 8), ('a', 1), ('b', 1), ('c', 1), ('d', 2), ('e', 4), ('f', 1),
+ ('g', 1), ('h', 2), ('i', 1), ('j', 1), ('k', 1), ('l', 1), ('m', 1),
+ ('n', 1), ('o', 4), ('p', 1), ('q', 1), ('r', 2), ('t', 2), ('u', 2),
+ ('v', 1), ('w', 1), ('x', 1), ('y', 1), ('z', 1)]
+ >>> sorted(frequencies('The Quick BROWN fox jumped! over... the ' \
+ '(9lazy) DOG').items()) # doctest: +NORMALIZE_WHITESPACE
+ [(' ', 8), ('!', 1), ('(', 1), (')', 1), ('.', 3), ('9', 1), ('B', 1),
+ ('D', 1), ('G', 1), ('N', 1), ('O', 2), ('Q', 1), ('R', 1), ('T', 1),
+ ('W', 1), ('a', 1), ('c', 1), ('d', 1), ('e', 4), ('f', 1), ('h', 2),
+ ('i', 1), ('j', 1), ('k', 1), ('l', 1), ('m', 1), ('o', 2), ('p', 1),
+ ('r', 1), ('t', 1), ('u', 2), ('v', 1), ('x', 1), ('y', 1), ('z', 1)]
+ >>> sorted(frequencies(sanitise('The Quick BROWN fox jumped! over... ' \
+ 'the (9lazy) DOG')).items()) # doctest: +NORMALIZE_WHITESPACE
+ [('a', 1), ('b', 1), ('c', 1), ('d', 2), ('e', 4), ('f', 1), ('g', 1),
+ ('h', 2), ('i', 1), ('j', 1), ('k', 1), ('l', 1), ('m', 1), ('n', 1),
+ ('o', 4), ('p', 1), ('q', 1), ('r', 2), ('t', 2), ('u', 2), ('v', 1),
+ ('w', 1), ('x', 1), ('y', 1), ('z', 1)]
+ >>> frequencies('abcdefabcdef')['x']
+ 0
+ """
+ #counts = collections.defaultdict(int)
+ #for c in text:
+ # counts[c] += 1
+ #return counts
+ return collections.Counter(c for c in text)
+
+
+def caesar_break(message, fitness=Pletters):
+ """Breaks a Caesar cipher using frequency analysis
+
+ >>> caesar_break('ibxcsyorsaqcheyklxivoexlevmrimwxsfiqevvmihrsasrxliwyrh' \
+ 'ecjsppsamrkwleppfmergefifvmhixscsymjcsyqeoixlm') # doctest: +ELLIPSIS
+ (4, -130.849890899...)
+ >>> caesar_break('wxwmaxdgheetgwuxztgptedbgznitgwwhpguxyhkxbmhvvtlbhgtee' \
+ 'raxlmhiixweblmxgxwmhmaxybkbgztgwztsxwbgmxgmert') # doctest: +ELLIPSIS
+ (19, -128.82516920...)
+ >>> caesar_break('yltbbqnqnzvguvaxurorgenafsbezqvagbnornfgsbevpnaabjurer' \
+ 'svaquvzyvxrnznazlybequrvfohgriraabjtbaruraprur') # doctest: +ELLIPSIS
+ (13, -126.25233502...)
