Entropy and Attack Models in Information Flow

International audienceKöpf and Basin have discussed the relation between brute-force guessing attacks and entropy, in the context of information flow induced by a deterministic program. In this talk, we extend the analysis of Köpf and Basin to the probabilistic scenario, and we consider also other notions of entropy, including the family of entropies proposed by Rényi

Differential Privacy versus Quantitative Information Flow

Differential privacy is a notion of privacy that has become very popular in the database community. Roughly, the idea is that a randomized query mechanism provides sufficient privacy protection if the ratio between the probabilities of two different entries to originate a certain answer is bound by e^\epsilon. In the fields of anonymity and information flow there is a similar concern for controlling information leakage, i.e. limiting the possibility of inferring the secret information from the observables. In recent years, researchers have proposed to quantify the leakage in terms of the information-theoretic notion of mutual information. There are two main approaches that fall in this category: One based on Shannon entropy, and one based on R\'enyi's min entropy. The latter has connection with the so-called Bayes risk, which expresses the probability of guessing the secret. In this paper, we show how to model the query system in terms of an information-theoretic channel, and we compare the notion of differential privacy with that of mutual information. We show that the notion of differential privacy is strictly stronger, in the sense that it implies a bound on the mutual information, but not viceversa

Studying Maximum Information Leakage Using Karush-Kuhn-Tucker Conditions

When studying the information leakage in programs or protocols, a natural question arises: "what is the worst case scenario?". This problem of identifying the maximal leakage can be seen as a channel capacity problem in the information theoretical sense. In this paper, by combining two powerful theories: Information Theory and Karush-Kuhn-Tucker conditions, we demonstrate a very general solution to the channel capacity problem. Examples are given to show how our solution can be applied to practical contexts of programs and anonymity protocols, and how this solution generalizes previous approaches to this problem

Quantitative Information Flow as Safety and Liveness Hyperproperties

We employ Clarkson and Schneider's "hyperproperties" to classify various verification problems of quantitative information flow. The results of this paper unify and extend the previous results on the hardness of checking and inferring quantitative information flow. In particular, we identify a subclass of liveness hyperproperties, which we call "k-observable hyperproperties", that can be checked relative to a reachability oracle via self composition.Comment: In Proceedings QAPL 2012, arXiv:1207.055

Bounds on the leakage of the input's distribution in information-hiding protocols

International audienceIn 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

Differential Privacy: on the trade-off between Utility and Information Leakage

Differential privacy is a notion of privacy that has become very popular in the database community. Roughly, the idea is that a randomized query mechanism provides sufficient privacy protection if the ratio between the probabilities that two adjacent datasets give the same answer is bound by e^epsilon. In the field of information flow there is a similar concern for controlling information leakage, i.e. limiting the possibility of inferring the secret information from the observables. In recent years, researchers have proposed to quantify the leakage in terms of R\'enyi min mutual information, a notion strictly related to the Bayes risk. In this paper, we show how to model the query system in terms of an information-theoretic channel, and we compare the notion of differential privacy with that of mutual information. We show that differential privacy implies a bound on the mutual information (but not vice-versa). Furthermore, we show that our bound is tight. Then, we consider the utility of the randomization mechanism, which represents how close the randomized answers are, in average, to the real ones. We show that the notion of differential privacy implies a bound on utility, also tight, and we propose a method that under certain conditions builds an optimal randomization mechanism, i.e. a mechanism which provides the best utility while guaranteeing differential privacy.Comment: 30 pages; HAL repositor

LIBQIF: a quantitative information flow C++ toolkit library

A fundamental concern in computer security is to control information ow, whether to protect con dential information from being leaked, or to protect trusted information from being tainted. A classic approach is to try to enforce non-interference. Unfortunately, achieving non-interference is often not possible, because often there is a correlation between secrets and observables, either by design or due to some physical feature of the computation (side channels). One promising approach to relaxing noninterference, is to develop a quantitative theory of information ow that allows us to reason about how much information is being leaked, thus paving the way to the possibility of tolerating small leaks. In this work, we aim at developing a quantitative information ow C++ toolkit library, implementing several algorithms from the areas of QIF (more speci cally from four theories: Shannon Entropy, Min-Entropy, Guessing Entropy and G-Leakage) and Di erential Privacy. The library can be used by academics to facilitate research in these areas, as well as by students as a learning tool. A primary use of the library is to compute QIF measures as well as to generate plots, useful for understanding their behavior. Moreover, the library allows users to compute optimal di erentially private mechanisms, compare the utility of known mechanisms, compare the leakage of channels, compute gain functions that separate channels, and various other functionalities related to QIF.Trabajo final de carreraSociedad Argentina de Informática e Investigación Operativa (SADIO

LIBQIF: a quantitative information flow C++ toolkit library

A fundamental concern in computer security is to control information ow, whether to protect con dential information from being leaked, or to protect trusted information from being tainted. A classic approach is to try to enforce non-interference. Unfortunately, achieving non-interference is often not possible, because often there is a correlation between secrets and observables, either by design or due to some physical feature of the computation (side channels). One promising approach to relaxing noninterference, is to develop a quantitative theory of information ow that allows us to reason about how much information is being leaked, thus paving the way to the possibility of tolerating small leaks. In this work, we aim at developing a quantitative information ow C++ toolkit library, implementing several algorithms from the areas of QIF (more speci cally from four theories: Shannon Entropy, Min-Entropy, Guessing Entropy and G-Leakage) and Di erential Privacy. The library can be used by academics to facilitate research in these areas, as well as by students as a learning tool. A primary use of the library is to compute QIF measures as well as to generate plots, useful for understanding their behavior. Moreover, the library allows users to compute optimal di erentially private mechanisms, compare the utility of known mechanisms, compare the leakage of channels, compute gain functions that separate channels, and various other functionalities related to QIF.Trabajo final de carreraSociedad Argentina de Informática e Investigación Operativa (SADIO