Q4. (14 pts) For the Mix Column Transformation explained below on an example, provide calculations showing that actually, S30=ED. Irreducible polynomial used in AES is m(x)= x + x + x + x +1.Give necessary explanations. "The forward mix column transformation, called MixColumns, operates on each column individually. Each byte is mapped into a new value that is a function of all four bytes in the column. The transformation can be defined as the following matrix multiplication on State (Fig. 5.5b): 02 03 01 01 SOO 501 SO2 S03 soo S01 SO2 S03 01 02 03 01 510 S10 S11 S12 S13 S10 ' S12 S13 (5.3) 01 01 02 03 s20 521 522 523 S20 S21 S22 03 01 01 02 S30 331 332 333 S30 532 533 Each element in the product matrix is the sum of products of elements of one row and one column. In this case, multiplications and additions are performed in GF(24). The following is the example of MixColumns; 87 4D 97 40 A3 4C S11' S23' S31' F2 47 6E 4C 90 EC 37 D4 70 9F 46 E7 4A C3 94 E4 42 A6 8C D8 95 ED A5 A6 BC Q4. (14 pts) For the Mix Column Transformation explained below on an example, provide calculations showing that actually, S30=ED. Irreducible polynomial used in AES is m(x)= x + x + x + x +1.Give necessary explanations. "The forward mix column transformation, called MixColumns, operates on each column individually. Each byte is mapped into a new value that is a function of all four bytes in the column. The transformation can be defined as the following matrix multiplication on State (Fig. 5.5b): 02 03 01 01 SOO 501 SO2 S03 soo S01 SO2 S03 01 02 03 01 510 S10 S11 S12 S13 S10 ' S12 S13 (5.3) 01 01 02 03 s20 521 522 523 S20 S21 S22 03 01 01 02 S30 331 332 333 S30 532 533 Each element in the product matrix is the sum of products of elements of one row and one column. In this case, multiplications and additions are performed in GF(24). The following is the example of MixColumns; 87 4D 97 40 A3 4C S11' S23' S31' F2 47 6E 4C 90 EC 37 D4 70 9F 46 E7 4A C3 94 E4 42 A6 8C D8 95 ED A5 A6 BC