Abstract. We put forward a general model intended for assessment of system security against passive eavesdroppers, both quantitatively (how much information is leaked) and qualitatively (what properties are leaked). To this purpose, we extend information hiding systems (ihs), a model where the secret-observable relation is represented as a noisy channel, with views: basically, partitions of the state-space. Given a view W and n independent observations of the system, one is interested in the probability that a Bayesian adversary wrongly predicts the class of W the underlying secret belongs to. We offer results that allow one to easily characterise the behaviour of this error probability as a function of the number of observations, in terms of the channel matrices defining the ihs and the view W. In particular, we provide expressions for the limit value as n → ∞, show by tight bounds that convergence is exponential, and also characterise the rate of convergence to predefined error thresholds. We then show a few instances of statistical attacks that can be assessed by a direct application of our model: attacks against modular exponentiation that exploit timing leaks, against anonymity in mix-nets and against privacy in sparse datasets.

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.

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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.

Abstract. In a variety of contexts, randomization is regarded as an effective technique to conceal sensitive information. We model randomization mechanisms as information-theoretic channels. Our starting point is a semantic notion of security that expresses absence of any privacy breach above a given level of seriousness , irrespective of any background information, represented as a prior probability on the secret inputs. We first examine this notion according to two dimensions: worst vs. average case, single vs. repeated observations. In each case, we characterize the security level achievable by a mechanism in a simple fashion that only depends on the channel matrix, and specifically on certain measures of "distance" between its rows, like norm-1 distance and Chernoff Information. We next clarify the relation between our worst-case security notion and differential privacy (dp): we show that, while the former is in general stronger, the two coincide if one confines to background information that can be factorised into the product of independent priors over individuals. We finally turn our attention to expected utility, in the sense of Ghosh et al., in the case of repeated independent observations. We characterize the exponential growth rate of any reasonable utility function. In the particular case the mechanism provides -dp, we study the relation of the utility rate with : we offer either exact expressions or upper-bounds for utility rate that apply to practically interesting cases, such as the (truncated) geometric mechanism.