From cb023a39e779de938dc6a3aac3273e26f9a2ab83 Mon Sep 17 00:00:00 2001 From: Neil Smith Date: Sun, 30 Nov 2014 12:32:39 +0000 Subject: [PATCH] Hill ciphers enciphering and deciphering done --- cipher.py | 41 ++ hill-ciphers.ipynb | 1392 ++++++++++++++++++++++++++++++++++++++++++++ 2 files changed, 1433 insertions(+) create mode 100644 hill-ciphers.ipynb diff --git a/cipher.py b/cipher.py index 6cce725..cd75d2c 100644 --- a/cipher.py +++ b/cipher.py @@ -3,6 +3,9 @@ import collections import math from enum import Enum from itertools import zip_longest, cycle, chain +import numpy as np +from numpy import matrix +from numpy import linalg from language_models import * @@ -630,6 +633,44 @@ def railfence_decipher(message, height, fillvalue=''): return ''.join(c for r in zip_longest(*(down_rows + up_rows), fillvalue='') for c in r) +def hill_encipher(matrix, message_letters, fillvalue='a'): + """Hill cipher + + >>> hill_encipher(np.matrix([[7,8], [11,11]]), 'hellothere') + 'drjiqzdrvx' + >>> hill_encipher(np.matrix([[6, 24, 1], [13, 16, 10], [20, 17, 15]]), \ + 'hello there') + 'tfjflpznvyac' + """ + n = len(matrix) + sanitised_message = sanitise(message_letters) + if len(sanitised_message) % n != 0: + padding = fillvalue[0] * (n - len(sanitised_message) % n) + else: + padding = '' + message = [ord(c) - ord('a') for c in sanitised_message + padding] + message_chunks = [message[i:i+n] for i in range(0, len(message), n)] + # message_chunks = chunks(message, len(matrix), fillvalue=None) + enciphered_chunks = [((matrix * np.matrix(c).T).T).tolist()[0] + for c in message_chunks] + return ''.join([chr(int(round(l)) % 26 + ord('a')) + for l in sum(enciphered_chunks, [])]) + + +def hill_decipher(matrix, message, fillvalue='a'): + """Hill cipher + + >>> hill_decipher(np.matrix([[7,8], [11,11]]), 'drjiqzdrvx') + 'hellothere' + >>> hill_decipher(np.matrix([[6, 24, 1], [13, 16, 10], [20, 17, 15]]), \ + 'tfjflpznvyac') + 'hellothereaa' + """ + adjoint = linalg.det(matrix)*linalg.inv(matrix) + inverse_determinant = modular_division_table[int(round(linalg.det(matrix))) % 26][1] + inverse_matrix = (inverse_determinant * adjoint) % 26 + return hill_encipher(inverse_matrix, message, fillvalue) + class PocketEnigma(object): """A pocket enigma machine The wheel is internally represented as a 26-element list self.wheel_map, diff --git a/hill-ciphers.ipynb b/hill-ciphers.ipynb new file mode 100644 index 0000000..909828a --- /dev/null +++ b/hill-ciphers.ipynb @@ -0,0 +1,1392 @@ +{ + "metadata": { + "name": "", + "signature": "sha256:0fe9165e4a65606dd93377df5e8d4ccf8671a4edf4adc8d5da4b33f83316516f" + }, + "nbformat": 3, + "nbformat_minor": 0, + "worksheets": [ + { + "cells": [ + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import matplotlib.pyplot as plt\n", + "import pandas as pd\n", + "import collections\n", + "import string\n", + "import numpy as np\n", + "from numpy import matrix\n", + "from numpy import linalg\n", + "%matplotlib inline\n", + "\n", + "from cipher import *\n", + "from cipherbreak import *\n", + "\n", + "c6a = open('2014/6a.ciphertext').read()\n", + "c6b = open('2014/6b.ciphertext').read()" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 54 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "key_a, score = railfence_break(sanitise(c6a))\n", + "key_a, score" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "pyout", + "prompt_number": 3, + "text": [ + "(3, -2314.997881051078)" + ] + } + ], + "prompt_number": 3 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "' '.join(segment(railfence_decipher(sanitise(c6a), key_a)))" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "pyout", + "prompt_number": 4, + "text": [ + "'mark the last message told usa lot the scuttling equipment is designed to pump water in and out of the vessel like a submarine dive control but clearly they werent planning to turn a container ship into a sub this ship is a largescale version of something i have seen in the caribbean drug runners use a similar technique to get below radar coverage for inshore runs sinking the vessel so that the deck remains just below the wave tops the fda pirates seem more interested in staying away from shore but getting close enough to track and record electronic communications without detection i am guessing this scuttling system is what they call nautilus in their log but i am still baffled by the references to seahorse the next page of the log looks harder to crack but the cipher clerk tells me it is a hill cipher and that they must have been in a hurry or have been enciphering by hand since they just used a two by two matrix actually we have been pretty lax with our security and i think the next message is end will use avi genere cipher given that we are using secure cables i dont think we have too much to worry about so i will keep the keyword short say three characters more later harry'" + ] + } + ], + "prompt_number": 4 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "c6bs = sanitise(c6b)\n", + "c6bs" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "pyout", + "prompt_number": 7, + "text": [ + "'hwssswxfewhhrfewpdrvttdhxbccleayphalnadhiehaoudrotwnrrvysabjlttbaytmelrkaidopthatlelrtwaamaneksvvzrvllatkcrjquicizgtoqcpnrrkttowandqehtqrvtbaydqealannohulanuzlwextlvjrvivhnohdqmgykaclmswrupdetfioftfelhzpxhaswftwprrsweiseohefpdrvttnvagdvswgoerbetnharvaeevtlltbmgaiatgelinmdawevhatterdhrznbnvoutnefoteveaehlaymhacglzeptvvdimworfisgtuzlwibeqohubtghamqornjnnrumqvjtxeltfovgawdaeevllgrtxibgtibevmpsaateoasevaeyqohameonncfuidoefafattemuimnflznbekofobrliaehhauihnnnwzaeevtlltpaalnanvtzlzuucptaelinanpaahewfthaosetaribnbnvhaevdhyytlmuxb'" + ] + } + ], + "prompt_number": 7 + }, + { + "cell_type": "code", + "collapsed": 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"prompt_number": 107 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "m.I" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "pyout", + "prompt_number": 108, + "text": [ + "matrix([[-1. , 0.72727273],\n", + " [ 1. , -0.63636364]])" + ] + } + ], + "prompt_number": 108 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "v = np.matrix([[7], [22]])\n", + "v" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "pyout", + "prompt_number": 37, + "text": [ + "matrix([[ 7],\n", + " [22]])" + ] + } + ], + "prompt_number": 37 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "c = (m*v) % 26\n", + "c" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "pyout", + "prompt_number": 46, + "text": [ + "matrix([[9],\n", + " [5]])" + ] + } + ], + "prompt_number": 46 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "np.linalg.solve(m, c) % 26" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "pyout", + "prompt_number": 48, + "text": [ + "matrix([[ 7.],\n", + " [ 22.]])" + ] + } + ], + "prompt_number": 48 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "m*v" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "pyout", + "prompt_number": 40, + "text": [ + "matrix([[ 87],\n", + " [109]])" + ] + } + ], + "prompt_number": 40 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "(m*v)%26" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "pyout", + "prompt_number": 41, + "text": [ + "matrix([[9],\n", + " [5]])" + ] + } + ], + "prompt_number": 41 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "np.linalg.solve(m, (m*v)%26)%26" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "pyout", + "prompt_number": 42, + "text": [ + "matrix([[ 7.],\n", + " [ 22.]])" + ] + } + ], + "prompt_number": 42 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "len(m)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "pyout", + "prompt_number": 51, + "text": [ + "2" + ] + } + ], + "prompt_number": 51 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "def hill_encipher(matrix, message_letters, fillvalue='a'):\n", + " n = len(matrix)\n", + " sanitised_message = sanitise(message_letters)\n", + " if len(sanitised_message) % n != 0:\n", + " padding = fillvalue[0] * (n - len(sanitised_message) % n)\n", + " else:\n", + " padding = ''\n", + " message = [ord(c) - ord('a') for c in sanitised_message + padding]\n", + " message_chunks = [message[i:i+n] for i in range(0, len(message), n)]\n", + " # message_chunks = chunks(message, len(matrix), fillvalue=None)\n", + " enciphered_chunks = [((matrix * np.matrix(c).T).T).tolist()[0] for c in message_chunks]\n", + " return ''.join([chr(int(round(l)) % 26 + ord('a')) for l in sum(enciphered_chunks, [])])" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 181 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "hill_encipher(m, 'hellothere')" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "pyout", + "prompt_number": 156, + "text": [ + "'drjiqzdrvx'" + ] + } + ], + "prompt_number": 156 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "msg = [ord(c) - ord('a') for c in 'hellothere']\n", + "msg" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "pyout", + "prompt_number": 68, + "text": [ + "[7, 4, 11, 11, 14, 19, 7, 4, 17, 4]" + ] + } + ], + "prompt_number": 68 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "msgc = [msg[i:i+len(m)] for i in range(0, len(msg), len(m))]\n", + "msgc" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "pyout", + "prompt_number": 112, + "text": [ + "[[7, 11], [14, 25], [21, 14], [7, 11], [11, 15], [0, 0]]" + ] + } + ], + "prompt_number": 112 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "((m*np.matrix(msgc[0]).T).T % 26).tolist()[0]" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "pyout", + "prompt_number": 87, + "text": [ + "[7, 11]" + ] + } + ], + "prompt_number": 87 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "def hill_decipher(matrix, message, fillvalue='a'):\n", + " adjugate = linalg.det(matrix)*linalg.inv(matrix)\n", + " inverse_determinant = modular_division_table[int(round(linalg.det(matrix))) % 26][1]\n", + " inverse_matrix = (inverse_determinant * adjugate) % 26\n", + " return hill_encipher(inverse_matrix, message, fillvalue) " + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 195 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "hill_decipher(m, 'drjiqzdrvx')" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "pyout", + "prompt_number": 161, + "text": [ + "'hellothere'" + ] + } + ], + "prompt_number": 161 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "msg = [ord(c) - ord('a') for c in 