linear cipher demo

#!/usr/bin/python
#
# aes.py: implements AES - Advanced Encryption Standard
# from the SlowAES project, http://code.google.com/p/slowaes/
#
# Copyright (c) 2008    Josh Davis ( http://www.josh-davis.org ),
#           Alex Martelli ( http://www.aleax.it )
#
# Ported from C code written by Laurent Haan ( http://www.progressive-coding.com )
#
# Licensed under the Apache License, Version 2.0
# http://www.apache.org/licenses/
#
# modified by Ella Rose to demonstrate the weakness of linear ciphers

import os
import sys
import math

class AES(object):
    '''AES funtions for a single block
    '''
    # Very annoying code:  all is for an object, but no state is kept!
    # Should just be plain functions in a AES modlule.

    # valid key sizes
    keySize = dict(SIZE_128=16, SIZE_192=24, SIZE_256=32)

    # Rijndael S-box
    #sbox =  [0x63, 0x7c, 0x77, 0x7b, 0xf2, 0x6b, 0x6f, 0xc5, 0x30, 0x01, 0x67,
    #        0x2b, 0xfe, 0xd7, 0xab, 0x76, 0xca, 0x82, 0xc9, 0x7d, 0xfa, 0x59,
    #        0x47, 0xf0, 0xad, 0xd4, 0xa2, 0xaf, 0x9c, 0xa4, 0x72, 0xc0, 0xb7,
    #        0xfd, 0x93, 0x26, 0x36, 0x3f, 0xf7, 0xcc, 0x34, 0xa5, 0xe5, 0xf1,
    #        0x71, 0xd8, 0x31, 0x15, 0x04, 0xc7, 0x23, 0xc3, 0x18, 0x96, 0x05,
    #        0x9a, 0x07, 0x12, 0x80, 0xe2, 0xeb, 0x27, 0xb2, 0x75, 0x09, 0x83,
    #        0x2c, 0x1a, 0x1b, 0x6e, 0x5a, 0xa0, 0x52, 0x3b, 0xd6, 0xb3, 0x29,
    #        0xe3, 0x2f, 0x84, 0x53, 0xd1, 0x00, 0xed, 0x20, 0xfc, 0xb1, 0x5b,
    #        0x6a, 0xcb, 0xbe, 0x39, 0x4a, 0x4c, 0x58, 0xcf, 0xd0, 0xef, 0xaa,
    #        0xfb, 0x43, 0x4d, 0x33, 0x85, 0x45, 0xf9, 0x02, 0x7f, 0x50, 0x3c,
    #        0x9f, 0xa8, 0x51, 0xa3, 0x40, 0x8f, 0x92, 0x9d, 0x38, 0xf5, 0xbc,
    #        0xb6, 0xda, 0x21, 0x10, 0xff, 0xf3, 0xd2, 0xcd, 0x0c, 0x13, 0xec,
    #        0x5f, 0x97, 0x44, 0x17, 0xc4, 0xa7, 0x7e, 0x3d, 0x64, 0x5d, 0x19,
    #        0x73, 0x60, 0x81, 0x4f, 0xdc, 0x22, 0x2a, 0x90, 0x88, 0x46, 0xee,
    #        0xb8, 0x14, 0xde, 0x5e, 0x0b, 0xdb, 0xe0, 0x32, 0x3a, 0x0a, 0x49,
    #        0x06, 0x24, 0x5c, 0xc2, 0xd3, 0xac, 0x62, 0x91, 0x95, 0xe4, 0x79,
    #        0xe7, 0xc8, 0x37, 0x6d, 0x8d, 0xd5, 0x4e, 0xa9, 0x6c, 0x56, 0xf4,
    #        0xea, 0x65, 0x7a, 0xae, 0x08, 0xba, 0x78, 0x25, 0x2e, 0x1c, 0xa6,
    #        0xb4, 0xc6, 0xe8, 0xdd, 0x74, 0x1f, 0x4b, 0xbd, 0x8b, 0x8a, 0x70,
