arXiv subjects

Catuscia Palamidessi

Publications and source records attributed to Catuscia Palamidessi.

79 records · Page 5Linked to original sources

arXiv2011

On the relation between Differential Privacy and Quantitative Information Flow

Differential privacy is a notion that has emerged in the community of statistical databases, as a response to the problem of protecting the privacy of the database's participants when performing statistical queries. The idea is that a randomized query satisfies differential privacy if the likelihood of obtaining a certain answer for a database $x$ is not too different from the likelihood of obtaining the same answer on adjacent databases, i.e. databases which differ from $x$ for only one individual. Information flow is an area of Security concerned with the problem of controlling the leakage of confidential information in programs and protocols. Nowadays, one of the most established approaches to quantify and to reason about leakage is based on the Rényi min entropy version of information theory. In this paper, we analyze critically the notion of differential privacy in light of the conceptual framework provided by the Rényi min information theory. We show that there is a close relation between differential privacy and leakage, due to the graph symmetries induced by the adjacency relation. Furthermore, we consider the utility of the randomized answer, which measures its expected degree of accuracy. We focus on certain kinds of utility functions called "binary", which have a close correspondence with the Rényi min mutual information. Again, it turns out that there can be a tight correspondence between differential privacy and utility, depending on the symmetries induced by the adjacency relation and by the query. Depending on these symmetries we can also build an optimal-utility randomization mechanism while preserving the required level of differential privacy. Our main contribution is a study of the kind of structures that can be induced by the adjacency relation and the query, and how to use them to derive bounds on the leakage and achieve the optimal utility.

cs.LO↗

arXiv2011

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 Rényi 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.

cs.CR↗

arXiv2010

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^ε. 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 Rényi'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.

cs.IT↗

arXiv2007

Making Random Choices Invisible to the Scheduler

When dealing with process calculi and automata which express both nondeterministic and probabilistic behavior, it is customary to introduce the notion of scheduler to solve the nondeterminism. It has been observed that for certain applications, notably those in security, the scheduler needs to be restricted so not to reveal the outcome of the protocol's random choices, or otherwise the model of adversary would be too strong even for ``obviously correct'' protocols. We propose a process-algebraic framework in which the control on the scheduler can be specified in syntactic terms, and we show how to apply it to solve the problem mentioned above. We also consider the definition of (probabilistic) may and must preorders, and we show that they are precongruences with respect to the restricted schedulers. Furthermore, we show that all the operators of the language, except replication, distribute over probabilistic summation, which is a useful property for verification.

cs.CR↗

arXiv2001

Probabilistic asynchronous pi-calculus

We propose an extension of the asynchronous pi-calculus with a notion of random choice. We define an operational semantics which distinguishes between probabilistic choice, made internally by the process, and nondeterministic choice, made externally by an adversary scheduler. This distinction will allow us to reason about the probabilistic correctness of algorithms under certain schedulers. We show that in this language we can solve the electoral problem, which was proved not possible in the asynchronous $π$-calculus. Finally, we show an implementation of the probabilistic asynchronous pi-calculus in a Java-like language.

cs.PL↗

arXiv2001

On the generalized dining philosophers problem

We consider a generalization of the dining philosophers problem to arbitrary connection topologies. We focus on symmetric, fully distributed systems, and we address the problem of guaranteeing progress and lockout-freedom, even in presence of adversary schedulers, by using randomized algorithms. We show that the well-known algorithms of Lehmann and Rabin do not work in the generalized case, and we propose an alternative algorithm based on the idea of letting the philosophers assign a random priority to their adjacent forks.

cs.PL↗

arXiv1998

Comparing the expressive power of the Synchronous and the Asynchronous pi-calculus

The Asynchronous pi-calculus, as recently proposed by Boudol and, independently, by Honda and Tokoro, is a subset of the pi-calculus which contains no explicit operators for choice and output-prefixing. The communication mechanism of this calculus, however, is powerful enough to simulate output-prefixing, as shown by Boudol, and input-guarded choice, as shown recently by Nestmann and Pierce. A natural question arises, then, whether or not it is possible to embed in it the full pi-calculus. We show that this is not possible, i.e. there does not exist any uniform, parallel-preserving, translation from the pi-calculus into the asynchronous pi-calculus, up to any ``reasonable'' notion of equivalence. This result is based on the incapablity of the asynchronous pi-calculus of breaking certain symmetries possibly present in the initial communication graph. By similar arguments, we prove a separation result between the pi-calculus and CCS.

cs.PL↗