#! /usr/bin/env python
# -*- coding: iso-8859-1 -*-
""" crypto.cipher.aes_sbox_analysis

    AES Sbox Analysis - a simple analysis of the AES Sbox that determines
    the number and size of the permutation subgroups in the transformation.
    Could be extended to examine any Sbox ...

    Copyright © (c) 2002 by Paul A. Lambert
    Read LICENSE.txt for license information.

    2002-12-05 Added validation of equation form of AES
    2002-06-01 Original
"""

# The AES Sbox
sbbytes = (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)

def groups(subbytes):
    gdict={}     # a dictionary of the cycles indexed by the first cycle element
    touched=[0 for i in range(len(subbytes))]
    for i in range(len(sbbytes)):
        touched.append(0) 
    for i in range(len(sbbytes)):
        element = i
        cycle = []
        if not touched[element]:
            for j in range (i,len(sbbytes)):
                touched[element] = 1
                cycle.append(element)
                element = sbbytes[element]
                if element == i:
                    break
            gdict[cycle[1]]=cycle
        else:
            pass
    return gdict

def grpv(subbytes):
    """" Returns a list of tuples (cycle start, cycle size) """
    v=[]
    z=groups(subbytes)
    for i in z.keys():
        v.append( [i, len(z[i])] )
    return v

def sgv(subbytes):
    x = grpv(subbytes)
    sum = 0
    for i in x:
        sum = sum + i[1]
    return sum


def main():
    cycles = grpv(sbbytes)
    print 'The AES sbox contains ',
    print len(cycles),
    print 'permutation subgroups'
    print 'The AES sbox subgroups (start, length) are:'
    print cycles

# Make this test module runnable from the command prompt
if __name__ == "__main__":
    main()