Utilities/crypto/py3AES.py

# -*- coding: utf-8 -*-

#
# 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/
#

#
# Ported to Python3
#
# Copyright (c) 2011 - 2018 Detlev Offenbach <detlev@die-offenbachs.de>
#

"""
Module implementing classes for encryption according
Advanced Encryption Standard.
"""

from __future__ import unicode_literals

import os
import math


def append_PKCS7_padding(b):
    """
    Function to pad the given data to a multiple of 16-bytes by PKCS7 padding.
    
    @param b data to be padded (bytes)
    @return padded data (bytes)
    """
    numpads = 16 - (len(b) % 16)
    return b + numpads * bytes(chr(numpads), encoding="ascii")


def strip_PKCS7_padding(b):
    """
    Function to strip off PKCS7 padding.
    
    @param b data to be stripped (bytes)
    @return stripped data (bytes)
    @exception ValueError data padding is invalid
    """
    if len(b) % 16 or not b:
        raise ValueError(
            "Data of len {0} can't be PCKS7-padded".format(len(b)))
    numpads = b[-1]
    if numpads > 16:
        raise ValueError(
            "Data ending with {0} can't be PCKS7-padded".format(b[-1]))
    return b[:-numpads]


class AES(object):
    """
    Class implementing the Advanced Encryption Standard algorithm.
    """
    # valid key sizes
    KeySize = {
        "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]

    # 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]

    # 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 __getSBoxValue(self, num):
        """
        Private method to retrieve a given S-Box value.
        
        @param num position of the value (integer)
        @return value of the S-Box (integer)
        """
        return self.sbox[num]

    def __getSBoxInvert(self, num):
        """
        Private method to retrieve a given Inverted S-Box value.
        
        @param num position of the value (integer)
        @return value of the Inverted S-Box (integer)
        """
        return self.rsbox[num]

    def __rotate(self, data):
        """
        Private method performing Rijndael's key schedule rotate operation.

        Rotate the data word eight bits to the left: eg,
        rotate(1d2c3a4f) == 2c3a4f1d.
        
        @param data data of size 4 (bytearray)
        @return rotated data (bytearray)
        """
        return data[1:] + data[:1]

    def __getRconValue(self, num):
        """
        Private method to retrieve a given Rcon value.
        
        @param num position of the value (integer)
        @return Rcon value (integer)
        """
        return self.Rcon[num]

    def __core(self, data, iteration):
        """
        Private method performing the key schedule core operation.
        
        @param data data to operate on (bytearray)
        @param iteration iteration counter (integer)
        @return modified data (bytearray)
        """
        # rotate the 32-bit word 8 bits to the left
        data = self.__rotate(data)
        # apply S-Box substitution on all 4 parts of the 32-bit word
        for i in range(4):
            data[i] = self.__getSBoxValue(data[i])
        # XOR the output of the rcon operation with i to the first part
        # (leftmost) only
        data[0] = data[0] ^ self.__getRconValue(iteration)
        return data

    def __expandKey(self, key, size, expandedKeySize):
        """
        Private method performing Rijndael's key expansion.

        Expands a 128, 192 or 256 bit key into a 176, 208 or 240 bit key.
        
        @param key key to be expanded (bytes or bytearray)
        @param size size of the key in bytes (16, 24 or 32)
        @param expandedKeySize size of the expanded key (integer)
        @return expanded key (bytearray)
        """
        # current expanded keySize, in bytes
        currentSize = 0
        rconIteration = 1
        expandedKey = bytearray(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):
        """
        Private method to add (XORs) the round key to the state.
        
        @param state state to be changed (bytearray)
        @param roundKey key to be used for the modification (bytearray)
        @return modified state (bytearray)
        """
        buf = state[:]
        for i in range(16):
            buf[i] ^= roundKey[i]
        return buf

    def __createRoundKey(self, expandedKey, roundKeyPointer):
        """
        Private method to create a round key.
        
        @param expandedKey expanded key to be used (bytearray)
        @param roundKeyPointer position within the expanded key (integer)
        @return round key (bytearray)
        """
        roundKey = bytearray(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):
        """
        Private method to perform a Galois multiplication of 8 bit characters
        a and b.
        
        @param a first factor (byte)
        @param b second factor (byte)
        @return result (byte)
        """
        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

    def __subBytes(self, state, isInv):
        """
        Private method to substitute all the values from the state with the
        value in the SBox using the state value as index for the SBox.
        
        @param state state to be worked on (bytearray)
        @param isInv flag indicating an inverse operation (boolean)
        @return modified state (bytearray)
        """
        state = state[:]
        if isInv:
            getter = self.__getSBoxInvert
        else:
            getter = self.__getSBoxValue
        for i in range(16):
            state[i] = getter(state[i])
        return state

    def __shiftRows(self, state, isInv):
        """
        Private method to iterate over the 4 rows and call __shiftRow() with
        that row.
        
