4. ** The core nonlinear part of the permutations in AES is the S-box, which is the 8-bit inverse function. Let a simplified AES 4-bit S-box, denoted by(x) (a) Let GF(24) be defined by the primitive polynomial a*++1 and a be a root. Compute the inverse function in GF(24), i.e., compute a and list them as a table. for ali-0,1, 14 (b) The mixcolumn operation is given by 1+ 1 1+ 1+ 1+ Compute the inverse matrix of L. (Note. The computation of the inverse of a matrix is the same as introduced in linear algebra, just the computation is done in GF(21).) (c) Assume that the 16-bit message P and 16-bit key K are given by P (0001. 0000. 1111, 1010) = (rn0.1n1.1n2.113) (0000. 0000. 1001. 1001)-ko. K1. k2-63) K Assume that the ciphertext is computed as C L (moko), (miki)-1, (m2 + k2)-1, (m3 k3)-) where T is the transpose of the vector. Compute the ciphertext of P 4. ** The core nonlinear part of the permutations in AES is the S-box, which is the 8-bit inverse function. Let a simplified AES 4-bit S-box, denoted by(x) (a) Let GF(24) be defined by the primitive polynomial a*++1 and a be a root. Compute the inverse function in GF(24), i.e., compute a and list them as a table. for ali-0,1, 14 (b) The mixcolumn operation is given by 1+ 1 1+ 1+ 1+ Compute the inverse matrix of L. (Note. The computation of the inverse of a matrix is the same as introduced in linear algebra, just the computation is done in GF(21).) (c) Assume that the 16-bit message P and 16-bit key K are given by P (0001. 0000. 1111, 1010) = (rn0.1n1.1n2.113) (0000. 0000. 1001. 1001)-ko. K1. k2-63) K Assume that the ciphertext is computed as C L (moko), (miki)-1, (m2 + k2)-1, (m3 k3)-) where T is the transpose of the vector. Compute the ciphertext of P