Consider a block encryption algorithm that encrypts blocks of length , and let N = 2n Say we have plaintext–cipher text pairs Pi, Ci = E(K, Pi) where we assume that the= key selects one of the N!  possible mappings. Imagine that we wish to find 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 plaintext– cipher text pairs , and agree on no other 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– cipher text pairs where 0≤ t’≤ N - t?