Calculation of 0x32
m(x) = 0x11b = 100011011 = x^8 + x^4 + x^3 + x + 1
a(x) = 0x32 = 00110010 = x^5 + x^4 + x
m(x) = (x^3 + x^2 + x + 1) * a(x) + (x^4 + x^2 + 1)
Calculation of 0x32-1 in the finite field GF(28)00010101 = 00000001 * 100011011 + 00001111 * 110010
00001101 = 00000011 * 100011011 + 00010000 * 110010
00000010 = 00000100 * 100011011 + 00111111 * 110010
00000001 = 00011011 * 100011011 +
10010010 * 110010
00000000 = 00110010 * 100011011 + 100011011 * 110010
a
-1(x) = x^7 + x^4 + x = 10010010 = 0x92
The calculation of 0x32
-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 1
1 1 1 0 0 0 1 1 0 0 0
1 1 1 1 0 0 0 1 0 0 0
SBOX(32) = 1 1 1 1 1 0 0 0 * 1 + 0 = 0
0 1 1 1 1 1 0 0 0 1 1
0 0 1 1 1 1 1 0 0 1 0
0 0 0 1 1 1 1 1 1 0 0
SBOX(32) = 00100011 = 23
For more information see
FIPS 197.
Implemented by bachph [at] philba [dot] com