On the Shannon cipher system with distortion and guessing wiretapper eavesdropping through a noisy channel

We investigated the Shannon cipher system with discrete memoryless source and noisy channel to the wiretapper. The wiretapper gains the noisy version of the cryptogram and tries to guess encrypted plaintext given some exactness. In each step of sequential guesses the wiretapper have testing mechanism. The security level of the encryption system is measured by the expected number of wiretapper's guesses. The upper and lower bounds are obtained for the guessing rate.