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Calculation of 0xc6

m(x) = 0x11b = 100011011 = x^8 + x^4 + x^3 + x + 1
a(x) =   0xc6 =  11000110 = x^7 + x^6 + x^2 + x
m(x) = (x + 1) * a(x) + (x^6 + x^4 + 1)

Calculation of 0xc6-1 in the finite field GF(28)

01010001 = 00000001 * 100011011 + 00000011 * 11000110
00110101 = 00000011 * 100011011 + 00000100 * 11000110
00001110 = 00000100 * 100011011 + 00001111 * 11000110
00000011 = 00010111 * 100011011 + 00110111 * 11000110
00000001 = 01001111 * 100011011 + 11100100 * 11000110
00000000 = 11000110 * 100011011 + 100011011 * 11000110

a-1(x) = x^7 + x^6 + x^5 + x^2 = 11100100 = 0xe4

The calculation of 0xc6-1 is made with the Extended Euclidean algorithm. Instead of normal division and multiplication you need to use Polynomialdivision and Polynomialmultiplication.


Affine transformation over GF(2)
           1 0 0 0 1 1 1 1      0     1     0
           1 1 0 0 0 1 1 1      0     1     0
           1 1 1 0 0 0 1 1      1     0     1
           1 1 1 1 0 0 0 1      0     0     0
SBOX(c6) = 1 1 1 1 1 0 0 0   *  0  +  0  =  1
           0 1 1 1 1 1 0 0      1     1     1
           0 0 1 1 1 1 1 0      1     1     0
           0 0 0 1 1 1 1 1      1     0     1


SBOX(c6) = 10110100 = b4

For more information see FIPS 197.



Implemented by bachph [at] philba [dot] com