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Asymptotic information leakage under one-try attacks†

Published online by Cambridge University Press:  10 November 2014

MICHELE BOREALE ,
FRANCESCA PAMPALONI  and
MICHELA PAOLINI
MICHELE BOREALE*
Affiliation:
Università di Firenze – Dipartimento di Statistica, Informatica, Applicazioni, Viale Morgagni 65, 50134 Firenze, Italy Email: [email protected]
FRANCESCA PAMPALONI
Affiliation:
IMT Lucca Institute for Advanced Studies - Piazza S. Ponziano 6, 55100 Lucca, Italy Email: [email protected], [email protected]
MICHELA PAOLINI
Affiliation:
IMT Lucca Institute for Advanced Studies - Piazza S. Ponziano 6, 55100 Lucca, Italy Email: [email protected], [email protected]
*
Corresponding author: Michele Boreale, Università di Firenze, Dipartimento di Sistemi e Informatica, Viale Morgagni 65, I-50134 Firenze, Italy. E-mail: [email protected].
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Abstract

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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 an a priori 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 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.

Type
Special Issue: Quantitative Information Flow
Information
Mathematical Structures in Computer Science , Volume 25 , Issue 2: Quantitative Information Flow , February 2015 , pp. 292 - 319
Copyright
Copyright © Cambridge University Press 2014 

Footnotes

†

Extended version of Boreale et al. (2011). Work partially supported by the eu project Ascens under the fet open initiative in fp7.

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