Verify the rst two elements in the SECOND column of MixColumn result. (25 points) (Show intermediate steps clearly. You do not receive any credit for just writing down the answer) Q4: In MixColumns transformation, each byte of a column is mapped into a new value that is a function of all four bytes in that column. The transformation can be defined by the following matrix multiplication on State. We assume Sij 15 the element in the input State and s'ij is the element in the output State. 02 03 01 01 $0.0 $0,1 $0.2 So.3 50.0 50,1 50,2 503 $1,3 01 02 03 01 $1,0 $1,1 $1,2 $1,3 $10 $1,1 $12 = 01 01 02 03 $2.0 $2,1 $2.2 $2.3 $2.0 $2,1 52,2 523 03 01 01 02 $3,0 53,1 $3,3 $30 $3,1 53,2 53,3 The MixColumns transformation on a single column of State can be expressed as So, i = (2 . 50, ; ) ( 3 . 51, ; ) $ $2, ; # $3, j s'1, i = so, ; @ (2 . $1,; ) @ ( 3 . $2,j ) @ $3, i 52, ; = So , ; @ $1,i + ( 2 . $2, ; ) + ( 3 . 53 , ; ) 53, j = ( 3 . 50, ; ) + $1, ; + $2, i + ( 2 . 53, 1 ) Given the following example of MixColumns, the left state is MixColumns input and right is MixColumns output