Bounds on entropy in a guessing game

We consider the guessing problem proposed by Massey (see Proc. Int. Symp. Information Theory, p.204, 1994) of a cryptanalyst that wants to break a ciphertext with a brute-force attack. The best strategy he can use is to try out all possible keys, one at time in order of decreasing probability, after narrowing the possibilities by some cryptanalysis. In this correspondence we provide both upper and lower bounds on the entropy of the probability distribution on the secret keys in terms of the number of secret keys and of the average number of trials of the cryptanalyst.