+ """Decipher a letter, given a shift amount
+
+ >>> caesar_decipher_letter('b', 1)
+ 'a'
+ >>> caesar_decipher_letter('b', 2)
+ 'z'
+ """
+ return caesar_encipher_letter(letter, -shift)
+
+def caesar_encipher(message, shift):
+ """Encipher a message with the Caesar cipher of given shift
+
+ >>> caesar_encipher('abc', 1)
+ 'bcd'
+ >>> caesar_encipher('abc', 2)
+ 'cde'
+ >>> caesar_encipher('abcxyz', 2)
+ 'cdezab'
+ >>> caesar_encipher('ab cx yz', 2)
+ 'cd ez ab'
+ """
+ enciphered = [caesar_encipher_letter(l, shift) for l in message]
+ return ''.join(enciphered)
+
+def caesar_decipher(message, shift):
+ """Encipher a message with the Caesar cipher of given shift
+
+ >>> caesar_decipher('bcd', 1)
+ 'abc'
+ >>> caesar_decipher('cde', 2)
+ 'abc'
+ >>> caesar_decipher('cd ez ab', 2)
+ 'ab cx yz'
+ """
+ return caesar_encipher(message, -shift)
+
+def affine_encipher_letter(letter, multiplier=1, adder=0, one_based=True):
+ """Encipher a letter, given a multiplier and adder
+
+ >>> ''.join([affine_encipher_letter(l, 3, 5, True) \
+ for l in string.ascii_uppercase])
+ 'HKNQTWZCFILORUXADGJMPSVYBE'
+ >>> ''.join([affine_encipher_letter(l, 3, 5, False) \
+ for l in string.ascii_uppercase])
+ 'FILORUXADGJMPSVYBEHKNQTWZC'
+ """
+ if letter in string.ascii_letters:
+ if letter in string.ascii_uppercase:
+ alphabet_start = ord('A')
+ else:
+ alphabet_start = ord('a')
+ letter_number = ord(letter) - alphabet_start
+ if one_based: letter_number += 1
+ cipher_number = (letter_number * multiplier + adder) % 26
+ if one_based: cipher_number -= 1
+ return chr(cipher_number % 26 + alphabet_start)
+ else:
+ return letter
+
+def affine_decipher_letter(letter, multiplier=1, adder=0, one_based=True):
+ """Encipher a letter, given a multiplier and adder
+
+ >>> ''.join([affine_decipher_letter(l, 3, 5, True) \
+ for l in 'HKNQTWZCFILORUXADGJMPSVYBE'])
+ 'ABCDEFGHIJKLMNOPQRSTUVWXYZ'
+ >>> ''.join([affine_decipher_letter(l, 3, 5, False) \
+ for l in 'FILORUXADGJMPSVYBEHKNQTWZC'])
+ 'ABCDEFGHIJKLMNOPQRSTUVWXYZ'
+ """
+ if letter in string.ascii_letters:
+ if letter in string.ascii_uppercase:
+ alphabet_start = ord('A')
+ else:
+ alphabet_start = ord('a')
+ cipher_number = ord(letter) - alphabet_start
+ if one_based: cipher_number += 1
+ plaintext_number = ( modular_division_table[multiplier]
+ [(cipher_number - adder) % 26] )
+ if one_based: plaintext_number -= 1
+ return chr(plaintext_number % 26 + alphabet_start)
+ else:
+ return letter
+
+def affine_encipher(message, multiplier=1, adder=0, one_based=True):
+ """Encipher a message
+
+ >>> affine_encipher('hours passed during which jerico tried every ' \
+ 'trick he could think of', 15, 22, True)
+ 'lmyfu bkuusd dyfaxw claol psfaom jfasd snsfg jfaoe ls omytd jlaxe mh'
+ """
+ enciphered = [affine_encipher_letter(l, multiplier, adder, one_based)
+ for l in message]
+ return ''.join(enciphered)
+
+def affine_decipher(message, multiplier=1, adder=0, one_based=True):
+ """Decipher a message
+
+ >>> affine_decipher('lmyfu bkuusd dyfaxw claol psfaom jfasd snsfg ' \
+ 'jfaoe ls omytd jlaxe mh', 15, 22, True)
+ 'hours passed during which jerico tried every trick he could think of'
+ """
+ enciphered = [affine_decipher_letter(l, multiplier, adder, one_based)
+ for l in message]
+ return ''.join(enciphered)
+
+
+def keyword_cipher_alphabet_of(keyword, wrap_alphabet=0):
+ """Find the cipher alphabet given a keyword.
