Calculation of 0x76
m(x) = 0x11b = 100011011 = x^8 + x^4 + x^3 + x + 1
a(x) = 0x76 = 01110110 = x^6 + x^5 + x^4 + x^2 + x
m(x) = (x^2 + x) * a(x) + (x^5 + x^3 + x^2 + x + 1)
Calculation of 0x76-1 in the finite field GF(28)00101111 = 00000001 * 100011011 + 00000110 * 1110110
00000111 = 00000011 * 100011011 + 00001011 * 1110110
00000010 = 00010000 * 100011011 + 01101111 * 1110110
00000001 = 00110011 * 100011011 +
10111010 * 1110110
00000000 = 01110110 * 100011011 + 100011011 * 1110110
a
-1(x) = x^7 + x^5 + x^4 + x^3 + x = 10111010 = 0xba
The calculation of 0x76
-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 0
1 1 1 1 0 0 0 1 1 0 1
SBOX(76) = 1 1 1 1 1 0 0 0 * 1 + 0 = 1
0 1 1 1 1 1 0 0 1 1 1
0 0 1 1 1 1 1 0 0 1 0
0 0 0 1 1 1 1 1 1 0 0
SBOX(76) = 00111000 = 38
For more information see
FIPS 197.
Implemented by bachph [at] philba [dot] com