    #        0x3e, 0xb5, 0x66, 0x48, 0x03, 0xf6, 0x0e, 0x61, 0x35, 0x57, 0xb9,
    #        0x86, 0xc1, 0x1d, 0x9e, 0xe1, 0xf8, 0x98, 0x11, 0x69, 0xd9, 0x8e,
    #        0x94, 0x9b, 0x1e, 0x87, 0xe9, 0xce, 0x55, 0x28, 0xdf, 0x8c, 0xa1,
    #        0x89, 0x0d, 0xbf, 0xe6, 0x42, 0x68, 0x41, 0x99, 0x2d, 0x0f, 0xb0,
    #        0x54, 0xbb, 0x16]
    sbox = range(256)
    # Rijndael Inverted S-box
    #rsbox = [0x52, 0x09, 0x6a, 0xd5, 0x30, 0x36, 0xa5, 0x38, 0xbf, 0x40, 0xa3,
    #        0x9e, 0x81, 0xf3, 0xd7, 0xfb , 0x7c, 0xe3, 0x39, 0x82, 0x9b, 0x2f,
    #        0xff, 0x87, 0x34, 0x8e, 0x43, 0x44, 0xc4, 0xde, 0xe9, 0xcb , 0x54,
    #        0x7b, 0x94, 0x32, 0xa6, 0xc2, 0x23, 0x3d, 0xee, 0x4c, 0x95, 0x0b,
    #        0x42, 0xfa, 0xc3, 0x4e , 0x08, 0x2e, 0xa1, 0x66, 0x28, 0xd9, 0x24,
    #        0xb2, 0x76, 0x5b, 0xa2, 0x49, 0x6d, 0x8b, 0xd1, 0x25 , 0x72, 0xf8,
    #        0xf6, 0x64, 0x86, 0x68, 0x98, 0x16, 0xd4, 0xa4, 0x5c, 0xcc, 0x5d,
    #        0x65, 0xb6, 0x92 , 0x6c, 0x70, 0x48, 0x50, 0xfd, 0xed, 0xb9, 0xda,
    #        0x5e, 0x15, 0x46, 0x57, 0xa7, 0x8d, 0x9d, 0x84 , 0x90, 0xd8, 0xab,
    #        0x00, 0x8c, 0xbc, 0xd3, 0x0a, 0xf7, 0xe4, 0x58, 0x05, 0xb8, 0xb3,
    #        0x45, 0x06 , 0xd0, 0x2c, 0x1e, 0x8f, 0xca, 0x3f, 0x0f, 0x02, 0xc1,
    #        0xaf, 0xbd, 0x03, 0x01, 0x13, 0x8a, 0x6b , 0x3a, 0x91, 0x11, 0x41,
    #        0x4f, 0x67, 0xdc, 0xea, 0x97, 0xf2, 0xcf, 0xce, 0xf0, 0xb4, 0xe6,
    #        0x73 , 0x96, 0xac, 0x74, 0x22, 0xe7, 0xad, 0x35, 0x85, 0xe2, 0xf9,
    #        0x37, 0xe8, 0x1c, 0x75, 0xdf, 0x6e , 0x47, 0xf1, 0x1a, 0x71, 0x1d,
    #        0x29, 0xc5, 0x89, 0x6f, 0xb7, 0x62, 0x0e, 0xaa, 0x18, 0xbe, 0x1b ,
    #        0xfc, 0x56, 0x3e, 0x4b, 0xc6, 0xd2, 0x79, 0x20, 0x9a, 0xdb, 0xc0,
    #        0xfe, 0x78, 0xcd, 0x5a, 0xf4 , 0x1f, 0xdd, 0xa8, 0x33, 0x88, 0x07,
    #        0xc7, 0x31, 0xb1, 0x12, 0x10, 0x59, 0x27, 0x80, 0xec, 0x5f , 0x60,
    #        0x51, 0x7f, 0xa9, 0x19, 0xb5, 0x4a, 0x0d, 0x2d, 0xe5, 0x7a, 0x9f,
    #        0x93, 0xc9, 0x9c, 0xef , 0xa0, 0xe0, 0x3b, 0x4d, 0xae, 0x2a, 0xf5,
    #        0xb0, 0xc8, 0xeb, 0xbb, 0x3c, 0x83, 0x53, 0x99, 0x61 , 0x17, 0x2b,
    #        0x04, 0x7e, 0xba, 0x77, 0xd6, 0x26, 0xe1, 0x69, 0x14, 0x63, 0x55,
    #        0x21, 0x0c, 0x7d]
    rsbox = range(256)
    def getSBoxValue(self,num):
        """Retrieves a given S-Box Value"""
        return self.sbox[num]

