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Calculation of 0x88

m(x) = 0x11b = 100011011 = x^8 + x^4 + x^3 + x + 1
a(x) = 0x88 =  10001000 = x^7 + x^3
m(x) = (x) * a(x) + (x^3 + x + 1)

Calculation of 0x88-1 in the finite field GF(28)

00001011 = 00000001 * 100011011 + 00000010 * 10001000
00000010 = 00010110 * 100011011 + 00101101 * 10001000
00000001 = 01001111 * 100011011 + 10011011 * 10001000
00000000 = 10001000 * 100011011 + 100011011 * 10001000

a-1(x) = x^7 + x^4 + x^3 + x + 1 = 10011011 = 0x9b

The calculation of 0x88-1 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 0
1 1 1 0 0 0 1 1 0 0 1
1 1 1 1 0 0 0 1 1 0 0
SBOX(88) = 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 1
0 0 0 1 1 1 1 1 1 0 1


SBOX(88) = 11000100 = c4

For more information see FIPS 197.



Implemented by bachph [at] philba [dot] com