3.3 Consider a block encryption algorithm that encrypts blocks of length n, and let N = 2 n . Say we have t plaintext-ciphertext pairs Pi, Ct = 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 C = 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-ciphertext 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? 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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