+ wrap_alphabet controls how the rest of the alphabet is added
+ after the keyword.
+ 0 : from 'a'
+ 1 : from the last letter in the sanitised keyword
+ 2 : from the largest letter in the sanitised keyword
+
+ >>> keyword_cipher_alphabet_of('bayes')
+ 'bayescdfghijklmnopqrtuvwxz'
+ >>> keyword_cipher_alphabet_of('bayes', 0)
+ 'bayescdfghijklmnopqrtuvwxz'
+ >>> keyword_cipher_alphabet_of('bayes', 1)
+ 'bayestuvwxzcdfghijklmnopqr'
+ >>> keyword_cipher_alphabet_of('bayes', 2)
+ 'bayeszcdfghijklmnopqrtuvwx'
+ """
+ if wrap_alphabet == 0:
+ cipher_alphabet = ''.join(deduplicate(sanitise(keyword) +
+ string.ascii_lowercase))
+ else:
+ if wrap_alphabet == 1:
+ last_keyword_letter = deduplicate(sanitise(keyword))[-1]
+ else:
+ last_keyword_letter = sorted(sanitise(keyword))[-1]
+ last_keyword_position = string.ascii_lowercase.find(
+ last_keyword_letter) + 1
+ cipher_alphabet = ''.join(
+ deduplicate(sanitise(keyword) +
+ string.ascii_lowercase[last_keyword_position:] +
+ string.ascii_lowercase))
+ return cipher_alphabet
+
+
+def keyword_encipher(message, keyword, wrap_alphabet=0):
+ """Enciphers a message with a keyword substitution cipher.
+ wrap_alphabet controls how the rest of the alphabet is added
+ after the keyword.
+ 0 : from 'a'
+ 1 : from the last letter in the sanitised keyword
+ 2 : from the largest letter in the sanitised keyword
+
+ >>> keyword_encipher('test message', 'bayes')
+ 'rsqr ksqqbds'
+ >>> keyword_encipher('test message', 'bayes', 0)
+ 'rsqr ksqqbds'
+ >>> keyword_encipher('test message', 'bayes', 1)
+ 'lskl dskkbus'
+ >>> keyword_encipher('test message', 'bayes', 2)
+ 'qspq jsppbcs'
+ """
+ cipher_alphabet = keyword_cipher_alphabet_of(keyword, wrap_alphabet)
+ cipher_translation = ''.maketrans(string.ascii_lowercase, cipher_alphabet)
+ return message.lower().translate(cipher_translation)
+
+def keyword_decipher(message, keyword, wrap_alphabet=0):
+ """Deciphers a message with a keyword substitution cipher.
+ wrap_alphabet controls how the rest of the alphabet is added
+ after the keyword.
+ 0 : from 'a'
+ 1 : from the last letter in the sanitised keyword
+ 2 : from the largest letter in the sanitised keyword
+
+ >>> keyword_decipher('rsqr ksqqbds', 'bayes')
+ 'test message'
+ >>> keyword_decipher('rsqr ksqqbds', 'bayes', 0)
+ 'test message'
+ >>> keyword_decipher('lskl dskkbus', 'bayes', 1)
+ 'test message'
+ >>> keyword_decipher('qspq jsppbcs', 'bayes', 2)
+ 'test message'
+ """
+ cipher_alphabet = keyword_cipher_alphabet_of(keyword, wrap_alphabet)
+ cipher_translation = ''.maketrans(cipher_alphabet, string.ascii_lowercase)
+ return message.lower().translate(cipher_translation)
+
+def scytale_encipher(message, rows):
+ """Enciphers using the scytale transposition cipher.