+ """
+ sanitised_message = sanitise(message)
+ best_shift = 0
+ best_fit = float('-inf')
+ for shift in range(26):
+ plaintext = caesar_decipher(sanitised_message, shift)
+ fit = fitness(plaintext)
+ logger.debug('Caesar break attempt using key {0} gives fit of {1} '
+ 'and decrypt starting: {2}'.format(shift, fit, plaintext[:50]))
+ if fit > best_fit:
+ best_fit = fit
+ best_shift = shift
+ logger.info('Caesar break best fit: key {0} gives fit of {1} and '
+ 'decrypt starting: {2}'.format(best_shift, best_fit,
+ caesar_decipher(sanitised_message, best_shift)[:50]))
+ return best_shift, best_fit
+
+def affine_break(message, fitness=Pletters):
+ """Breaks an affine cipher using frequency analysis
+
+ >>> affine_break('lmyfu bkuusd dyfaxw claol psfaom jfasd snsfg jfaoe ls ' \
+ 'omytd jlaxe mh jm bfmibj umis hfsul axubafkjamx. ls kffkxwsd jls ' \
+ 'ofgbjmwfkiu olfmxmtmwaokttg jlsx ls kffkxwsd jlsi zg tsxwjl. jlsx ' \
+ 'ls umfjsd jlsi zg hfsqysxog. ls dmmdtsd mx jls bats mh bkbsf. ls ' \
+ 'bfmctsd kfmyxd jls lyj, mztanamyu xmc jm clm cku tmmeaxw kj lai ' \
+ 'kxd clm ckuxj.') # doctest: +ELLIPSIS
+ ((15, 22, True), -340.611412245...)
+ """
+ sanitised_message = sanitise(message)
+ best_multiplier = 0
+ best_adder = 0
+ best_one_based = True
+ best_fit = float("-inf")
+ for one_based in [True, False]:
+ for multiplier in [x for x in range(1, 26, 2) if x != 13]:
+ for adder in range(26):
+ plaintext = affine_decipher(sanitised_message,
+ multiplier, adder, one_based)
+ fit = fitness(plaintext)
+ logger.debug('Affine break attempt using key {0}x+{1} ({2}) '
+ 'gives fit of {3} and decrypt starting: {4}'.
+ format(multiplier, adder, one_based, fit,
+ plaintext[:50]))
+ if fit > best_fit:
+ best_fit = fit
+ best_multiplier = multiplier
+ best_adder = adder
+ best_one_based = one_based
+ logger.info('Affine break best fit with key {0}x+{1} ({2}) gives fit of {3} '
+ 'and decrypt starting: {4}'.format(
+ best_multiplier, best_adder, best_one_based, best_fit,
+ affine_decipher(sanitised_message, best_multiplier,
+ best_adder, best_one_based)[:50]))
+ return (best_multiplier, best_adder, best_one_based), best_fit
+
+def keyword_break(message, wordlist=keywords, fitness=Pletters):
+ """Breaks a keyword substitution cipher using a dictionary and
+ frequency analysis
+
+ >>> keyword_break(keyword_encipher('this is a test message for the ' \
+ 'keyword decipherment', 'elephant', 1), \
+ wordlist=['cat', 'elephant', 'kangaroo']) # doctest: +ELLIPSIS
+ (('elephant', 1), -52.8345642265...)
+ """
+ best_keyword = ''
+ best_wrap_alphabet = True
+ best_fit = float("-inf")
+ for wrap_alphabet in range(3):
+ for keyword in wordlist:
+ plaintext = keyword_decipher(message, keyword, wrap_alphabet)
+ fit = fitness(plaintext)
+ logger.debug('Keyword break attempt using key {0} (wrap={1}) '
+ 'gives fit of {2} and decrypt starting: {3}'.format(
+ keyword, wrap_alphabet, fit,
+ sanitise(plaintext)[:50]))
+ if fit > best_fit:
+ best_fit = fit
+ best_keyword = keyword
+ best_wrap_alphabet = wrap_alphabet
+ logger.info('Keyword break best fit with key {0} (wrap={1}) gives fit of '
+ '{2} and decrypt starting: {3}'.format(best_keyword,
+ best_wrap_alphabet, best_fit, sanitise(
+ keyword_decipher(message, best_keyword,
+ best_wrap_alphabet))[:50]))
+ return (best_keyword, best_wrap_alphabet), best_fit
+
+def keyword_break_mp(message, wordlist=keywords, fitness=Pletters, chunksize=500):
+ """Breaks a keyword substitution cipher using a dictionary and
+ frequency analysis
+
+ >>> keyword_break_mp(keyword_encipher('this is a test message for the ' \
+ 'keyword decipherment', 'elephant', 1), \
+ wordlist=['cat', 'elephant', 'kangaroo']) # doctest: +ELLIPSIS
+ (('elephant', 1), -52.834564226507...)
