Calculation of 0xa0
m(x) = 0x11b = 100011011 = x^8 + x^4 + x^3 + x + 1
a(x) = 0xa0 = 10100000 = x^7 + x^5
m(x) = (x) * a(x) + (x^6 + x^4 + x^3 + x + 1)
Calculation of 0xa0-1 in the finite field GF(28)01011011 = 00000001 * 100011011 + 00000010 * 10100000
00010110 = 00000010 * 100011011 + 00000101 * 10100000
00000011 = 00001001 * 100011011 + 00010110 * 10100000
00000001 = 01100111 * 100011011 +
11111011 * 10100000
00000000 = 10100000 * 100011011 + 100011011 * 10100000
a
-1(x) = x^7 + x^6 + x^5 + x^4 + x^3 + x + 1 = 11111011 = 0xfb
The calculation of 0xa0
-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 1 1 0
1 1 0 0 0 1 1 1 1 1 0
1 1 1 0 0 0 1 1 0 0 0
1 1 1 1 0 0 0 1 1 0 0
SBOX(a0) = 1 1 1 1 1 0 0 0 * 1 + 0 = 0
0 1 1 1 1 1 0 0 1 1 1
0 0 1 1 1 1 1 0 1 1 1
0 0 0 1 1 1 1 1 1 0 1
SBOX(a0) = 11100000 = e0
For more information see
FIPS 197.
Implemented by bachph [at] philba [dot] com