This problem deals with the AES$-128$ block cipher.

a$)$ Assume that the first column of the input to the InvMixColumn step is $S_{i,0}=(B4,52,E0,AE{)}_{16},$

find the $3$rd element of the corresponding column of the output state of the InvMixColumn step.

b$)$ Given the input $S_{2,1}=(7A{)}_{16},$ find InvSubByte $(S_{2,1}).$

c$)$ Assume that round key $6(k_6)$ is $0$F $71$ AF $15$ C$947$ D$90$C B$7$ E$859$ D$67$F $67$ AD$){?}_{16},$ find

the round keys for round $5(k_5)$ and round $7(k_7).$