Calculation of 0x9f
m(x) = 0x11b = 100011011 = x^8 + x^4 + x^3 + x + 1
a(x) = 0x9f = 10011111 = x^7 + x^4 + x^3 + x^2 + x + 1
m(x) = (x) * a(x) + (x^5 + x^2 + 1)
Calculation of 0x9f-1 in the finite field GF(28)00100101 = 00000001 * 100011011 + 00000010 * 10011111
00001011 = 00000100 * 100011011 + 00001001 * 10011111
00000010 = 00010101 * 100011011 + 00101111 * 10011111
00000001 = 01000101 * 100011011 +
10011010 * 10011111
00000000 = 10011111 * 100011011 + 100011011 * 10011111
a
-1(x) = x^7 + x^4 + x^3 + x = 10011010 = 0x9a
The calculation of 0x9f
-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 1 0 1
SBOX(9f) = 1 1 1 1 1 0 0 0 * 1 + 0 = 1
0 1 1 1 1 1 0 0 0 1 0
0 0 1 1 1 1 1 0 0 1 1
0 0 0 1 1 1 1 1 1 0 1
SBOX(9f) = 11011011 = db
For more information see
FIPS 197.
Implemented by bachph [at] philba [dot] com