Calculation of 0xdf
m(x) = 0x11b = 100011011 = x^8 + x^4 + x^3 + x + 1
a(x) = 0xdf = 11011111 = x^7 + x^6 + x^4 + x^3 + x^2 + x + 1
m(x) = (x + 1) * a(x) + (x^6 + x^5 + x^4 + x^3 + x)
Calculation of 0xdf-1 in the finite field GF(28)01111010 = 00000001 * 100011011 + 00000011 * 11011111
00101011 = 00000010 * 100011011 + 00000111 * 11011111
00000111 = 00000111 * 100011011 + 00001010 * 11011111
00000001 = 00101000 * 100011011 +
01101011 * 11011111
00000000 = 11011111 * 100011011 + 100011011 * 11011111
a
-1(x) = x^6 + x^5 + x^3 + x + 1 = 01101011 = 0x6b
The calculation of 0xdf
-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 0
1 1 0 0 0 1 1 1 1 1 1
1 1 1 0 0 0 1 1 0 0 1
1 1 1 1 0 0 0 1 1 0 1
SBOX(df) = 1 1 1 1 1 0 0 0 * 0 + 0 = 1
0 1 1 1 1 1 0 0 1 1 0
0 0 1 1 1 1 1 0 1 1 0
0 0 0 1 1 1 1 1 0 0 1
SBOX(df) = 10011110 = 9e
For more information see
FIPS 197.
Implemented by bachph [at] philba [dot] com