Question

Suppose we apply the Mix Columns operation to a *column* vector [0x63,0x62,0x61,0x60]T

(given with bytes in hex).

What are the entries of the resulting column (in decimal)?

Answer 1

The input array is called the state array - [0x63,0x62,0x61,0x60]^T.

To do the Mix Column operation, we need to do the following:

Note that all multiplications are performed in GF(2⁸) and the additions are just XOR. The resulting array is a four element column vector.

First Element=(02*0x63)+(03*0x62)+(01*0x61)+(01*0x60)

=11000110+100100110+1100001+1100000

=1010101101(decimal=685)

Second Element=(01*0x63)+(02*0x62)+(03*0x61)+(01*0x60)

=1100011+11000100+100100011+1100000

=1010101010(decimal=682)

Third Element=(01*0x63)+(01*0x62)+(02*0x61)+(03*0x60)

=1100011+1100010+11000010+100100000

=1010100111(decimal=679)

Fourth Element=(03*0x63)+(01*0x62)+(01*0x61)+(02*0x60)

=100101001+1100010+1100001+11000000

=1010101100(decimal=684)

So the resulting column is [685,682,679,684]