Impressum und Datenschutzerklaerung

Calculation of 0xd4

m(x) = 0x11b = 100011011 = x^8 + x^4 + x^3 + x + 1
a(x) =   0xd4 =  11010100 = x^7 + x^6 + x^4 + x^2
m(x) = (x + 1) * a(x) + (x^6 + x^5 + x^2 + x + 1)

Calculation of 0xd4-1 in the finite field GF(28)

01100111 = 00000001 * 100011011 + 00000011 * 11010100
00011010 = 00000010 * 100011011 + 00000111 * 11010100
00001111 = 00001001 * 100011011 + 00011111 * 11010100
00000100 = 00010000 * 100011011 + 00111001 * 11010100
00000011 = 00111001 * 100011011 + 01010100 * 11010100
00000001 = 01011011 * 100011011 + 11000101 * 11010100
00000000 = 11010100 * 100011011 + 100011011 * 11010100

a-1(x) = x^7 + x^6 + x^2 + 1 = 11000101 = 0xc5

The calculation of 0xd4-1 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      1     1     0
           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     1
SBOX(d4) = 1 1 1 1 1 0 0 0   *  0  +  0  =  0
           0 1 1 1 1 1 0 0      0     1     0
           0 0 1 1 1 1 1 0      1     1     1
           0 0 0 1 1 1 1 1      1     0     0


SBOX(d4) = 01001000 = 48

For more information see FIPS 197.



Implemented by bachph [at] philba [dot] com