In information-hiding, an adversary that tries to infer the secret information has a higher probability of success if it knows the distribution on the secrets. We show that if the system leaks probabilistically some information about the secrets, (that is, if there is a probabilistic correlation between the secrets and some observables) then the adversary can approximate such distribution by repeating the observations. More precisely, it can approximate the distribution on the observables by computing their frequencies, and then derive the distribution on the secrets by using the correlation in the inverse direction. We illustrate this method, and then we study the bounds on the approximation error associated with it, for various natural notions of error. As a case study, we apply our results to Crowds, a protocol for anonymous communication.
In information-hiding, an adversary that tries to infer the secret information has a higher probability of success if it knows the distribution on the secrets. We show that if the system leaks probabilistically some information about the secrets, (that is, if there is a probabilistic correlation between the secrets and some observables) then the adversary can approximate such distribution by repeating the observations. More precisely, it can approximate the distribution on the observables by computing their frequencies, and then derive the distribution on the secrets by using the correlation in the inverse direction. We illustrate this method, and then we study the bounds on the approximation error associated with it, for various natural notions of error. As a case study, we apply our results to Crowds, a protocol for anonymous communication.
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.
This paper introduces g-leakage, a rich generalization of the min-entropy model of quantitative information flow. In g-leakage, the benefit that an adversary derives from a certain guess about a secret is specified using a gain function g. Gain functions allow a wide variety of operational scenarios to be modeled, including those where the adversary benefits from guessing a value close to the secret, guessing a part of the secret, guessing a property of the secret, or guessing the secret within some number of tries. We prove important properties of g-leakage, including bounds between min-capacity, g-capacity, and Shannon capacity. We also show a deep connection between a strong leakage ordering on two channels, C1and C2, and the possibility of factoring C1into C2C3, for some C3. Based on this connection, we propose a generalization of the Lattice of Information from deterministic to probabilistic channels.
We study the design of cryptographic primitives resilient to key-leakage attacks, where an attacker can repeatedly and adaptively learn information about the secret key, subject only to the constraint that the overall amount of such information is bounded by some parameter ℓ. We construct a variety of leakage-resilient public-key systems including the first known identification schemes (ID), signature schemes and authenticated key agreement protocols (AKA). Our main result is an efficient three-round leakage-resilient AKA in the Random-Oracle model. This protocol ensures that session keys are private and authentic even if (1) the adversary leaks a large fraction of the long-term secret keys of both users prior to the protocol execution and (2) the adversary completely learns the long-term secret keys after the protocol execution. In particular, our AKA protocol provides qualitatively stronger privacy guarantees than leakage-resilient public-encryption schemes (constructed in prior and concurrent works), since such schemes necessarily become insecure if the adversary can perform leakage attacks after seing a ciphertext. Moreover, our schemes can be flexibly extended to the Bounded-Retrieval Model, allowing us to tolerate very large absolute amount of adversarial leakage ℓ (potentially many gigabytes of
Every quantum key distribution (QKD) protocol must limit the information available outside the users' laboratories. In device-independent QKD this is essentially the only assumption made on the devices. In a prepare-and-measure setting it cannot be imposed strictly, since the sender's device must emit a signal that depends on her private input. The natural replacement, and a minimal one, is a leakage bound: a bound on how much information about the input leaves the sender's laboratory, through the intended signal or through any side channel. We ask how far this unavoidable requirement can replace a detailed model of the source. We show that this single bound, quantified by the probability of guessing the input from everything the source emits, suffices to prove security against collective attacks. In our analysis, nothing is assumed about the precise form of the emitted states, their dimension, energy or purity, nor about the receiver's measurement device, beyond the standard requirement that it does not leak Bob's data. The standard B92 and BB84 protocols do not certify any key under this minimal leakage bound assumption. But closely related protocols can and, in the ideal limit, achieve one secret bit per key round. For noisy implementations, we compute key rates using semidefinite programming relaxations. Our best protocols tolerate visibilities down to 0.84, corresponding to an 8% quantum bit error rate, compared with the 11% threshold of standard device-dependent BB84.
Secret sharing is an instrumental tool for sharing secret keys in distributed systems. In a classical threshold setting, this involves a dealer who has a secret/key, a set of parties/users to which shares of the secret are sent, and a threshold on the number of users whose presence is needed in order to recover the secret. In secret sharing, secure links with no leakage are often assumed between the involved parties. However, when the users are nodes in a communication network and all the links are physical links, e.g., wireless, such assumptions are not valid anymore. In order to study this critical problem, we propose a statistical leakage model of secret sharing, where some noisy versions of all the secret shares might be independently leaked to an adversary. We then study the resilience of the seminal Shamir's secret sharing scheme with statistical leakage, and bound certain measures of security (i.e., semantic security, mutual information security), given other parameters of the system including the amount of leakage from each secret share. We show that for an extreme scenario of Shamir's scheme, in particular when the underlying field characteristic is 2, the security of each bit of the secret against leakage improves exponentially with the number of users. To the best of our knowledge, this is the first attempt towards understanding secret sharing under general statistical noisy leakage.
Information flow is the branch of security that studies the leakage of information due to correlation between secrets and observables. Since in general such correlation cannot be avoided completely, it is important to quantify the leakage. The most followed approaches to defining appropriate measures are those based on information theory. In particular, one of the most successful approaches is the recently proposed g-leakage framework, which encompasses most of the information-theoretic ones. A problem with g-leakage, however, is that it is defined in terms of a minimization problem, which, in the case of large systems, can be computationally rather heavy. In this paper we study the case in which the channel associated to the system can be decomposed into simpler channels, which typically happens when the observables consist of multiple components. Our main contribution is the derivation of bounds on the (multiplicative version of) g-leakage of the whole system in terms of the g-leakages of its components. We also consider the particular cases of min-entropy leakage and of parallel channels, generalizing and systematizing results from the literature. We demonstrate the effectiveness of our method and evaluate the precision of our bounds using examples.