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, K_{0}), K_{1}), K_{2}), K_{3}), K_{4}), K_{5}), K_{6}), K_{7}),

where K_{o}, K_{1},…, Κ_{7} 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?

Recall that for a block cipher, a key schedule algorithm determines the subkey for each round, based on the key K. Let K = (fcofci&2 · · · ^55) be a 56-bit DES key.

a. List the 48 bits for each of the 16 DES subkeys K\, K_{i}, ■ ■ ■, Kie, in terms of the key bits fcj.

b. Make a table that contains the number of subkeys in which each key bit k_{i} is used.

c. Can you design a DES key schedule algorithm in which each key bit is used an equal number of times?

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