+ """
+ with Pool() as pool:
+ helper_args = [(message, word, wrap, fitness)
+ for word in wordlist for wrap in range(3)]
+ # Gotcha: the helper function here needs to be defined at the top level
+ # (limitation of Pool.starmap)
+ breaks = pool.starmap(keyword_break_worker, helper_args, chunksize)
+ return max(breaks, key=lambda k: k[1])
+
+def keyword_break_worker(message, keyword, wrap_alphabet, fitness):
+ plaintext = keyword_decipher(message, keyword, wrap_alphabet)
+ fit = fitness(plaintext)
+ logger.debug('Keyword break attempt using key {0} (wrap={1}) gives fit of '
+ '{2} and decrypt starting: {3}'.format(keyword,
+ wrap_alphabet, fit, sanitise(plaintext)[:50]))
+ return (keyword, wrap_alphabet), fit
+
+def scytale_break(message, fitness=Pbigrams):
+ """Breaks a Scytale cipher
+
+ >>> scytale_break('tfeulchtrtteehwahsdehneoifeayfsondmwpltmaoalhikotoere' \
+ 'dcweatehiplwxsnhooacgorrcrcraotohsgullasenylrendaianeplscdriioto' \
+ 'aek') # doctest: +ELLIPSIS
+ (6, -281.276219108...)
+ """
+ best_key = 0
+ best_fit = float("-inf")
+ for key in range(1, 20):
+ if len(message) % key == 0:
+ plaintext = scytale_decipher(message, key)
+ fit = fitness(sanitise(plaintext))
+ logger.debug('Scytale break attempt using key {0} gives fit of '
+ '{1} and decrypt starting: {2}'.format(key,
+ fit, sanitise(plaintext)[:50]))
+ if fit > best_fit:
+ best_fit = fit
+ best_key = key
+ logger.info('Scytale break best fit with key {0} gives fit of {1} and '
+ 'decrypt starting: {2}'.format(best_key, best_fit,
+ sanitise(scytale_decipher(message, best_key))[:50]))
+ return best_key, best_fit
+
+
+def column_transposition_break_mp(message, translist=transpositions,
+ fitness=Pbigrams, chunksize=500):
+ """Breaks a column transposition cipher using a dictionary and
+ n-gram frequency analysis
+ """
+ # >>> column_transposition_break_mp(column_transposition_encipher(sanitise( \
+ # "It is a truth universally acknowledged, that a single man in \
+ # possession of a good fortune, must be in want of a wife. However \
+ # little known the feelings or views of such a man may be on his \
+ # first entering a neighbourhood, this truth is so well fixed in the \
+ # minds of the surrounding families, that he is considered the \
+ # rightful property of some one or other of their daughters."), \
+ # 'encipher'), \
+ # translist={(2, 0, 5, 3, 1, 4, 6): ['encipher'], \
+ # (5, 0, 6, 1, 3, 4, 2): ['fourteen'], \
+ # (6, 1, 0, 4, 5, 3, 2): ['keyword']}) # doctest: +ELLIPSIS
+ # (((2, 0, 5, 3, 1, 4, 6), False), 0.0628106372...)
+ # >>> column_transposition_break_mp(column_transposition_encipher(sanitise( \
+ # "It is a truth universally acknowledged, that a single man in \
+ # possession of a good fortune, must be in want of a wife. However \
+ # little known the feelings or views of such a man may be on his \
+ # first entering a neighbourhood, this truth is so well fixed in the \
+ # minds of the surrounding families, that he is considered the \
+ # rightful property of some one or other of their daughters."), \
+ # 'encipher'), \
+ # translist={(2, 0, 5, 3, 1, 4, 6): ['encipher'], \
+ # (5, 0, 6, 1, 3, 4, 2): ['fourteen'], \
+ # (6, 1, 0, 4, 5, 3, 2): ['keyword']}, \
+ # target_counts=normalised_english_trigram_counts) # doctest: +ELLIPSIS
+ # (((2, 0, 5, 3, 1, 4, 6), False), 0.0592259560...)
