Calculation of 0xaf
m(x) = 0x11b = 100011011 = x^8 + x^4 + x^3 + x + 1
a(x) = 0xaf = 10101111 = x^7 + x^5 + x^3 + x^2 + x + 1
m(x) = (x) * a(x) + (x^6 + x^2 + 1)
Calculation of 0xaf-1 in the finite field GF(28)01000101 = 00000001 * 100011011 + 00000010 * 10101111
00100101 = 00000010 * 100011011 + 00000101 * 10101111
00001111 = 00000101 * 100011011 + 00001000 * 10101111
00000111 = 00011100 * 100011011 + 00110101 * 10101111
00000001 = 00111101 * 100011011 +
01100010 * 10101111
00000000 = 10101111 * 100011011 + 100011011 * 10101111
a
-1(x) = x^6 + x^5 + x = 01100010 = 0x62
The calculation of 0xaf
-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 1 1 0
1 1 1 0 0 0 1 1 0 0 0
1 1 1 1 0 0 0 1 0 0 1
SBOX(af) = 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 1 1 1
0 0 0 1 1 1 1 1 0 0 0
SBOX(af) = 01111001 = 79
For more information see
FIPS 197.
Implemented by bachph [at] philba [dot] com