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In this paper we discuss the processes in the Shannon cipher system with discrete memoryless source and a guessing wiretapper. The wiretapper observes a cryptogram of Nvector of ciphered messages in the public channel and tries to guess successively the vector of messages within given distortion level ∆ and small probability of error less than exp{−NE} with positive reliability index E. The security of the system is measured by the expected number of guesses which wiretapper needs for the approximate reconstruction of the vector of source messages. The distortion, the reliability criteria and the possibility of upper limiting the number of guesses extend the approach studied by Merhav and Arikan. A single-letter characterization is given for the region of pairs (R L , R) (of the rate R L of the maximum number of guesses L(N) and the rate R of the average number of guesses) in dependence on key rate R K , distortion level ∆ and reliability E.

The procedure of many hypotheses logarithmically asymptotically optimal (LAO) testing for a model consisting of three or more independent objects is analyzed. It is supposed that M probability distributions are known and each object follows one of them independently of others. The matrix of asymptotic interdependencies (reliability-reliability functions) of all possible pairs of the error probability exponents (reliabilities) in optimal testing for this model is studied. This problem was introduced (and solved for the case of two objects and two given probability distributions) by Ahlswede and Haroutunian; it is a generalization of two hypotheses LAO testing problem for one object investigated