-def index_of_coincidence(text):
- stext = sanitise(text)
- counts = collections.Counter(stext)
- denom = len(stext) * (len(text) - 1) / 26
- return (
- sum(max(counts[l] * counts[l] - 1, 0) for l in string.ascii_lowercase)
- /
- denom
- )
-
-
-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
- """
- 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, -130.849989015...)
- >>> caesar_break('wxwmaxdgheetgwuxztgptedbgznitgwwhpguxyhkxbmhvvtlbhgtee' \
- 'raxlmhiixweblmxgxwmhmaxybkbgztgwztsxwbgmxgmert') # doctest: +ELLIPSIS
- (19, -128.82410410...)
- >>> caesar_break('yltbbqnqnzvguvaxurorgenafsbezqvagbnornfgsbevpnaabjurer' \
- 'svaquvzyvxrnznazlybequrvfohgriraabjtbaruraprur') # doctest: +ELLIPSIS
- (13, -126.25403935...)
- """
- 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), -340.601181913...)
- """
- 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', KeywordWrapAlphabet.from_last), \
- wordlist=['cat', 'elephant', 'kangaroo']) # doctest: +ELLIPSIS
- (('elephant', <KeywordWrapAlphabet.from_last: 2>), -52.834575011...)
- """
- best_keyword = ''
- best_wrap_alphabet = True
- best_fit = float("-inf")
- for wrap_alphabet in KeywordWrapAlphabet:
- 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,
- number_of_solutions=1, 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', KeywordWrapAlphabet.from_last), \
- wordlist=['cat', 'elephant', 'kangaroo']) # doctest: +ELLIPSIS
- (('elephant', <KeywordWrapAlphabet.from_last: 2>), -52.834575011...)
- >>> keyword_break_mp(keyword_encipher('this is a test message for the ' \
- 'keyword decipherment', 'elephant', KeywordWrapAlphabet.from_last), \
- wordlist=['cat', 'elephant', 'kangaroo'], \
- number_of_solutions=2) # doctest: +ELLIPSIS, +NORMALIZE_WHITESPACE
- [(('elephant', <KeywordWrapAlphabet.from_last: 2>), -52.834575011...),
- (('elephant', <KeywordWrapAlphabet.from_largest: 3>), -52.834575011...)]
- """
- with Pool() as pool:
- helper_args = [(message, word, wrap, fitness)
- for word in wordlist
- for wrap in KeywordWrapAlphabet]
- # 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)
- if number_of_solutions == 1:
- return max(breaks, key=lambda k: k[1])
- else:
- return sorted(breaks, key=lambda k: k[1], reverse=True)[:number_of_solutions]
-
-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 monoalphabetic_break_hillclimbing(message, max_iterations=10000000,
-# alphabet=None, fitness=Pletters):
-# ciphertext = unaccent(message).lower()
-# if not alphabet:
-# alphabet = list(string.ascii_lowercase)
-# random.shuffle(alphabet)
-# alphabet = cat(alphabet)
-# return monoalphabetic_break_hillclimbing_worker(ciphertext, alphabet,
-# max_iterations, fitness)
-
-# def monoalphabetic_break_hillclimbing_mp(message, workers=10,
-# max_iterations = 10000000, alphabet=None, fitness=Pletters, chunksize=1):
-# worker_args = []
-# ciphertext = unaccent(message).lower()
-# for i in range(workers):
-# if alphabet:
-# this_alphabet = alphabet
-# else:
-# this_alphabet = list(string.ascii_lowercase)
-# random.shuffle(this_alphabet)
-# this_alphabet = cat(this_alphabet)
-# worker_args.append((ciphertext, this_alphabet, max_iterations, fitness))
-# with Pool() as pool:
-# breaks = pool.starmap(monoalphabetic_break_hillclimbing_worker,
-# worker_args, chunksize)
-# return max(breaks, key=lambda k: k[1])
-
-# def monoalphabetic_break_hillclimbing_worker(message, alphabet,
-# max_iterations, fitness):
-# def swap(letters, i, j):
-# if i > j:
-# i, j = j, i
-# if i == j:
-# return letters
-# else:
-# return (letters[:i] + letters[j] + letters[i+1:j] + letters[i] +
-# letters[j+1:])
-# best_alphabet = alphabet
-# best_fitness = float('-inf')
-# for i in range(max_iterations):
-# alphabet = swap(best_alphabet, random.randrange(26), random.randrange(26))
-# cipher_translation = ''.maketrans(string.ascii_lowercase, alphabet)
-# plaintext = message.translate(cipher_translation)
-# if fitness(plaintext) > best_fitness:
-# best_fitness = fitness(plaintext)
-# best_alphabet = alphabet
-# print(i, best_alphabet, best_fitness, plaintext[:50])
-# return best_alphabet, best_fitness
