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Equivocation rate has been widely used as an information-theoretic measure ofsecurity after Shannon[10]. It simplifies problems by removing the effect ofatypical behavior from the system. In [9], however, Merhav and Arikanconsidered the alternative of using guessing exponent to analyze the Shannon'scipher system. Because guessing exponent captures the atypical behavior, thestrongest expressible notion of secrecy requires the more stringent conditionthat the size of the key, instead of its entropy rate, to be equal to the sizeof the message. The relationship between equivocation and guessing exponent arealso investigated in [6][7] but it is unclear which is a better measure, andwhether there is a unifying measure of security.  Instead of using equivocation rate or guessing exponent, we study the wiretapchannel in [2] using the success exponent, defined as the exponent of awiretapper successfully learn the secret after making an exponential number ofguesses to a sequential verifier that gives yes/no answer to each guess. Byextending the coding scheme in [2][5] and the converse proof in [4] with thenew Overlap Lemma 5.2, we obtain a tradeoff between secrecy and reliabilityexpressed in terms of lower bounds on the error and success exponents ofauthorized and respectively unauthorized decoding of the transmitted messages.  From this, we obtain an inner bound to the region of strongly achievablepublic, private and guessing rate triples for which the exponents are strictlypositive. The closure of this region is equivalent to the closure of the regionin Theorem 1 of [2] when we treat equivocation rate as the guessing rate.However, it is unclear if the inner bound is tight.

Success Exponent of Wiretapper: A Tradeoff between Secrecy and Reliability