+ Message is padded with spaces to allow all rows to be the same length.
+
+ >>> scytale_encipher('thequickbrownfox', 3)
+ 'tcnhkfeboqrxuo iw '
+ >>> scytale_encipher('thequickbrownfox', 4)
+ 'tubnhirfecooqkwx'
+ >>> scytale_encipher('thequickbrownfox', 5)
+ 'tubn hirf ecoo qkwx '
+ >>> scytale_encipher('thequickbrownfox', 6)
+ 'tqcrnxhukof eibwo '
+ >>> scytale_encipher('thequickbrownfox', 7)
+ 'tqcrnx hukof eibwo '
+ """
+ if len(message) % rows != 0:
+ message += ' '*(rows - len(message) % rows)
+ row_length = round(len(message) / rows)
+ slices = [message[i:i+row_length]
+ for i in range(0, len(message), row_length)]
+ return ''.join([''.join(r) for r in zip_longest(*slices, fillvalue='')])
+
+def scytale_decipher(message, rows):
+ """Deciphers using the scytale transposition cipher.
+ Assumes the message is padded so that all rows are the same length.
+
+ >>> scytale_decipher('tcnhkfeboqrxuo iw ', 3)
+ 'thequickbrownfox '
+ >>> scytale_decipher('tubnhirfecooqkwx', 4)
+ 'thequickbrownfox'
+ >>> scytale_decipher('tubn hirf ecoo qkwx ', 5)
+ 'thequickbrownfox '
+ >>> scytale_decipher('tqcrnxhukof eibwo ', 6)
+ 'thequickbrownfox '
+ >>> scytale_decipher('tqcrnx hukof eibwo ', 7)
+ 'thequickbrownfox '
+ """
+ cols = round(len(message) / rows)
+ columns = [message[i:i+rows] for i in range(0, cols * rows, rows)]
+ return ''.join([''.join(c) for c in zip_longest(*columns, fillvalue='')])
+
+
+def transpositions_of(keyword):
+ """
+ >>> transpositions_of('clever')
+ [0, 2, 1, 4, 3]
+ """
+ key = deduplicate(keyword)
+ transpositions = [key.index(l) for l in sorted(key)]
+ return transpositions
+
+def column_transposition_encipher(message, keyword):
+ """
+ >>> column_transposition_encipher('hellothere', 'clever')
+ 'hleolteher'
+ """
+ return column_transposition_worker(message, keyword, encipher=True)
+
+def column_transposition_decipher(message, keyword):
+ """
+ >>> column_transposition_decipher('hleolteher', 'clever')
+ 'hellothere'
+ """
+ return column_transposition_worker(message, keyword, encipher=False)
+
+def column_transposition_worker(message, keyword, encipher=True):
+ """
+ >>> column_transposition_worker('hellothere', 'clever')
+ 'hleolteher'
+ >>> column_transposition_worker('hellothere', 'clever', encipher=True)
+ 'hleolteher'
+ >>> column_transposition_worker('hleolteher', 'clever', encipher=False)
+ 'hellothere'
+ """
+ transpositions = transpositions_of(keyword)
+ columns = every_nth(message, len(transpositions), fillvalue=' ')
+ if encipher:
+ transposed_columns = transpose(columns, transpositions)
+ else:
+ transposed_columns = untranspose(columns, transpositions)
+ return combine_every_nth(transposed_columns)
+
+
+
+def caesar_break(message,
+ metric=norms.euclidean_distance,
+ target_counts=normalised_english_counts,
+ message_frequency_scaling=norms.normalise):
+ """Breaks a Caesar cipher using frequency analysis
+
+ >>> caesar_break('ibxcsyorsaqcheyklxivoexlevmrimwxsfiqevvmihrsasrxliwyrh' \
+ 'ecjsppsamrkwleppfmergefifvmhixscsymjcsyqeoixlm') # doctest: +ELLIPSIS
+ (4, 0.31863952890183...)
