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Asymptotic Information Leakage under One-Try Attacks

  • Michele Boreale
  • Francesca Pampaloni
  • Michela Paolini
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6604)

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.

Keywords

security quantitative information leakage information theory Bayes risk hidden Markov models 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Michele Boreale
    • 1
  • Francesca Pampaloni
    • 2
  • Michela Paolini
    • 2
  1. 1.Università di FirenzeItaly
  2. 2.IMTLuccaItaly

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