A young engineer designs a simple cipher based on Shannon's concept of a "product cipher". The ciphertext output, y, is generated by applying an affine cipher to the plaintext, x, to produce an intermediate result, z, and then applying another affine cipher to the immediate result, z, to produce the ciphertext output, y. This is represented mathematically as follows: y=a2z + b mod n z = aix + b mod n The pairs (a, bi) and (a2, b2) form the key. (a) Determine an expression for the number of distinct mappings from plaintext to ciphertext in terms of n. HINT: It could be that the cipher can be simplified from its two step process. (b) Comment on the usefulness of the approach used in the cipher.