Calculation of 0x4e
m(x) = 0x11b = 100011011 = x^8 + x^4 + x^3 + x + 1
a(x) = 0x4e = 01001110 = x^6 + x^3 + x^2 + x
m(x) = (x^2) * a(x) + (x^5 + x + 1)
Calculation of 0x4e-1 in the finite field GF(28)00100011 = 00000001 * 100011011 + 00000100 * 1001110
00001000 = 00000010 * 100011011 + 00001001 * 1001110
00000011 = 00001001 * 100011011 + 00100000 * 1001110
00000001 = 00111101 * 100011011 +
11101001 * 1001110
00000000 = 01001110 * 100011011 + 100011011 * 1001110
a
-1(x) = x^7 + x^6 + x^5 + x^3 + 1 = 11101001 = 0xe9
The calculation of 0x4e
-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 0 1 1
1 1 1 0 0 0 1 1 0 0 1
1 1 1 1 0 0 0 1 1 0 1
SBOX(4e) = 1 1 1 1 1 0 0 0 * 0 + 0 = 0
0 1 1 1 1 1 0 0 1 1 1
0 0 1 1 1 1 1 0 1 1 0
0 0 0 1 1 1 1 1 1 0 0
SBOX(4e) = 00101111 = 2f
For more information see
FIPS 197.
Implemented by bachph [at] philba [dot] com