Impressum und Datenschutzerklaerung

Calculation of 0xd8

m(x) = 0x11b = 100011011 = x^8 + x^4 + x^3 + x + 1
a(x) =   0xd8 =  11011000 = x^7 + x^6 + x^4 + x^3
m(x) = (x + 1) * a(x) + (x^6 + x^5 + x^4 + x + 1)

Calculation of 0xd8-1 in the finite field GF(28)

01110011 = 00000001 * 100011011 + 00000011 * 11011000
00111110 = 00000010 * 100011011 + 00000111 * 11011000
00001111 = 00000101 * 100011011 + 00001101 * 11011000
00000010 = 00010110 * 100011011 + 00110011 * 11011000
00000001 = 01100111 * 100011011 + 10010100 * 11011000
00000000 = 11011000 * 100011011 + 100011011 * 11011000

a-1(x) = x^7 + x^4 + x^2 = 10010100 = 0x94

The calculation of 0xd8-1 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     0
           1 1 1 0 0 0 1 1      1     0     0
           1 1 1 1 0 0 0 1      0     0     0
SBOX(d8) = 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      0     1     1
           0 0 0 1 1 1 1 1      1     0     0


SBOX(d8) = 01100001 = 61

For more information see FIPS 197.



Implemented by bachph [at] philba [dot] com