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Calculation of 0x94

m(x) = 0x11b = 100011011 = x^8 + x^4 + x^3 + x + 1
a(x) =   0x94 =  10010100 = x^7 + x^4 + x^2
m(x) = (x) * a(x) + (x^5 + x^4 + x + 1)

Calculation of 0x94-1 in the finite field GF(28)

00110011 = 00000001 * 100011011 + 00000010 * 10010100
00001101 = 00000111 * 100011011 + 00001111 * 10010100
00000111 = 00011101 * 100011011 + 00111110 * 10010100
00000011 = 00111101 * 100011011 + 01110011 * 10010100
00000001 = 01100111 * 100011011 + 11011000 * 10010100
00000000 = 10010100 * 100011011 + 100011011 * 10010100

a-1(x) = x^7 + x^6 + x^4 + x^3 = 11011000 = 0xd8

The calculation of 0x94-1 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     1
           1 1 1 0 0 0 1 1      0     0     0
           1 1 1 1 0 0 0 1      1     0     0
SBOX(94) = 1 1 1 1 1 0 0 0   *  1  +  0  =  0
           0 1 1 1 1 1 0 0      0     1     1
           0 0 1 1 1 1 1 0      1     1     0
           0 0 0 1 1 1 1 1      1     0     0


SBOX(94) = 00100010 = 22

For more information see FIPS 197.



Implemented by bachph [at] philba [dot] com