szyfrow/hill.py

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