%0 Book Section
%A Boreale, Michele
%A Pampaloni, Francesca
%A Paolini, Michela
%B Foundations of Software Science and Computational Structures
%D 2011
%E Hoffman, Martin
%F eprints:1243
%I Springer
%K Security; quantitative information leakage; information theory; Bayes risk; hidden Markov models 
%N 6604
%P 396-410
%S Lecture Notes in Computer Science
%T Asymptotic information leakage under one-try attacks
%U http://eprints.imtlucca.it/1243/
%V 6604
%X We study the asymptotic behaviour of (a) information leakage and (b) adversary’s error probability in information hiding systems modelled as noisy channels. Specifically, we assume the attacker can make a single guess after observing n independent executions of the system, throughout which the secret information is kept fixed. We show that the asymptotic behaviour of quantities (a) and (b) can be determined in a simple way from the channel matrix. Moreover, simple and tight bounds on them as functions of n show that the convergence is exponential. We also discuss feasible methods to evaluate the rate of convergence. Our results cover both the Bayesian case, where a prior probability distribution on the secrets is assumed known to the attacker, and the maximum-likelihood case, where the attacker does not know such distribution. In the Bayesian case, we identify the distributions that maximize the leakage. We consider both the min-entropy setting studied by Smith and the additive form recently proposed by Braun et al., and show the two forms do agree asymptotically. Next, we extend these results to a more sophisticated eavesdropping scenario, where the attacker can perform a (noisy) observation at each state of the computation and the systems are modelled as hidden Markov models.
%Z Proceedings of the 14th International Conference, FOSSACS 2011, Held as Part of the Joint European Conferences on Theory and Practice of Software, ETAPS 2011, Saarbrücken, Germany, March 26–April 3, 2011