        @param state state to be worked on (bytearray)
        @param isInv flag indicating an inverse operation (boolean)
        @return modified state (bytearray)
        """
        state = state[:]
        for i in range(4):
            state = self.__shiftRow(state, i * 4, i, isInv)
        return state

    def __shiftRow(self, state, statePointer, nbr, isInv):
        """
        Private method to shift the bytes of a row to the left.
        
        @param state state to be worked on (bytearray)
        @param statePointer index into the state (integer)
        @param nbr number of positions to shift (integer)
        @param isInv flag indicating an inverse operation (boolean)
        @return modified state (bytearray)
        """
        state = state[:]
        for _ 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

    def __mixColumns(self, state, isInv):
        """
        Private method to perform a galois multiplication of the 4x4 matrix.
        
        @param state state to be worked on (bytearray)
        @param isInv flag indicating an inverse operation (boolean)
        @return modified state (bytearray)
        """
        state = state[:]
        # 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):
        """
        Private method to perform a galois multiplication of 1 column the
        4x4 matrix.
        
        @param column column to be worked on (bytearray)
        @param isInv flag indicating an inverse operation (boolean)
        @return modified column (bytearray)
        """
        column = column[:]
        if isInv:
            mult = [14, 9, 13, 11]
        else:
            mult = [2, 1, 1, 3]
        cpy = 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

    def __aes_round(self, state, roundKey):
        """
        Private method to apply the 4 operations of the forward round in
        sequence.
        
        @param state state to be worked on (bytearray)
        @param roundKey round key to be used (bytearray)
        @return modified state (bytearray)
        """
        state = self.__subBytes(state, False)
        state = self.__shiftRows(state, False)
        state = self.__mixColumns(state, False)
        state = self.__addRoundKey(state, roundKey)
        return state

    def __aes_invRound(self, state, roundKey):
        """
        Private method to apply the 4 operations of the inverse round in
        sequence.
        
        @param state state to be worked on (bytearray)
        @param roundKey round key to be used (bytearray)
        @return modified state (bytearray)
        """
        state = self.__shiftRows(state, True)
        state = self.__subBytes(state, True)
        state = self.__addRoundKey(state, roundKey)
        state = self.__mixColumns(state, True)
        return state

    def __aes_main(self, state, expandedKey, nbrRounds):
        """
        Private method to do the AES encryption for one round.
        
        Perform the initial operations, the standard round, and the
        final operations of the forward AES, creating a round key for
        each round.
        
        @param state state to be worked on (bytearray)
        @param expandedKey expanded key to be used (bytearray)
        @param nbrRounds number of rounds to be done (integer)
        @return modified state (bytearray)
        """
        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

    def __aes_invMain(self, state, expandedKey, nbrRounds):
        """
        Private method to do the inverse AES encryption for one round.
        
        Perform the initial operations, the standard round, and the
        final operations of the inverse AES, creating a round key for
        each round.
        
        @param state state to be worked on (bytearray)
        @param expandedKey expanded key to be used (bytearray)
        @param nbrRounds number of rounds to be done (integer)
        @return modified state (bytearray)
        """
        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

    def encrypt(self, iput, key, size):
        """
        Public method to encrypt a 128 bit input block against the given key
        of size specified.
        
        @param iput input data (bytearray)
        @param key key to be used (bytes or bytearray)
        @param size key size (16, 24 or 32)
        @return encrypted data (bytes)
        @exception ValueError key size is invalid
        """
        output = bytearray(16)
        # the number of rounds
        nbrRounds = 0
        # the 128 bit block to encode
        block = bytearray(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:
            raise ValueError("Wrong key size given ({0}).".format(size))

        # 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 bytes(output)

    # decrypts a 128 bit input block against the given key of size specified
    def decrypt(self, iput, key, size):
        """
        Public method to decrypt a 128 bit input block against the given key
        of size specified.
        
        @param iput input data (bytearray)
        @param key key to be used (bytes or bytearray)
        @param size key size (16, 24 or 32)
        @return decrypted data (bytes)
        @exception ValueError key size is invalid
        """
        output = bytearray(16)
        # the number of rounds
        nbrRounds = 0
        # the 128 bit block to decode
        block = bytearray(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:
            raise ValueError("Wrong key size given ({0}).".format(size))

        # 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


class AESModeOfOperation(object):
    """
    Class implementing the different AES mode of operations.
    """
    aes = AES()

    # structure of supported modes of operation
    ModeOfOperation = {
        "OFB": 0,
        "CFB": 1,
        "CBC": 2,
    }

    def __extractBytes(self, inputData, start, end, mode):
        """
        Private method to extract a range of bytes from the input.
        
