Véronique Cortier

Deciding knowledge in security protocols under equational theories

The analysis of security protocols requires precise formulations of the knowledge of protocol participants and attackers. In formal approaches, this knowledge is often treated in terms of message deducibility and indistinguishability relations. In this paper we study the decidability of these two relations. The messages in question may employ functions (encryption, decryption, etc.) axiomatized in an equational theory. Our main positive results say that, for a large and useful class of equational theories, deducibility and indistinguishability are both decidable in polynomial time.

A survey of algebraic properties used in cryptographic protocols

Cryptographic protocols are successfully analyzed using formal methods. However, formal approaches usually consider the encryption schemes as black boxes and assume that an adversary cannot learn anything from an encrypted message except if he has the key. Such an assumption is too strong in general since some attacks exploit in a clever way the interaction between protocol rules and properties of cryptographic operators. Moreover, the executability of some protocols relies explicitly on some algebraic properties of cryptographic primitives such as commutative encryption. We give a list of some relevant algebraic properties of cryptographic operators, and for each of them, we provide examples of protocols or attacks using these properties. We also give an overview of the existing methods in formal approaches for analyzing cryptographic protocols.

Computationally sound, automated proofs for security protocols

Since the 1980s, two approaches have been developed for analyzing security protocols. One of the approaches relies on a computational model that considers issues of complexity and probability. This approach captures a strong notion of security, guaranteed against all probabilistic polynomial-time attacks. The other approach relies on a symbolic model of protocol executions in which cryptographic primitives are treated as black boxes. Since the seminal work of Dolev and Yao, it has been realized that this latter approach enables significantly simpler and often automated proofs. However, the guarantees that it offers have been quite unclear. In this paper, we show that it is possible to obtain the best of both worlds: fully automated proofs and strong, clear security guarantees. Specifically, for the case of protocols that use signatures and asymmetric encryption, we establish that symbolic integrity and secrecy proofs are sound with respect to the computational model. The main new challenges concern secrecy properties for which we obtain the first soundness result for the case of active adversaries. Our proofs are carried out using Casrul, a fully automated tool.

Computational soundness of observational equivalence

Many security properties are naturally expressed as indistinguishability between two versions of a protocol. In this paper, we show that computational proofs of indistinguishability can be considerably simplified, for a class of processes that covers most existing protocols. More precisely, we show a soundness theorem, following the line of research launched by Abadi and Rogaway in 2000: computational indistinguishability in presence of an active attacker is implied by the observational equivalence of the corresponding symbolic processes. We prove our result for symmetric encryption, but the same techniques can be applied to other security primitives such as signatures and public-key encryption. The proof requires the introduction of new concepts, which are general and can be reused in other settings.

Attacking and fixing Helios: An analysis of ballot secrecy

Helios 2.0 is an open-source web-based end-to-end verifiable electronic voting system, suitable for use in low-coercion environments. In this article, we analyse ballot secrecy in Helios and discover a vulnerability which allows an adversary to compromise the privacy of voters. The vulnerability exploits the absence of ballot independence in Helios and works by replaying a voters ballot or a variant of it, the replayed ballot magnifies the voters contribution to the election outcome and this magnification can be used to violated privacy. We demonstrate the practicality of the attack by violating a voters privacy in a mock election using the software implementation of Helios. Moreover, the feasibility of an attack is considered in the context of French legislative elections and, based upon our findings, we believe it constitutes a real threat to ballot secrecy. We present a fix and show that our solution satisfies a formal definition of ballot secrecy using the applied pi calculus. Furthermore, we present similar vulnerabilities in other electronic voting protocols --namely, the schemes by Lee et al., Sako and Kilian and Schoenmakers --which do not assure ballot independence. Finally, we argue that independence and privacy properties are unrelated, and non-malleability is stronger than independence.

Computationally sound implementations of equational theories against passive adversaries

In this paper we study the link between formal and cryptographic models for security protocols in the presence of passive adversaries. In contrast to other works, we do not consider a fixed set of primitives but aim at results for arbitrary equational theories. We define a framework for comparing a cryptographic implementation and its idealization with respect to various security notions. In particular, we concentrate on the computational soundness of static equivalence, a standard tool in cryptographic pi calculi. We present a soundness criterion, which for many theories is not only sufficient but also necessary. Finally, to illustrate our framework, we establish the soundness of static equivalence for the exclusive OR and a theory of ciphers and lists.

Measuring vote privacy, revisited

We propose a new measure for privacy of votes. Our measure relies on computational conditional entropy, an extension of the traditional notion of entropy that incorporates both information-theoretic and computational aspects. As a result, we capture in a unified manner privacy breaches due to two orthogonal sources of insecurity: combinatorial aspects that have to do with the number of participants, the distribution of their votes and published election outcome as well as insecurity of the cryptography used in an implementation. Our privacy measure overcomes limitations of two previous approaches to defining vote privacy and we illustrate its applicability through several case studies. We offer a generic way of applying our measure to a large class of cryptographic protocols that includes the protocols implemented in Helios. We also describe a practical application of our metric on Scantegrity audit data from a real election.

Attacking and Fixing Helios: An Analysis of Ballot Secrecy

Helios 2.0 is an open-source web-based end-to-end verifiable electronic voting system, suitable for use in low-coercion environments. In this paper, we analyse ballot secrecy and discover a vulnerability which allows an adversary to compromise the privacy of voters. This vulnerability has been successfully exploited to break privacy in a mock election using the current Helios implementation. Moreover, the feasibility of an attack is considered in the context of French legislative elections and, based upon our findings, we believe it constitutes a real threat to ballot secrecy in such settings. Finally, we present a fix and show that our solution satisfies a formal definition of ballot secrecy using the applied pi calculus.

Adapting helios for provable ballot privacy

Recent results show that the current implementation of Helios, a practical e-voting protocol, does not ensure independence of the cast votes, and demonstrate the impact of this lack of independence on vote privacy. Some simple fixes seem to be available and security of the revised scheme has been studied with respect to symbolic models. In this paper we study the security of Helios using computational models. Our first contribution is a model for the property known as ballot privacy that generalizes and extends several existing ones. Using this model, we investigate an abstract voting scheme (of which the revised Helios is an instantiation) built from an arbitrary encryption scheme with certain functional properties. We prove, generically, that whenever this encryption scheme falls in the class of voting-friendly schemes that we define, the resulting voting scheme provably satisfies ballot privacy. We explain how our general result yields cryptographic security guarantees for the revised version of Helios (albeit from non-standard assumptions). Furthermore, we show (by giving two distinct constructions) that it is possible to construct voting-friendly encryption, and therefore voting schemes, using only standard cryptographic tools. We detail an instantiation based on ElGamal encryption and Fiat-Shamir noninteractive zero-knowledge proofs that closely resembles Helios and which provably satisfies ballot privacy.

A Method for Proving Observational Equivalence

Formal methods have proved their usefulness for analyzing the security of protocols. Most existing results focus on trace properties like secrecy (expressed as a reachability property) or authentication. There are however several security properties, which cannot be defined (or cannot be naturally defined) as trace properties and require the notion of observational equivalence. Typical examples are anonymity, privacy related properties or statements closer to security properties used in cryptography.In this paper, we consider the applied pi calculus and we show that for determinate processes, observational equivalence actually coincides with trace equivalence, a notion simpler to reason with.We exhibit a large class of determinate processes, called simple processes, that capture most existing protocols and cryptographic primitives. Then, for simple processes without replication nor else branch,we reduce the decidability of trace equivalence to deciding an equivalence relation introduced by M. Baudet. Altogether, this yields the first decidability result of observational equivalence for a general class of equational theories.