    def getSBoxInvert(self,num):
        """Retrieves a given Inverted S-Box Value"""
        return self.rsbox[num]

    def rotate(self, word):
        """ Rijndael's key schedule rotate operation.

        Rotate a word eight bits to the left: eg, rotate(1d2c3a4f) == 2c3a4f1d
        Word is an char list of size 4 (32 bits overall).
        """
        return word[1:] + word[:1]

    # Rijndael Rcon
    Rcon = [0x8d, 0x01, 0x02, 0x04, 0x08, 0x10, 0x20, 0x40, 0x80, 0x1b, 0x36,
            0x6c, 0xd8, 0xab, 0x4d, 0x9a, 0x2f, 0x5e, 0xbc, 0x63, 0xc6, 0x97,
            0x35, 0x6a, 0xd4, 0xb3, 0x7d, 0xfa, 0xef, 0xc5, 0x91, 0x39, 0x72,
            0xe4, 0xd3, 0xbd, 0x61, 0xc2, 0x9f, 0x25, 0x4a, 0x94, 0x33, 0x66,
            0xcc, 0x83, 0x1d, 0x3a, 0x74, 0xe8, 0xcb, 0x8d, 0x01, 0x02, 0x04,
            0x08, 0x10, 0x20, 0x40, 0x80, 0x1b, 0x36, 0x6c, 0xd8, 0xab, 0x4d,
            0x9a, 0x2f, 0x5e, 0xbc, 0x63, 0xc6, 0x97, 0x35, 0x6a, 0xd4, 0xb3,
            0x7d, 0xfa, 0xef, 0xc5, 0x91, 0x39, 0x72, 0xe4, 0xd3, 0xbd, 0x61,
            0xc2, 0x9f, 0x25, 0x4a, 0x94, 0x33, 0x66, 0xcc, 0x83, 0x1d, 0x3a,
            0x74, 0xe8, 0xcb, 0x8d, 0x01, 0x02, 0x04, 0x08, 0x10, 0x20, 0x40,
            0x80, 0x1b, 0x36, 0x6c, 0xd8, 0xab, 0x4d, 0x9a, 0x2f, 0x5e, 0xbc,
            0x63, 0xc6, 0x97, 0x35, 0x6a, 0xd4, 0xb3, 0x7d, 0xfa, 0xef, 0xc5,
            0x91, 0x39, 0x72, 0xe4, 0xd3, 0xbd, 0x61, 0xc2, 0x9f, 0x25, 0x4a,
            0x94, 0x33, 0x66, 0xcc, 0x83, 0x1d, 0x3a, 0x74, 0xe8, 0xcb, 0x8d,
            0x01, 0x02, 0x04, 0x08, 0x10, 0x20, 0x40, 0x80, 0x1b, 0x36, 0x6c,
            0xd8, 0xab, 0x4d, 0x9a, 0x2f, 0x5e, 0xbc, 0x63, 0xc6, 0x97, 0x35,
            0x6a, 0xd4, 0xb3, 0x7d, 0xfa, 0xef, 0xc5, 0x91, 0x39, 0x72, 0xe4,
            0xd3, 0xbd, 0x61, 0xc2, 0x9f, 0x25, 0x4a, 0x94, 0x33, 0x66, 0xcc,
            0x83, 0x1d, 0x3a, 0x74, 0xe8, 0xcb, 0x8d, 0x01, 0x02, 0x04, 0x08,
            0x10, 0x20, 0x40, 0x80, 0x1b, 0x36, 0x6c, 0xd8, 0xab, 0x4d, 0x9a,
            0x2f, 0x5e, 0xbc, 0x63, 0xc6, 0x97, 0x35, 0x6a, 0xd4, 0xb3, 0x7d,
            0xfa, 0xef, 0xc5, 0x91, 0x39, 0x72, 0xe4, 0xd3, 0xbd, 0x61, 0xc2,
            0x9f, 0x25, 0x4a, 0x94, 0x33, 0x66, 0xcc, 0x83, 0x1d, 0x3a, 0x74,
            0xe8, 0xcb ]

