Calculation of 0xc1
m(x) = 0x11b = 100011011 = x^8 + x^4 + x^3 + x + 1
a(x) = 0xc1 = 11000001 = x^7 + x^6 + 1
m(x) = (x + 1) * a(x) + (x^6 + x^4 + x^3)
Calculation of 0xc1-1 in the finite field GF(28)01011000 = 00000001 * 100011011 + 00000011 * 11000001
00101001 = 00000011 * 100011011 + 00000100 * 11000001
00001010 = 00000111 * 100011011 + 00001011 * 11000001
00000001 = 00011111 * 100011011 +
00101000 * 11000001
00000000 = 11000001 * 100011011 + 100011011 * 11000001
a
-1(x) = x^5 + x^3 = 00101000 = 0x28
The calculation of 0xc1
-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 0 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(c1) = 1 1 1 1 1 0 0 0 * 0 + 0 = 1
0 1 1 1 1 1 0 0 1 1 1
0 0 1 1 1 1 1 0 0 1 1
0 0 0 1 1 1 1 1 0 0 0
SBOX(c1) = 01111000 = 78
For more information see
FIPS 197.
Implemented by bachph [at] philba [dot] com