Calculation of 0x26
m(x) = 0x11b = 100011011 = x^8 + x^4 + x^3 + x + 1
a(x) = 0x26 = 00100110 = x^5 + x^2 + x
m(x) = (x^3 + 1) * a(x) + (x^3 + x^2 + 1)
Calculation of 0x26-1 in the finite field GF(28)00001101 = 00000001 * 100011011 + 00001001 * 100110
00000101 = 00000111 * 100011011 + 00111110 * 100110
00000010 = 00001000 * 100011011 + 01001011 * 100110
00000001 = 00010111 * 100011011 +
10101000 * 100110
00000000 = 00100110 * 100011011 + 100011011 * 100110
a
-1(x) = x^7 + x^5 + x^3 = 10101000 = 0xa8
The calculation of 0x26
-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 1
1 1 1 1 0 0 0 1 1 0 0
SBOX(26) = 1 1 1 1 1 0 0 0 * 0 + 0 = 1
0 1 1 1 1 1 0 0 1 1 1
0 0 1 1 1 1 1 0 0 1 1
0 0 0 1 1 1 1 1 1 0 1
SBOX(26) = 11110111 = f7
For more information see
FIPS 197.
Implemented by bachph [at] philba [dot] com