+def hill_break(message, matrix_size=2, fitness=Pletters,
+ number_of_solutions=1, chunksize=500):
+
+ all_matrices = [np.matrix(list(m))
+ for m in itertools.product([list(r)
+ for r in itertools.product(range(26), repeat=matrix_size)],
+ repeat=matrix_size)]
+ valid_matrices = [m for m, d in
+ zip(all_matrices, (int(round(linalg.det(m))) for m in all_matrices))
+ if d != 0
+ if d % 2 != 0
+ if d % 13 != 0 ]
+ with Pool() as pool:
+ helper_args = [(message, matrix, fitness)
+ for matrix in valid_matrices]
+ # Gotcha: the helper function here needs to be defined at the top level
+ # (limitation of Pool.starmap)
+ breaks = pool.starmap(hill_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 hill_break_worker(message, matrix, fitness):
+ plaintext = hill_decipher(matrix, message)
+ fit = fitness(plaintext)
+ logger.debug('Hill cipher break attempt using key {0} gives fit of '
+ '{1} and decrypt starting: {2}'.format(matrix,
+ fit, sanitise(plaintext)[:50]))
+ return matrix, fit
+
+