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 Ko, 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?
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\, Ki, ■ ■ ■, Kie, in terms of the key bits fcj.
b. Make a table that contains the number of subkeys in which each key bit ki 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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