Calculation of 0x36
m(x) = 0x11b = 100011011 = x^8 + x^4 + x^3 + x + 1
a(x) = 0x36 = 00110110 = x^5 + x^4 + x^2 + x
m(x) = (x^3 + x^2 + x) * a(x) + (x^4 + x^3 + x^2 + x + 1)
Calculation of 0x36-1 in the finite field GF(28)00011111 = 00000001 * 100011011 + 00001110 * 110110
00001000 = 00000010 * 100011011 + 00011101 * 110110
00000111 = 00000111 * 100011011 + 00101001 * 110110
00000001 = 00001011 * 100011011 +
01100110 * 110110
00000000 = 00110110 * 100011011 + 100011011 * 110110
a
-1(x) = x^6 + x^5 + x^2 + x = 01100110 = 0x66
The calculation of 0x36
-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 1 0 1
1 1 1 1 0 0 0 1 0 0 0
SBOX(36) = 1 1 1 1 1 0 0 0 * 0 + 0 = 0
0 1 1 1 1 1 0 0 1 1 0
0 0 1 1 1 1 1 0 1 1 0
0 0 0 1 1 1 1 1 0 0 0
SBOX(36) = 00000101 = 5
For more information see
FIPS 197.
Implemented by bachph [at] philba [dot] com