+ # """
+ with Pool() as pool:
+ helper_args = [(message, trans, columnwise, fitness)
+ for trans in translist.keys()
+ for columnwise in [True, False]]
+ # Gotcha: the helper function here needs to be defined at the top level
+ # (limitation of Pool.starmap)
+ breaks = pool.starmap(column_transposition_break_worker,
+ helper_args, chunksize)
+ return max(breaks, key=lambda k: k[1])
+column_transposition_break = column_transposition_break_mp
+
+def column_transposition_break_worker(message, transposition, columnwise,
+ fitness):
+ plaintext = column_transposition_decipher(message, transposition, columnwise=columnwise)
+ fit = fitness(sanitise(plaintext))
+ logger.debug('Column transposition break attempt using key {0} '
+ 'gives fit of {1} and decrypt starting: {2}'.format(
+ transposition, fit,
+ sanitise(plaintext)[:50]))
+ return (transposition, columnwise), fit
+
+
+def transposition_break_exhaustive(message, fitness=Pbigrams):
+ best_transposition = ''
+ best_pw = float('-inf')
+ for keylength in range(1, 21):
+ if len(message) % keylength == 0:
+ for transposition in permutations(range(keylength)):
+ for columnwise in [True, False]:
+ plaintext = column_transposition_decipher(message,
+ transposition, columnwise=columnwise)
+ fit=fitness(plaintext)
+ logger.debug('Column transposition break attempt using key {0} {1} '
+ 'gives fit of {2} and decrypt starting: {3}'.format(
+ transposition, columnwise, pw,
+ sanitise(plaintext)[:50]))
+ if fit > best_fit:
+ best_transposition = transposition
+ best_columnwise = columnwise
+ best_fit = fit
+ return (best_transposition, best_columnwise), best_pw
+
+
+def vigenere_keyword_break(message, wordlist=keywords, fitness=Pletters):
+ """Breaks a vigenere cipher using a dictionary and
+ frequency analysis
+
+ >>> vigenere_keyword_break(vigenere_encipher(sanitise('this is a test ' \
+ 'message for the vigenere decipherment'), 'cat'), \
+ wordlist=['cat', 'elephant', 'kangaroo']) # doctest: +ELLIPSIS
+ ('cat', -52.9479167030...)
+ """
+ best_keyword = ''
+ best_fit = float("-inf")
+ for keyword in wordlist:
+ plaintext = vigenere_decipher(message, keyword)
+ fit = fitness(plaintext)
+ logger.debug('Vigenere break attempt using key {0} '
+ 'gives fit of {1} and decrypt starting: {2}'.format(
+ keyword, fit,
+ sanitise(plaintext)[:50]))
+ if fit > best_fit:
+ best_fit = fit
+ best_keyword = keyword
+ logger.info('Vigenere break best fit with key {0} gives fit '
+ 'of {1} and decrypt starting: {2}'.format(best_keyword,
+ best_fit, sanitise(
+ vigenere_decipher(message, best_keyword))[:50]))
+ return best_keyword, best_fit
+
+def vigenere_keyword_break_mp(message, wordlist=keywords, fitness=Pletters,
+ chunksize=500):
+ """Breaks a vigenere cipher using a dictionary and
+ frequency analysis
+
+ >>> vigenere_keyword_break_mp(vigenere_encipher(sanitise('this is a test ' \
+ 'message for the vigenere decipherment'), 'cat'), \
+ wordlist=['cat', 'elephant', 'kangaroo']) # doctest: +ELLIPSIS
+ ('cat', -52.9479167030...)