'drjiqzdrvxaa']\n", + "msg" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "pyout", + "prompt_number": 114, + "text": [ + "[3, 17, 9, 8, 16, 25, 3, 17, 21, 23, 0, 0]" + ] + } + ], + "prompt_number": 114 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "msgc = [msg[i:i+len(m)] for i in range(0, len(msg), len(m))]\n", + "msgc" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "pyout", + "prompt_number": 115, + "text": [ + "[[3, 17], [9, 8], [16, 25], [3, 17], [21, 23], [0, 0]]" + ] + } + ], + "prompt_number": 115 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "(np.linalg.solve(m, np.matrix(msgc[0]).T).T % 26)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "pyout", + "prompt_number": 116, + "text": [ + "matrix([[ 9.36363636, 18.18181818]])" + ] + } + ], + "prompt_number": 116 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "m_adj = linalg.det(m)*linalg.inv(m)\n", + "m_adj" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "pyout", + "prompt_number": 142, + "text": [ + "matrix([[ 11., -8.],\n", + " [-11., 7.]])" + ] + } + ], + "prompt_number": 142 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "modular_division_table[int(round(linalg.det(m))) % 26][1]" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "pyout", + "prompt_number": 148, + "text": [ + "7" + ] + } + ], + "prompt_number": 148 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "m_inv = (modular_division_table[int(round(linalg.det(m))) % 26][1] * m_adj) % 26\n", + "m_inv" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "pyout", + "prompt_number": 150, + "text": [ + "matrix([[ 25., 22.],\n", + " [ 1., 23.]])" + ] + } + ], + "prompt_number": 150 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "hill_encipher(m_inv, 'drjiqzdrvx')" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "pyout", + "prompt_number": 157, + "text": [ + "'hellothere'" + ] + } + ], + "prompt_number": 157 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "np.dot(m , 1/linalg.det(m) * mc)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "pyout", + "prompt_number": 120, + "text": [ + "matrix([[ 1., 0.],\n", + " [ 0., 1.]])" + ] + } + ], + "prompt_number": 120 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "ml = np.matrix([[6, 24, 1], [13, 16, 10], [20, 17, 15]])\n", + "ml" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "pyout", + "prompt_number": 122, + "text": [ + "matrix([[ 6, 24, 1],\n", + " [13, 16, 10],\n", + " [20, 17, 15]])" + ] + } + ], + "prompt_number": 122 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "ml_adj = linalg.det(ml)*linalg.inv(ml) % 26\n", + "ml_adj" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "pyout", + "prompt_number": 137, + "text": [ + "matrix([[ 18., 21., 16.],\n", + " [ 5., 18., 5.],\n", + " [ 5., 14., 18.]])" + ] + } + ], + "prompt_number": 137 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "modular_division_table[int(linalg.det(ml) % 26)][1]" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "pyout", + "prompt_number": 138, + "text": [ + "25" + ] + } + ], + "prompt_number": 138 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "ml_inv = (modular_division_table[int(linalg.det(ml) % 26)][1] * ml_adj) % 26\n", + "ml_inv" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "pyout", + "prompt_number": 139, + "text": [ + "matrix([[ 8., 5., 10.],\n", + " [ 21., 8., 21.],\n", + " [ 21., 12., 8.]])" + ] + } + ], + "prompt_number": 139 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "hill_encipher(ml, 'hello there')" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "pyout", + "prompt_number": 193, + "text": [ + "'tfjflpznvyac'" + ] + } + ], + "prompt_number": 193 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "hill_decipher(ml, 'tfjflpznvyac')" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "pyout", + "prompt_number": 196, + "text": [ + "'hellothereaa'" + ] + } + ], + "prompt_number": 196 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "hill_encipher(ml, 'act')" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "pyout", + "prompt_number": 182, + "text": [ + "'poh'" + ] + } + ], + "prompt_number": 182 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "hill_decipher(ml, 'poh')" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "[[ 8. 5. 10.]\n", + " [ 21. 8. 21.]\n", + " [ 21. 12. 8.]]\n" + ] + }, + { + "metadata": {}, + "output_type": "pyout", + "prompt_number": 192, + "text": [ + "'act'" + ] + } + ], + "prompt_number": 192 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "[chr(int(round(i)) % 26 + ord('a')) for i in (ml_inv * np.matrix([ord(c) - ord('a') for c in 'poh']).T).T.tolist()[0]]" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "pyout", + "prompt_number": 180, + "text": [ + "['a', 'c', 't']" + ] + } + ], + "prompt_number": 180 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "hill_encipher(ml_inv, 'poh')" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "pyout", + "prompt_number": 184, + "text": [ + "'act'" + ] + } + ], + "prompt_number": 184 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [], + "language": "python", + "metadata": {}, + "outputs": [] + } + ], + "metadata": {} + } + ] +} \ No newline at end of file -- 2.34.1