Asymptotic information leakage under one-try attacks

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 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.

Quantitative Information Flow under Generic Leakage Functions and Adaptive Adversaries

“…The attacker is in a position to ask a source, perhaps the hospital db, queries concerning non sensitive information (ZIP code, age and discharge date) of any individual, including JD, and compare the answers with the table's entries. 5 This situation can be modeled quite simply as an action-based mechanism S, as follows. We pose: Act = {ZIP, Age, Date}; X = {1, .…”

“…Like in the static case, this dynamic g-leakage does not lend itself to be recast in the present framework. A dynamic approach is also at the core of a model in [5] based on Hidden Markov Models, where the observed system evolves over time, although the secret is fixed.…”

“…Quantitative Information Flow (qif) is a well-established approach to confidentiality analysis: the basic idea is measuring how much information flows from sensitive to observable data, relying on tools from Information Theory [14,3,12,32,11,4,27,5,6].…”

Searching secrets rationally

“…[12,11,3,30,4,5,21] and references therein. In the last few years, various extensions of the basic model have been considered: to mention but a few, [6] considers the case of one-try (min-entropy) attacks under repeated observations, while the worst-vs. average-case dimension is examined in [9]. Especially relevant to the present paper is the issue of partial secret disclosure [7] and, more generally, of leakage characterization in terms of adversary's (generic) gain, or g-leakage [1].…”

Foundations of Quantitative Information Flow: Channels, Cascades, and the Information Order

“…Boreale et al [BPP11] proved that ML(C (n) ) converges exponentially quickly to the logarithm of the number of distinct rows in C. (Intuitively, distinct rows of the channel matrix can be distinguished by repeatedly sampling the output.) More precisely, their Theorem 1 restricted to the case of a uniform prior (which realizes min-capacity) can be restated in the following form:…”