From: Neil Smith Date: Mon, 7 Oct 2013 13:45:53 +0000 (+0100) Subject: Affine ciphers enciphered, deciphered, and broken. Still needs testing. X-Git-Url: https://git.njae.me.uk/?a=commitdiff_plain;h=47c343dd0e80238c835742982a22b36b87fb58de;p=cipher-tools.git Affine ciphers enciphered, deciphered, and broken. Still needs testing. --- diff --git a/cipher.py b/cipher.py index 55d99b6..b086a5d 100644 --- a/cipher.py +++ b/cipher.py @@ -10,6 +10,13 @@ with open('count_1l.txt', 'r') as f: normalised_english_counts = norms.normalise(english_counts) +modular_division_table = [[0]*26 for x in range(26)] +for a in range(26): + for b in range(26): + c = (a * b) % 26 + modular_division_table[b][c] = a + + def sanitise(text): """Remove all non-alphabetic characters and convert the text to lowercase @@ -107,13 +114,52 @@ def caesar_decipher(message, shift): """ return caesar_encipher(message, -shift) +def affine_encipher_letter(letter, multiplier, adder, multiply_then_add=True): + 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 + cipher_number = 0 + if multiply_then_add: + cipher_number = (letter_number * multiplier + adder) % 26 + else: + cipher_number = ((letter_number + adder) * multiplier) % 26 + return chr(cipher_number + alphabet_start) + else: + return letter + +def affine_decipher_letter(letter, multiplier, adder, multiply_then_add=True): + 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 + plaintext_number = 0 + if multiply_then_add: + plaintext_number = modular_division_table[multiplier][(cipher_number - adder + 26) % 26] + else: + plaintext_number = (modular_division_table[multiplier][cipher_number] - adder) % 26 + return chr(plaintext_number + alphabet_start) + else: + return letter + +def affine_encipher(message, multiplier, adder, multiply_then_add=True): + enciphered = [affine_encipher_letter(l, multiplier, adder, multiply_then_add) for l in message] + return ''.join(enciphered) + +def affine_decipher(message, multiplier, adder, multiply_then_add=True): + enciphered = [affine_decipher_letter(l, multiplier, adder, multiply_then_add) for l in message] + return ''.join(enciphered) + + def caesar_break(message, metric=norms.euclidean_distance, target_frequencies=normalised_english_counts, message_frequency_scaling=norms.normalise): """Breaks a Caesar cipher using frequency analysis >>> caesar_break('ibxcsyorsaqcheyklxivoexlevmrimwxsfiqevvmihrsasrxliwyrhecjsppsamrkwleppfmergefifvmhixscsymjcsyqeoixlm') (4, 0.3186395289018361) - >>> caesar_break('jhzhuhfrqilqhgwrdevwudfwuhdvrqlqjwkhqkdylqjvxemhfwhgwrfulwlflvpwkhhasodqdwlrqrisrzhuwkdwmxulglfdovfl') - (3, 0.3290204286173084) >>> caesar_break('wxwmaxdgheetgwuxztgptedbgznitgwwhpguxyhkxbmhvvtlbhgteeraxlmhiixweblmxgxwmhmaxybkbgztgwztsxwbgmxgmert') (19, 0.4215290123583277) >>> caesar_break('yltbbqnqnzvguvaxurorgenafsbezqvagbnornfgsbevpnaabjurersvaquvzyvxrnznazlybequrvfohgriraabjtbaruraprur') @@ -131,6 +177,31 @@ def caesar_break(message, metric=norms.euclidean_distance, target_frequencies=no best_shift = shift return best_shift, best_fit +def affine_break(message, metric=norms.euclidean_distance, target_frequencies=normalised_english_counts, message_frequency_scaling=norms.normalise): + """Breaks a Caesar cipher using frequency analysis + + >>> caesar_break('ibxcsyorsaqcheyklxivoexlevmrimwxsfiqevvmihrsasrxliwyrhecjsppsamrkwleppfmergefifvmhixscsymjcsyqeoixlm') + (4, 0.3186395289018361) + >>> caesar_break('wxwmaxdgheetgwuxztgptedbgznitgwwhpguxyhkxbmhvvtlbhgteeraxlmhiixweblmxgxwmhmaxybkbgztgwztsxwbgmxgmert') + (19, 0.4215290123583277) + >>> caesar_break('yltbbqnqnzvguvaxurorgenafsbezqvagbnornfgsbevpnaabjurersvaquvzyvxrnznazlybequrvfohgriraabjtbaruraprur') + (13, 0.31602920807545154) + """ + sanitised_message = sanitise(message) + best_multiplier = 0 + best_adder = 0 + best_fit = float("inf") + for multiplier in range(1, 26, 2): + for adder in range(26): + plaintext = affine_decipher(sanitised_message, multiplier, adder) + frequencies = message_frequency_scaling(letter_frequencies(plaintext)) + fit = metric(target_frequencies, frequencies) + if fit < best_fit: + best_fit = fit + best_multiplier = multiplier + best_adder = adder + return (best_multiplier, best_adder), best_fit + if __name__ == "__main__": import doctest