Impressum und Datenschutzerklaerung

Calculation of 0xea

m(x) = 0x11b = 100011011 = x^8 + x^4 + x^3 + x + 1
a(x) =   0xea =  11101010 = x^7 + x^6 + x^5 + x^3 + x
m(x) = (x + 1) * a(x) + (x^5 + x^2 + 1)

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

00100101 = 00000001 * 100011011 + 00000011 * 11101010
00010001 = 00000111 * 100011011 + 00001000 * 11101010
00000111 = 00001111 * 100011011 + 00010011 * 11101010
00000011 = 00100101 * 100011011 + 01100010 * 11101010
00000001 = 01000101 * 100011011 + 11010111 * 11101010
00000000 = 11101010 * 100011011 + 100011011 * 11101010

a-1(x) = x^7 + x^6 + x^4 + x^2 + x + 1 = 11010111 = 0xd7

The calculation of 0xea-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     1
           1 1 0 0 0 1 1 1      1     1     1
           1 1 1 0 0 0 1 1      1     0     1
           1 1 1 1 0 0 0 1      0     0     0
SBOX(ea) = 1 1 1 1 1 0 0 0   *  1  +  0  =  0
           0 1 1 1 1 1 0 0      0     1     0
           0 0 1 1 1 1 1 0      1     1     0
           0 0 0 1 1 1 1 1      1     0     1


SBOX(ea) = 10000111 = 87

For more information see FIPS 197.



Implemented by bachph [at] philba [dot] com