Calculation of 0x92

m(x) = 0x11b = 100011011 = x^8 + x^4 + x^3 + x + 1
a(x) =   0x92 =  10010010 = x^7 + x^4 + x

m(x) = (x) * a(x) + (x^5 + x^4 + x^3 + x^2 + x + 1)

Calculation of 0x92^-1 in the finite field GF(2⁸)

00111111 = 00000001 * 100011011 + 00000010 * 10010010
00010000 = 00000110 * 100011011 + 00001101 * 10010010
00001111 = 00001011 * 100011011 + 00010101 * 10010010
00000001 = 00011011 * 100011011 + 00110010 * 10010010
00000000 = 10010010 * 100011011 + 100011011 * 10010010

a^-1(x) = x^5 + x^4 + x = 00110010 = 0x32

The calculation of 0x92^-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     1
           1 1 0 0 0 1 1 1      1     1     1
           1 1 1 0 0 0 1 1      0     0     1
           1 1 1 1 0 0 0 1      0     0     1
SBOX(92) = 1 1 1 1 1 0 0 0   *  1  +  0  =  0
           0 1 1 1 1 1 0 0      1     1     0
           0 0 1 1 1 1 1 0      0     1     1
           0 0 0 1 1 1 1 1      0     0     0

SBOX(92) = 01001111 = 4f

For more information see FIPS 197.

Implemented by bachph [at] philba [dot] com