        @param inputData input data (bytes)
        @param start start index (integer)
        @param end end index (integer)
        @param mode mode of operation (0, 1, 2)
        @return extracted bytes (bytearray)
        """
        if end - start > 16:
            end = start + 16
        if mode == self.ModeOfOperation["CBC"]:
            ar = bytearray(16)
        else:
            ar = bytearray()

        i = start
        j = 0
        while len(ar) < end - start:
            ar.append(0)
        while i < end:
            ar[j] = inputData[i]
            j += 1
            i += 1
        return ar

    def encrypt(self, inputData, mode, key, size, IV):
        """
        Public method to perform the encryption operation.
        
        @param inputData data to be encrypted (bytes)
        @param mode mode of operation (0, 1 or 2)
        @param key key to be used (bytes)
        @param size length of the key (16, 24 or 32)
        @param IV initialisation vector (bytearray)
        @return tuple with mode of operation, length of the input data and
            the encrypted data (integer, integer, bytes)
        @exception ValueError key size is invalid or decrypted data is invalid
        """
        if len(key) % size:
            raise ValueError("Illegal size ({0}) for key '{1}'.".format(
                size, key))
        if len(IV) % 16:
            raise ValueError("IV is not a multiple of 16.")
        # the AES input/output
        iput = bytearray(16)
        output = bytearray()
        ciphertext = bytearray(16)
        # the output cipher string
        cipherOut = bytearray()
        # char firstRound
        firstRound = True
        if inputData:
            for j in range(int(math.ceil(float(len(inputData)) / 16))):
                start = j * 16
                end = j * 16 + 16
                if end > len(inputData):
                    end = len(inputData)
                plaintext = self.__extractBytes(inputData, start, end, mode)
                if mode == self.ModeOfOperation["CFB"]:
                    if firstRound:
                        output = self.aes.encrypt(IV, key, size)
                        firstRound = False
                    else:
                        output = self.aes.encrypt(iput, key, size)
                    for i in range(16):
                        if len(plaintext) - 1 < i:
                            ciphertext[i] = 0 ^ output[i]
                        elif len(output) - 1 < i:
                            ciphertext[i] = plaintext[i] ^ 0
                        elif len(plaintext) - 1 < i and len(output) < i:
                            ciphertext[i] = 0 ^ 0
                        else:
                            ciphertext[i] = plaintext[i] ^ output[i]
                    for k in range(end - start):
                        cipherOut.append(ciphertext[k])
                    iput = ciphertext
                elif mode == self.ModeOfOperation["OFB"]:
                    if firstRound:
                        output = self.aes.encrypt(IV, key, size)
                        firstRound = False
                    else:
                        output = self.aes.encrypt(iput, key, size)
                    for i in range(16):
                        if len(plaintext) - 1 < i:
                            ciphertext[i] = 0 ^ output[i]
                        elif len(output) - 1 < i:
                            ciphertext[i] = plaintext[i] ^ 0
                        elif len(plaintext) - 1 < i and len(output) < i:
                            ciphertext[i] = 0 ^ 0
                        else:
                            ciphertext[i] = plaintext[i] ^ output[i]
                    for k in range(end - start):
                        cipherOut.append(ciphertext[k])
                    iput = output
                elif mode == self.ModeOfOperation["CBC"]:
                    for i in range(16):
                        if firstRound:
                            iput[i] = plaintext[i] ^ IV[i]
                        else:
                            iput[i] = plaintext[i] ^ ciphertext[i]
                    firstRound = False
                    ciphertext = self.aes.encrypt(iput, key, size)
                    # always 16 bytes because of the padding for CBC
                    for k in range(16):
                        cipherOut.append(ciphertext[k])
        return mode, len(inputData), bytes(cipherOut)

    # Mode of Operation Decryption
    # cipherIn - Encrypted String
    # originalsize - The unencrypted string length - required for CBC
    # mode - mode of type modeOfOperation
    # key - a number array of the bit length size
    # size - the bit length of the key
    # IV - the 128 bit number array Initilization Vector
    def decrypt(self, cipherIn, originalsize, mode, key, size, IV):
        """
        Public method to perform the decryption operation.
        
