Calculation of 0x2a
m(x) = 0x11b = 100011011 = x^8 + x^4 + x^3 + x + 1
a(x) = 0x2a = 00101010 = x^5 + x^3 + x
m(x) = (x^3 + x) * a(x) + (x^4 + x^3 + x^2 + x + 1)
Calculation of 0x2a-1 in the finite field GF(28)00011111 = 00000001 * 100011011 + 00001010 * 101010
00001011 = 00000011 * 100011011 + 00011111 * 101010
00000010 = 00000100 * 100011011 + 00101011 * 101010
00000001 = 00010111 * 100011011 +
10011000 * 101010
00000000 = 00101010 * 100011011 + 100011011 * 101010
a
-1(x) = x^7 + x^4 + x^3 = 10011000 = 0x98
The calculation of 0x2a
-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 0 0 1
1 1 1 1 0 0 0 1 1 0 0
SBOX(2a) = 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 1
SBOX(2a) = 11100101 = e5
For more information see
FIPS 197.
Implemented by bachph [at] philba [dot] com