Calculation of 0xb4
m(x) = 0x11b = 100011011 = x^8 + x^4 + x^3 + x + 1
a(x) = 0xb4 = 10110100 = x^7 + x^5 + x^4 + x^2
m(x) = (x) * a(x) + (x^6 + x^5 + x^4 + x + 1)
Calculation of 0xb4-1 in the finite field GF(28)01110011 = 00000001 * 100011011 + 00000010 * 10110100
00100001 = 00000011 * 100011011 + 00000111 * 10110100
00010000 = 00000100 * 100011011 + 00001011 * 10110100
00000001 = 00001011 * 100011011 +
00010001 * 10110100
00000000 = 10110100 * 100011011 + 100011011 * 10110100
a
-1(x) = x^4 + 1 = 00010001 = 0x11
The calculation of 0xb4
-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 1 1 1
1 1 0 0 0 1 1 1 0 1 0
1 1 1 0 0 0 1 1 0 0 1
1 1 1 1 0 0 0 1 0 0 1
SBOX(b4) = 1 1 1 1 1 0 0 0 * 1 + 0 = 0
0 1 1 1 1 1 0 0 0 1 0
0 0 1 1 1 1 1 0 0 1 0
0 0 0 1 1 1 1 1 0 0 1
SBOX(b4) = 10001101 = 8d
For more information see
FIPS 197.
Implemented by bachph [at] philba [dot] com