Calculation of 0xae
m(x) = 0x11b = 100011011 = x^8 + x^4 + x^3 + x + 1
a(x) = 0xae = 10101110 = x^7 + x^5 + x^3 + x^2 + x
m(x) = (x) * a(x) + (x^6 + x^2 + x + 1)
Calculation of 0xae-1 in the finite field GF(28)01000111 = 00000001 * 100011011 + 00000010 * 10101110
00100000 = 00000010 * 100011011 + 00000101 * 10101110
00000111 = 00000101 * 100011011 + 00001000 * 10101110
00000011 = 00111011 * 100011011 + 01101101 * 10101110
00000001 = 01110011 * 100011011 +
11010010 * 10101110
00000000 = 10101110 * 100011011 + 100011011 * 10101110
a
-1(x) = x^7 + x^6 + x^4 + x = 11010010 = 0xd2
The calculation of 0xae
-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 0
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(ae) = 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 1 1 1
0 0 0 1 1 1 1 1 1 0 1
SBOX(ae) = 11100100 = e4
For more information see
FIPS 197.
Implemented by bachph [at] philba [dot] com