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The Shannon cipher system with discrete memoryless sources is considered. The wiretapper gains the cryptogram through the public noiseless channel and tries to guess the secret information which is related to the encrypted plaintext. It is assumed that at each step of sequential guesses the wiretapper has a testing mechanism to identify the secret message within the given distortion level. The security level of the encryption system is measured by the guessing rate which is the highest asymptotic exponential growth rat.