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Calculation of 0x60

m(x) = 0x11b = 100011011 = x^8 + x^4 + x^3 + x + 1
a(x) =   0x60 =  01100000 = x^6 + x^5
m(x) = (x^2 + x + 1) * a(x) + (x^5 + x^4 + x^3 + x + 1)

Calculation of 0x60-1 in the finite field GF(28)

00111011 = 00000001 * 100011011 + 00000111 * 1100000
00010110 = 00000010 * 100011011 + 00001111 * 1100000
00000001 = 00000111 * 100011011 + 00010110 * 1100000
00000000 = 01100000 * 100011011 + 100011011 * 1100000

a-1(x) = x^4 + x^2 + x = 00010110 = 0x16

The calculation of 0x60-1 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      1     0     0
           1 1 1 1 0 0 0 1      0     0     0
SBOX(60) = 1 1 1 1 1 0 0 0   *  1  +  0  =  1
           0 1 1 1 1 1 0 0      0     1     0
           0 0 1 1 1 1 1 0      0     1     1
           0 0 0 1 1 1 1 1      0     0     1


SBOX(60) = 11010000 = d0

For more information see FIPS 197.



Implemented by bachph [at] philba [dot] com