+ """
+ with Pool() as pool:
+ helper_args = [(message, word, fitness)
+ for word in wordlist]
+ # Gotcha: the helper function here needs to be defined at the top level
+ # (limitation of Pool.starmap)
+ breaks = pool.starmap(vigenere_keyword_break_worker, helper_args, chunksize)
+ return max(breaks, key=lambda k: k[1])
+
+def vigenere_keyword_break_worker(message, keyword, fitness):
+ plaintext = vigenere_decipher(message, keyword)
+ fit = fitness(plaintext)
+ logger.debug('Vigenere keyword break attempt using key {0} gives fit of '
+ '{1} and decrypt starting: {2}'.format(keyword,
+ fit, sanitise(plaintext)[:50]))
+ return keyword, fit
+
+
+
+def vigenere_frequency_break(message, fitness=Pletters):
+ """Breaks a Vigenere cipher with frequency analysis
+
+ >>> vigenere_frequency_break(vigenere_encipher(sanitise("It is time to " \
+ "run. She is ready and so am I. I stole Daniel's pocketbook this " \
+ "afternoon when he left his jacket hanging on the easel in the " \
+ "attic. I jump every time I hear a footstep on the stairs, " \
+ "certain that the theft has been discovered and that I will " \
+ "be caught. The SS officer visits less often now that he is " \
+ "sure"), 'florence')) # doctest: +ELLIPSIS
+ ('florence', -307.5549865898...)
+ """
+ best_fit = float("-inf")
+ best_key = ''
+ sanitised_message = sanitise(message)
+ for trial_length in range(1, 20):
+ splits = every_nth(sanitised_message, trial_length)
+ key = ''.join([chr(caesar_break(s)[0] + ord('a')) for s in splits])
+ plaintext = vigenere_decipher(sanitised_message, key)
+ fit = fitness(plaintext)
+ logger.debug('Vigenere key length of {0} ({1}) gives fit of {2}'.
+ format(trial_length, key, fit))
+ if fit > best_fit:
+ best_fit = fit
+ best_key = key
+ logger.info('Vigenere break best fit with key {0} gives fit '
+ 'of {1} and decrypt starting: {2}'.format(best_key,
+ best_fit, sanitise(
+ vigenere_decipher(message, best_key))[:50]))
+ return best_key, best_fit
+
+def beaufort_frequency_break(message, fitness=Pletters):
+ """Breaks a Beaufort cipher with frequency analysis
+
+ >>> beaufort_frequency_break(beaufort_encipher(sanitise("It is time to " \
+ "run. She is ready and so am I. I stole Daniel's pocketbook this " \
+ "afternoon when he left his jacket hanging on the easel in the " \
+ "attic. I jump every time I hear a footstep on the stairs, " \
+ "certain that the theft has been discovered and that I will " \
+ "be caught. The SS officer visits less often now " \
+ "that he is sure"), 'florence')) # doctest: +ELLIPSIS
+ ('florence', -307.5549865898...)
+ """
+ best_fit = float("-inf")
+ best_key = ''
+ sanitised_message = sanitise(message)
+ for trial_length in range(1, 20):
+ splits = every_nth(sanitised_message, trial_length)
+ key = ''.join([chr(-caesar_break(s)[0] % 26 + ord('a')) for s in splits])
+ plaintext = beaufort_decipher(sanitised_message, key)
+ fit = fitness(plaintext)
+ logger.debug('Beaufort key length of {0} ({1}) gives fit of {2}'.
+ format(trial_length, key, fit))
+ if fit > best_fit:
+ best_fit = fit
+ best_key = key
+ logger.info('Beaufort break best fit with key {0} gives fit '
+ 'of {1} and decrypt starting: {2}'.format(best_key,
+ best_fit, sanitise(
+ beaufort_decipher(message, best_key))[:50]))
+ return best_key, best_fit
+
+
+
+def plot_frequency_histogram(freqs, sort_key=None):
+ x = range(len(freqs.keys()))
+ y = [freqs[l] for l in sorted(freqs.keys(), key=sort_key)]
+ f = plt.figure()
+ ax = f.add_axes([0.1, 0.1, 0.9, 0.9])
+ ax.bar(x, y, align='center')
+ ax.set_xticks(x)
+ ax.set_xticklabels(sorted(freqs.keys(), key=sort_key))
+ f.show()
+
+
+if __name__ == "__main__":
+ import doctest
+ doctest.testmod()
+