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.

A one-restricted key agreement scheme is a method by which initially a trusted authority distributes private individual pieces of information to a set of users. Later, each member of any group of users of a given size, referred to as a conference, can compute a common key by exchanging messages over a broadcast channel all users have access to. Such schemes can be used to establish only one common key. In this paper we analyse τ-restricted key agreement schemes. Such schemes allow the computation of up to rτ common keys for τ distinct conferences. For certain values of the parameters the scheme that we propose distributes less information than the trivial one obtained by considering τ copies of a one-restricted scheme.

/spl acute/A secret sharing scheme permits a secret to be shared among participants in such a way that only qualified subsets of participants can recover the secret, but any nonqualified subset has absolutely no information on the secret. We derive new limitations on the information rate of secret sharing schemes, that measures how much information is being distributed as shares as compared to the size of the secret key, and the average information rate, that is the ratio between the secret size and the arithmetic mean of the size of the shares. By applying the substitution technique, we are able to construct many new examples of access structures where the information rate is bounded away from 1. The substitution technique is a method used to obtain a new access structure by replacing a participant in a previous structure with a new access structure.>