@incollection{eprints1243,
       booktitle = {Foundations of Software Science and Computational Structures},
          editor = {Martin Hoffman},
          author = {Michele Boreale and Francesca Pampaloni and Michela Paolini},
       publisher = {Springer},
            note = {Proceedings of the 14th International Conference, FOSSACS 2011, Held as Part of the Joint European Conferences on Theory and Practice of Software, ETAPS 2011, Saarbr{\"u}cken, Germany, March 26?April 3, 2011},
            year = {2011},
           title = {Asymptotic information leakage under one-try attacks},
          series = {Lecture Notes in Computer Science},
           pages = {396--410},
          number = {6604},
          volume = {6604},
        keywords = {Security; quantitative information leakage; information theory; Bayes risk; hidden Markov models },
        abstract = {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.},
             url = {http://eprints.imtlucca.it/1243/}
}