1. (a) List the field elements of Z2[X] (mod X3+X+1), i.e., all polynomials over Z2[X] of degree ≤ 2.
(b) Construct the multiplication table for Z2[X] (mod X3 + X + 1). Make sure to label the rows and columns with the field elements from part (a). Also make sure that all of the entries in the table are listed in part (a).
2. Compute the output of the AES S-box on input 10110010 by working through the mathematical definition of the S-box. That is, view this input an element of GF(28), compute the inverse of this field element using the extended Euclidean algorithm, view this element as a bit vector, multiply this vector by the matrix on page 103, and add vector (1,1,0,0,0,1,1,0). View the resulting vector as a byte. This is the output of the S-box. Give all your calculations.