Suppose that Alice has a secure block cipher, but the cipher only uses an 8-bit key. To make this cipher "more secure," Alice generates a random 64-bit key K, and iterates the cipher eight times, that is, she encrypts the plaintext P according to the rule

C = E(E(E(E(E(E(E(E(P, K0), Kx), K2), K3), KA), K5), K6), K7),

where Ko, K1,..., are the bytes of the 64-bit key K.

a. Assuming a ciphertext-only attack, how much work is required to break this encryption scheme? Show the work or formulas used to obtain the answer.