Calculation of 0x64
m(x) = 0x11b = 100011011 = x^8 + x^4 + x^3 + x + 1
a(x) = 0x64 = 01100100 = x^6 + x^5 + x^2
m(x) = (x^2 + x + 1) * a(x) + (x^5 + x^2 + x + 1)
Calculation of 0x64-1 in the finite field GF(28)00100111 = 00000001 * 100011011 + 00000111 * 1100100
00001101 = 00000011 * 100011011 + 00001000 * 1100100
00000100 = 00001000 * 100011011 + 00111111 * 1100100
00000001 = 00011011 * 100011011 +
01001001 * 1100100
00000000 = 01100100 * 100011011 + 100011011 * 1100100
a
-1(x) = x^6 + x^3 + 1 = 01001001 = 0x49
The calculation of 0x64
-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 0
1 1 1 1 0 0 0 1 1 0 0
SBOX(64) = 1 1 1 1 1 0 0 0 * 0 + 0 = 0
0 1 1 1 1 1 0 0 0 1 0
0 0 1 1 1 1 1 0 1 1 1
0 0 0 1 1 1 1 1 0 0 0
SBOX(64) = 01000011 = 43
For more information see
FIPS 197.
Implemented by bachph [at] philba [dot] com