Calculation of 0x00

m(x) = 0x11b = 100011011 = x^8 + x^4 + x^3 + x + 1
a(x) =   0x0 =  00000000 = 0

m(x) = (x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) * a(x) + (x^8 + x^4 + x^3 + x + 1)

Calculation of 0x00^-1 in the finite field GF(2⁸)

a^-1(x) = 0 = 00000000 = 0x00

The calculation of 0x00^-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      0     1     1
           1 1 1 0 0 0 1 1      0     0     0
           1 1 1 1 0 0 0 1      0     0     0
SBOX(00) = 1 1 1 1 1 0 0 0   *  0  +  0  =  0
           0 1 1 1 1 1 0 0      0     1     1
           0 0 1 1 1 1 1 0      0     1     1
           0 0 0 1 1 1 1 1      0     0     0

SBOX(00) = 01100011 = 63

For more information see FIPS 197.

Implemented by bachph [at] philba [dot] com