    def getRconValue(self, num):
        """Retrieves a given Rcon Value"""
        return self.Rcon[num]

    def core(self, word, iteration):
        """Key schedule core."""
        # rotate the 32-bit word 8 bits to the left
        word = self.rotate(word)
        # apply S-Box substitution on all 4 parts of the 32-bit word
        for i in range(4):
            word[i] = self.getSBoxValue(word[i])
        # XOR the output of the rcon operation with i to the first part
        # (leftmost) only
        word[0] = word[0] ^ self.getRconValue(iteration)
        return word

    def expandKey(self, key, size, expandedKeySize):
        """Rijndael's key expansion.

        Expands an 128,192,256 key into an 176,208,240 bytes key

        expandedKey is a char list of large enough size,
        key is the non-expanded key.
        """
        # current expanded keySize, in bytes
        currentSize = 0
        rconIteration = 1
        expandedKey = [0] * expandedKeySize

        # set the 16, 24, 32 bytes of the expanded key to the input key
        for j in range(size):
            expandedKey[j] = key[j]
        currentSize += size

        while currentSize < expandedKeySize:
            # assign the previous 4 bytes to the temporary value t
            t = expandedKey[currentSize-4:currentSize]

            # every 16,24,32 bytes we apply the core schedule to t
            # and increment rconIteration afterwards
            if currentSize % size == 0:
                t = self.core(t, rconIteration)
                rconIteration += 1
            # For 256-bit keys, we add an extra sbox to the calculation
            if size == self.keySize["SIZE_256"] and ((currentSize % size) == 16):
                for l in range(4): t[l] = self.getSBoxValue(t[l])

            # We XOR t with the four-byte block 16,24,32 bytes before the new
            # expanded key.  This becomes the next four bytes in the expanded
            # key.
            for m in range(4):
                expandedKey[currentSize] = expandedKey[currentSize - size] ^ \
                        t[m]
                currentSize += 1

        return expandedKey

    def addRoundKey(self, state, roundKey):
        """Adds (XORs) the round key to the state."""
        for i in range(16):
            state[i] ^= roundKey[i]
        return state

    def createRoundKey(self, expandedKey, roundKeyPointer):
        """Create a round key.
        Creates a round key from the given expanded key and the
        position within the expanded key.
        """
        roundKey = [0] * 16
        for i in range(4):
            for j in range(4):
                roundKey[j*4+i] = expandedKey[roundKeyPointer + i*4 + j]
        return roundKey

    def galois_multiplication(self, a, b):
        """Galois multiplication of 8 bit characters a and b."""
        p = 0
        for counter in range(8):
            if b & 1: p ^= a
            hi_bit_set = a & 0x80
            a <<= 1
            # keep a 8 bit
            a &= 0xFF
            if hi_bit_set:
                a ^= 0x1b
            b >>= 1
        return p

    #
    # substitute all the values from the state with the value in the SBox
    # using the state value as index for the SBox
    #
    def subBytes(self, state, isInv):
        if isInv: getter = self.getSBoxInvert
        else: getter = self.getSBoxValue
        for i in range(16): state[i] = getter(state[i])
        return state

