cipher/hill.py

   1 from utilities import *
   2 from language_models import *
   3 import multiprocessing
   4 import numpy as np
   5 from numpy import matrix
   6 from numpy import linalg
   7
   8 from logger import logger
   9
  10
  11 def hill_encipher(matrix, message_letters, fillvalue='a'):
  12     """Hill cipher
  13
  14     >>> hill_encipher(np.matrix([[7,8], [11,11]]), 'hellothere')
  15     'drjiqzdrvx'
  16     >>> hill_encipher(np.matrix([[6, 24, 1], [13, 16, 10], [20, 17, 15]]), \
  17         'hello there')
  18     'tfjflpznvyac'
  19     """
  20     n = len(matrix)
  21     sanitised_message = sanitise(message_letters)
  22     if len(sanitised_message) % n != 0:
  23         padding = fillvalue[0] * (n - len(sanitised_message) % n)
  24     else:
  25         padding = ''
  26     message = [pos(c) for c in sanitised_message + padding]
  27     message_chunks = [message[i:i+n] for i in range(0, len(message), n)]
  28     # message_chunks = chunks(message, len(matrix), fillvalue=None)
  29     enciphered_chunks = [((matrix * np.matrix(c).T).T).tolist()[0]
  30             for c in message_chunks]
  31     return cat([unpos(round(l))
  32             for l in sum(enciphered_chunks, [])])
  33
  34 def hill_decipher(matrix, message, fillvalue='a'):
  35     """Hill cipher
  36
  37     >>> hill_decipher(np.matrix([[7,8], [11,11]]), 'drjiqzdrvx')
  38     'hellothere'
  39     >>> hill_decipher(np.matrix([[6, 24, 1], [13, 16, 10], [20, 17, 15]]), \
  40         'tfjflpznvyac')
  41     'hellothereaa'
  42     """
  43     adjoint = linalg.det(matrix)*linalg.inv(matrix)
  44     inverse_determinant = modular_division_table[int(round(linalg.det(matrix))) % 26][1]
  45     inverse_matrix = (inverse_determinant * adjoint) % 26
  46     return hill_encipher(inverse_matrix, message, fillvalue)
  47
  48 def hill_break(message, matrix_size=2, fitness=Pletters,
  49     number_of_solutions=1, chunksize=500):
  50
  51     all_matrices = [np.matrix(list(m))
  52         for m in itertools.product([list(r)
  53             for r in itertools.product(range(26), repeat=matrix_size)],
  54         repeat=matrix_size)]
  55     valid_matrices = [m for m, d in
  56         zip(all_matrices, (int(round(linalg.det(m))) for m in all_matrices))
  57                   if d != 0
  58                   if d % 2 != 0
  59                   if d % 13 != 0 ]
  60     with multiprocessing.Pool() as pool:
  61         helper_args = [(message, matrix, fitness)
  62                        for matrix in valid_matrices]
  63         # Gotcha: the helper function here needs to be defined at the top level
  64         #   (limitation of Pool.starmap)
  65         breaks = pool.starmap(hill_break_worker, helper_args, chunksize)
  66         if number_of_solutions == 1:
  67             return max(breaks, key=lambda k: k[1])
  68         else:
  69             return sorted(breaks, key=lambda k: k[1], reverse=True)[:number_of_solutions]
  70
  71 def hill_break_worker(message, matrix, fitness):
  72     plaintext = hill_decipher(matrix, message)
  73     fit = fitness(plaintext)
  74     logger.debug('Hill cipher break attempt using key {0} gives fit of '
  75                  '{1} and decrypt starting: {2}'.format(matrix,
  76                      fit, sanitise(plaintext)[:50]))
  77     return matrix, fit
  78
  79 if __name__ == "__main__":
  80     import doctest