3.4 Consider a block encryption algorithm that encrypts blocks of length n, and let N = 2n. Say we have t plaintext-ciphertext pairs Pi, Ci = E(K, Pi), where we assume that the key K selects one of the N! possible mappings. Imagine that we wish to find K by exhaustive search. We could generate key K′ and test whether Ci = E(K′, Pi) for 1 . i . t. If K′ encrypts each Pi to its proper Ci, then we have evidence that K = K′. However, it may be the case that the mappings E(K, #) and E(K′, #) exactly agree on the t plaintext-cipher text pairs Pi, Ci and agree on no other pairs. a. What is the probability that E(K, #) and E(K′, #) are in fact distinct mappings? b. What is the probability that E(K, #) and E(K′, #) agree on another t′ plaintext- ciphertext pairs where 0 . t′ . N - t? | |
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