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We modify the problem studied by Merhav and Arikan (see IEEE Trans. Inform. Theory, vol.45, no.6, p.1860-6, 1999) of discrete memoryless source encrypted messages guessing by wiretapper within given distortion level Δ in the case of Shannon cipher system. The security of the system is measured by the expected number of guesses of a wiretapper needed for the reconstruction of the source messages on the base of cryptograms. The main modification is consideration of the distortion and reliability criteria and of possibility to limit the number of guesses.