+ >>> caesar_break('wxwmaxdgheetgwuxztgptedbgznitgwwhpguxyhkxbmhvvtlbhgtee' \
+ 'raxlmhiixweblmxgxwmhmaxybkbgztgwztsxwbgmxgmert') # doctest: +ELLIPSIS
+ (19, 0.42152901235832...)
+ >>> caesar_break('yltbbqnqnzvguvaxurorgenafsbezqvagbnornfgsbevpnaabjurer' \
+ 'svaquvzyvxrnznazlybequrvfohgriraabjtbaruraprur') # doctest: +ELLIPSIS
+ (13, 0.316029208075451...)
+ """
+ sanitised_message = sanitise(message)
+ best_shift = 0
+ best_fit = float("inf")
+ for shift in range(26):
+ plaintext = caesar_decipher(sanitised_message, shift)
+ counts = message_frequency_scaling(letter_frequencies(plaintext))
+ fit = metric(target_counts, counts)
+ 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,
+ metric=norms.euclidean_distance,
+ target_counts=normalised_english_counts,
+ message_frequency_scaling=norms.normalise):
+ """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), 0.23570361818655...)
+ """
+ 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 range(1, 26, 2):
+ for adder in range(26):
+ plaintext = affine_decipher(sanitised_message,
+ multiplier, adder, one_based)
+ counts = message_frequency_scaling(letter_frequencies(plaintext))
+ fit = metric(target_counts, counts)
+ 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,
+ metric=norms.euclidean_distance,
+ target_counts=normalised_english_counts,
+ message_frequency_scaling=norms.normalise):
+ """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), 0.41643991598441...)
+ """
+ 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)
+ counts = message_frequency_scaling(letter_frequencies(plaintext))
+ fit = metric(target_counts, counts)
+ 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,
+ metric=norms.euclidean_distance,
+ target_counts=normalised_english_counts,
+ message_frequency_scaling=norms.normalise,
+ 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), 0.41643991598441...)
+ """
+ with Pool() as pool:
+ helper_args = [(message, word, wrap, metric, target_counts,
+ message_frequency_scaling)
+ 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_one, helper_args, chunksize)
+ return min(breaks, key=lambda k: k[1])
+
+def keyword_break_one(message, keyword, wrap_alphabet, metric, target_counts,
+ message_frequency_scaling):
+ plaintext = keyword_decipher(message, keyword, wrap_alphabet)
+ counts = message_frequency_scaling(letter_frequencies(plaintext))
+ fit = metric(target_counts, counts)
+ 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,
+ metric=norms.euclidean_distance,
+ target_counts=normalised_english_bigram_counts,
+ message_frequency_scaling=norms.normalise):
+ """Breaks a Scytale cipher
+
+ >>> scytale_break('tfeulchtrtteehwahsdehneoifeayfsondmwpltmaoalhikotoere' \
+ 'dcweatehiplwxsnhooacgorrcrcraotohsgullasenylrendaianeplscdriioto' \
+ 'aek') # doctest: +ELLIPSIS
+ (6, 0.83453041115025...)
+ """
+ best_key = 0
+ best_fit = float("inf")
+ for key in range(1, 20):
+ if len(message) % key == 0:
+ plaintext = scytale_decipher(message, key)
+ counts = message_frequency_scaling(frequencies(
+ ngrams(sanitise(plaintext), 2)))
+ fit = metric(target_counts, counts)
+ 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