        @param cipherIn data to be decrypted (bytes)
        @param originalsize unencrypted string length (required for CBC)
            (integer)
        @param mode mode of operation (0, 1 or 2)
        @param key key to be used (bytes)
        @param size length of the key (16, 24 or 32)
        @param IV initialisation vector (bytearray)
        @return decrypted data (bytes)
        @exception ValueError key size is invalid or decrypted data is invalid
        """
        if len(key) % size:
            raise ValueError("Illegal size ({0}) for key '{1}'.".format(
                size, key))
        if len(IV) % 16:
            raise ValueError("IV is not a multiple of 16.")
        # the AES input/output
        ciphertext = bytearray()
        iput = bytearray()
        output = bytearray()
        plaintext = bytearray(16)
        # the output bytes
        bytesOut = bytearray()
        # char firstRound
        firstRound = True
        if cipherIn is not None:
            for j in range(int(math.ceil(float(len(cipherIn)) / 16))):
                start = j * 16
                end = j * 16 + 16
                if j * 16 + 16 > len(cipherIn):
                    end = len(cipherIn)
                ciphertext = cipherIn[start:end]
                if mode == self.ModeOfOperation["CFB"]:
                    if firstRound:
                        output = self.aes.encrypt(IV, key, size)
                        firstRound = False
                    else:
                        output = self.aes.encrypt(iput, key, size)
                    for i in range(16):
                        if len(output) - 1 < i:
                            plaintext[i] = 0 ^ ciphertext[i]
                        elif len(ciphertext) - 1 < i:
                            plaintext[i] = output[i] ^ 0
                        elif len(output) - 1 < i and len(ciphertext) < i:
                            plaintext[i] = 0 ^ 0
                        else:
                            plaintext[i] = output[i] ^ ciphertext[i]
                    for k in range(end - start):
                        bytesOut.append(plaintext[k])
                    iput = ciphertext
                elif mode == self.ModeOfOperation["OFB"]:
                    if firstRound:
                        output = self.aes.encrypt(IV, key, size)
                        firstRound = False
                    else:
                        output = self.aes.encrypt(iput, key, size)
                    for i in range(16):
                        if len(output) - 1 < i:
                            plaintext[i] = 0 ^ ciphertext[i]
                        elif len(ciphertext) - 1 < i:
                            plaintext[i] = output[i] ^ 0
                        elif len(output) - 1 < i and len(ciphertext) < i:
                            plaintext[i] = 0 ^ 0
                        else:
                            plaintext[i] = output[i] ^ ciphertext[i]
                    for k in range(end - start):
                        bytesOut.append(plaintext[k])
                    iput = output
                elif mode == self.ModeOfOperation["CBC"]:
                    output = self.aes.decrypt(ciphertext, key, size)
                    for i in range(16):
                        if firstRound:
                            plaintext[i] = IV[i] ^ output[i]
                        else:
                            plaintext[i] = iput[i] ^ output[i]
                    firstRound = False
                    if originalsize is not None and originalsize < end:
                        for k in range(originalsize - start):
                            bytesOut.append(plaintext[k])
                    else:
                        for k in range(end - start):
                            bytesOut.append(plaintext[k])
                    iput = ciphertext
        return bytes(bytesOut)


def encryptData(key, data, mode=AESModeOfOperation.ModeOfOperation["CBC"]):
    """
    Module function to encrypt the given data with the given key.
    
    @param key key to be used for encryption (bytes)
    @param data data to be encrypted (bytes)
    @param mode mode of operations (0, 1 or 2)
    @return encrypted data prepended with the initialization vector (bytes)
    """
    key = bytearray(key)
    if mode == AESModeOfOperation.ModeOfOperation["CBC"]:
        data = append_PKCS7_padding(data)
    keysize = len(key)
    assert keysize in AES.KeySize.values(), \
        'invalid key size: {0}'.format(keysize)
    # create a new iv using random data
    iv = bytearray([i for i in os.urandom(16)])
    moo = AESModeOfOperation()
    mode, length, ciph = moo.encrypt(data, mode, key, keysize, iv)
    # With padding, the original length does not need to be known. It's a bad
    # idea to store the original message length.
    # prepend the iv.
    return bytes(iv) + bytes(ciph)


def decryptData(key, data, mode=AESModeOfOperation.ModeOfOperation["CBC"]):
    """
    Module function to decrypt the given data with the given key.
    
    @param key key to be used for decryption (bytes)
    @param data data to be decrypted (with initialization vector prepended)
        (bytes)
    @param mode mode of operations (0, 1 or 2)
    @return decrypted data (bytes)
    """
    key = bytearray(key)
    keysize = len(key)
    assert keysize in AES.KeySize.values(), \
        'invalid key size: {0}'.format(keysize)
    # iv is first 16 bytes
    iv = bytearray(data[:16])
    data = bytearray(data[16:])
    moo = AESModeOfOperation()
    decr = moo.decrypt(data, None, mode, key, keysize, iv)
    if mode == AESModeOfOperation.ModeOfOperation["CBC"]:
        decr = strip_PKCS7_padding(decr)
    return bytes(decr)