-
-
-def monoalphabetic_break_hillclimbing(message,
- max_iterations=20000,
- plain_alphabet=None,
- cipher_alphabet=None,
- fitness=Pletters, chunksize=1):
- return simulated_annealing_break(message,
- workers=1,
- initial_temperature=0,
- max_iterations=max_iterations,
- plain_alphabet=plain_alphabet,
- cipher_alphabet=cipher_alphabet,
- fitness=fitness, chunksize=chunksize)
-
-
-def monoalphabetic_break_hillclimbing_mp(message,
- workers=10,
- max_iterations=20000,
- plain_alphabet=None,
- cipher_alphabet=None,
- fitness=Pletters, chunksize=1):
- return simulated_annealing_break(message,
- workers=workers,
- initial_temperature=0,
- max_iterations=max_iterations,
- plain_alphabet=plain_alphabet,
- cipher_alphabet=cipher_alphabet,
- fitness=fitness, chunksize=chunksize)
-
-
-def simulated_annealing_break(message, workers=10,
- initial_temperature=200,
- max_iterations=20000,
- plain_alphabet=None,
- cipher_alphabet=None,
- fitness=Pletters, chunksize=1):
- worker_args = []
- ciphertext = sanitise(message)
- for i in range(workers):
- if not plain_alphabet:
- plain_alphabet = string.ascii_lowercase
- if not cipher_alphabet:
- cipher_alphabet = list(string.ascii_lowercase)
- random.shuffle(cipher_alphabet)
- cipher_alphabet = cat(cipher_alphabet)
- worker_args.append((ciphertext, plain_alphabet, cipher_alphabet,
- initial_temperature, max_iterations, fitness))
- with Pool() as pool:
- breaks = pool.starmap(simulated_annealing_break_worker,
- worker_args, chunksize)
- return max(breaks, key=lambda k: k[1])
-
-
-def simulated_annealing_break_worker(message, plain_alphabet, cipher_alphabet,
- t0, max_iterations, fitness):
- def swap(letters, i, j):
- if i > j:
- i, j = j, i
- if i == j:
- return letters
- else:
- return (letters[:i] + letters[j] + letters[i+1:j] + letters[i] +
- letters[j+1:])
-
- temperature = t0
-
- dt = t0 / (0.9 * max_iterations)
-
- current_alphabet = cipher_alphabet
- alphabet = current_alphabet
- cipher_translation = ''.maketrans(current_alphabet, plain_alphabet)
- plaintext = message.translate(cipher_translation)
- current_fitness = fitness(plaintext)
-
- best_alphabet = current_alphabet
- best_fitness = current_fitness
- best_plaintext = plaintext
-
- # print('starting for', max_iterations)
- for i in range(max_iterations):
- swap_a = random.randrange(26)
- swap_b = (swap_a + int(random.gauss(0, 4))) % 26
- alphabet = swap(current_alphabet, swap_a, swap_b)
- cipher_translation = ''.maketrans(alphabet, plain_alphabet)
- plaintext = message.translate(cipher_translation)
- new_fitness = fitness(plaintext)
- try:
- sa_chance = math.exp((new_fitness - current_fitness) / temperature)
- except (OverflowError, ZeroDivisionError):
- # print('exception triggered: new_fit {}, current_fit {}, temp {}'.format(new_fitness, current_fitness, temperature))
- sa_chance = 0
- if (new_fitness > current_fitness or random.random() < sa_chance):
- # logger.debug('Simulated annealing: iteration {}, temperature {}, '
- # 'current alphabet {}, current_fitness {}, '
- # 'best_plaintext {}'.format(i, temperature, current_alphabet,
- # current_fitness, best_plaintext[:50]))
-
- # logger.debug('new_fit {}, current_fit {}, temp {}, sa_chance {}'.format(new_fitness, current_fitness, temperature, sa_chance))
- current_fitness = new_fitness
- current_alphabet = alphabet
-
- if current_fitness > best_fitness:
- best_alphabet = current_alphabet
- best_fitness = current_fitness
- best_plaintext = plaintext
- if i % 500 == 0:
- logger.debug('Simulated annealing: iteration {}, temperature {}, '
- 'current alphabet {}, current_fitness {}, '
- 'best_plaintext {}'.format(i, temperature, current_alphabet,
- current_fitness, plaintext[:50]))
- temperature = max(temperature - dt, 0.001)
-
- return best_alphabet, best_fitness # current_alphabet, current_fitness
-
-
-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', -52.9472712...)
- """
- 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])
-vigenere_keyword_break = vigenere_keyword_break_mp
-
-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
-