    # iterate over the 4 rows and call shiftRow() with that row
    def shiftRows(self, state, isInv):
        for i in range(4):
            state = self.shiftRow(state, i*4, i, isInv)
        return state

    # each iteration shifts the row to the left by 1
    def shiftRow(self, state, statePointer, nbr, isInv):
        for i in range(nbr):
            if isInv:
                state[statePointer:statePointer+4] = \
                        state[statePointer+3:statePointer+4] + \
                        state[statePointer:statePointer+3]
            else:
                state[statePointer:statePointer+4] = \
                        state[statePointer+1:statePointer+4] + \
                        state[statePointer:statePointer+1]
        return state

    # galois multiplication of the 4x4 matrix
    def mixColumns(self, state, isInv):
        # iterate over the 4 columns
        for i in range(4):
            # construct one column by slicing over the 4 rows
            column = state[i:i+16:4]
            # apply the mixColumn on one column
            column = self.mixColumn(column, isInv)
            # put the values back into the state
            state[i:i+16:4] = column

        return state

    # galois multiplication of 1 column of the 4x4 matrix
    def mixColumn(self, column, isInv):
        if isInv: mult = [14, 9, 13, 11]
        else: mult = [2, 1, 1, 3]
        cpy = list(column)
        g = self.galois_multiplication

        column[0] = g(cpy[0], mult[0]) ^ g(cpy[3], mult[1]) ^ \
                    g(cpy[2], mult[2]) ^ g(cpy[1], mult[3])
        column[1] = g(cpy[1], mult[0]) ^ g(cpy[0], mult[1]) ^ \
                    g(cpy[3], mult[2]) ^ g(cpy[2], mult[3])
        column[2] = g(cpy[2], mult[0]) ^ g(cpy[1], mult[1]) ^ \
                    g(cpy[0], mult[2]) ^ g(cpy[3], mult[3])
        column[3] = g(cpy[3], mult[0]) ^ g(cpy[2], mult[1]) ^ \
                    g(cpy[1], mult[2]) ^ g(cpy[0], mult[3])
        return column

    # applies the 4 operations of the forward round in sequence
    def aes_round(self, state, roundKey):
        state = self.subBytes(state, False)
        state = self.shiftRows(state, False)
        state = self.mixColumns(state, False)
        state = self.addRoundKey(state, roundKey)
        return state

    def aes_round_no_key(self, state):
        state = self.subBytes(state, False)
        state = self.shiftRows(state, False)
        state = self.mixColumns(state, False)
        return state

    # applies the 4 operations of the inverse round in sequence
    def aes_invRound(self, state, roundKey):
        state = self.shiftRows(state, True)
        state = self.subBytes(state, True)
        state = self.addRoundKey(state, roundKey)
        state = self.mixColumns(state, True)
        return state

    # Perform the initial operations, the standard round, and the final
    # operations of the forward aes, creating a round key for each round
    def aes_main(self, state, expandedKey, nbrRounds):
        state = self.addRoundKey(state, self.createRoundKey(expandedKey, 0))
        i = 1
        while i < nbrRounds:
            state = self.aes_round(state,
                                   self.createRoundKey(expandedKey, 16*i))
            i += 1
        state = self.subBytes(state, False)
        state = self.shiftRows(state, False)
        state = self.addRoundKey(state,
                                 self.createRoundKey(expandedKey, 16*nbrRounds))
        return state

    # Perform the initial operations, the standard round, and the final
    # operations of the inverse aes, creating a round key for each round
    def aes_invMain(self, state, expandedKey, nbrRounds):
        state = self.addRoundKey(state,
                                 self.createRoundKey(expandedKey, 16*nbrRounds))
        i = nbrRounds - 1
        while i > 0:
            state = self.aes_invRound(state,
                                      self.createRoundKey(expandedKey, 16*i))
            i -= 1
        state = self.shiftRows(state, True)
        state = self.subBytes(state, True)
        state = self.addRoundKey(state, self.createRoundKey(expandedKey, 0))
        return state

