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...

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), K₁), K₂), K₃), K₄), K₅), K₆), K₇),

where K_o, K₁,..., Κ₇
are the bytes of the 64-bit key K.

a. Assuming known plaintext is available, how much work is required to determine the key K1

b. Assuming a ciphertext-only attack, how much work is required to break this encryption scheme?