Calculation of 0x2f
m(x) = 0x11b = 100011011 = x^8 + x^4 + x^3 + x + 1
a(x) = 0x2f = 00101111 = x^5 + x^3 + x^2 + x + 1
m(x) = (x^3 + x + 1) * a(x) + (x^4 + x)
Calculation of 0x2f-1 in the finite field GF(28)00010010 = 00000001 * 100011011 + 00001011 * 101111
00001011 = 00000010 * 100011011 + 00010111 * 101111
00000100 = 00000101 * 100011011 + 00100101 * 101111
00000011 = 00001000 * 100011011 + 01011101 * 101111
00000001 = 00011101 * 100011011 +
11000010 * 101111
00000000 = 00101111 * 100011011 + 100011011 * 101111
a
-1(x) = x^7 + x^6 + x = 11000010 = 0xc2
The calculation of 0x2f
-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 0 0 1
1 1 1 1 0 0 0 1 0 0 0
SBOX(2f) = 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 0
SBOX(2f) = 00010101 = 15
For more information see
FIPS 197.
Implemented by bachph [at] philba [dot] com