    # encrypts a 128 bit input block against the given key of size specified
    def encrypt(self, iput, key, size):
        output = [0] * 16
        # the number of rounds
        nbrRounds = 0
        # the 128 bit block to encode
        block = [0] * 16
        # set the number of rounds
        if size == self.keySize["SIZE_128"]: nbrRounds = 10
        elif size == self.keySize["SIZE_192"]: nbrRounds = 12
        elif size == self.keySize["SIZE_256"]: nbrRounds = 14
        else: return None

        # the expanded keySize
        expandedKeySize = 16*(nbrRounds+1)

        # Set the block values, for the block:
        # a0,0 a0,1 a0,2 a0,3
        # a1,0 a1,1 a1,2 a1,3
        # a2,0 a2,1 a2,2 a2,3
        # a3,0 a3,1 a3,2 a3,3
        # the mapping order is a0,0 a1,0 a2,0 a3,0 a0,1 a1,1 ... a2,3 a3,3
        #
        # iterate over the columns
        for i in range(4):
            # iterate over the rows
            for j in range(4):
                block[(i+(j*4))] = iput[(i*4)+j]

        # expand the key into an 176, 208, 240 bytes key
        # the expanded key
        expandedKey = self.expandKey(key, size, expandedKeySize)

        # encrypt the block using the expandedKey
        block = self.aes_main(block, expandedKey, nbrRounds)

        # unmap the block again into the output
        for k in range(4):
            # iterate over the rows
            for l in range(4):
                output[(k*4)+l] = block[(k+(l*4))]
        return output

    # decrypts a 128 bit input block against the given key of size specified
    def decrypt(self, iput, key, size):
        output = [0] * 16
        # the number of rounds
        nbrRounds = 0
        # the 128 bit block to decode
        block = [0] * 16
        # set the number of rounds
        if size == self.keySize["SIZE_128"]: nbrRounds = 10
        elif size == self.keySize["SIZE_192"]: nbrRounds = 12
        elif size == self.keySize["SIZE_256"]: nbrRounds = 14
        else: return None

        # the expanded keySize
        expandedKeySize = 16*(nbrRounds+1)

        # Set the block values, for the block:
        # a0,0 a0,1 a0,2 a0,3
        # a1,0 a1,1 a1,2 a1,3
        # a2,0 a2,1 a2,2 a2,3
        # a3,0 a3,1 a3,2 a3,3
        # the mapping order is a0,0 a1,0 a2,0 a3,0 a0,1 a1,1 ... a2,3 a3,3

        # iterate over the columns
        for i in range(4):
            # iterate over the rows
            for j in range(4):
                block[(i+(j*4))] = iput[(i*4)+j]
        # expand the key into an 176, 208, 240 bytes key
        expandedKey = self.expandKey(key, size, expandedKeySize)
        # decrypt the block using the expandedKey
        block = self.aes_invMain(block, expandedKey, nbrRounds)
        # unmap the block again into the output
        for k in range(4):
            # iterate over the rows
            for l in range(4):
                output[(k*4)+l] = block[(k+(l*4))]
        return output

def test_break():
    size = 16
    key = range(size)
    attack_plaintext = [0] * size
    encryptor = AES()

    equivalent_key = encryptor.encrypt(attack_plaintext[:], key, size)
    _check1 = encryptor.decrypt(equivalent_key[:], key, size)
    assert _check1 == attack_plaintext

    from os import urandom
    random_plaintext = list(bytearray(urandom(size)))
    ciphertext = encryptor.encrypt(random_plaintext[:], key, size)

    partial_plaintext = [equivalent_key[i] ^ ciphertext[i] for i in range(16)]
    encryptor.addRoundKey = lambda state, __: state
    recovered_plaintext = encryptor.decrypt(partial_plaintext, key, size) # key not actually used now
    assert recovered_plaintext == random_plaintext, (recovered_plaintext, random_plaintext)

if __name__ == "__main__":
    test_break()