Calculation of 0xac
m(x) = 0x11b = 100011011 = x^8 + x^4 + x^3 + x + 1
a(x) = 0xac = 10101100 = x^7 + x^5 + x^3 + x^2
m(x) = (x) * a(x) + (x^6 + x + 1)
Calculation of 0xac-1 in the finite field GF(28)01000011 = 00000001 * 100011011 + 00000010 * 10101100
00101010 = 00000010 * 100011011 + 00000101 * 10101100
00010111 = 00000101 * 100011011 + 00001000 * 10101100
00000100 = 00001000 * 100011011 + 00010101 * 10101100
00000011 = 00101101 * 100011011 + 01001001 * 10101100
00000001 = 01111111 * 100011011 +
11001110 * 10101100
00000000 = 10101100 * 100011011 + 100011011 * 10101100
a
-1(x) = x^7 + x^6 + x^3 + x^2 + x = 11001110 = 0xce
The calculation of 0xac
-1 is made with the
Extended Euclidean algorithm. Instead of normal division and multiplication you need to use Polynomialdivision and Polynomialmultiplication.
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 1 0 0
1 1 1 1 0 0 0 1 1 0 0
SBOX(ac) = 1 1 1 1 1 0 0 0 * 0 + 0 = 1
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(ac) = 10010001 = 91
For more information see
FIPS 197.
Implemented by bachph [at] philba [dot] com