Formal Verification of e-Auction Protocols

International audienceAuctions have a long history, having been recorded as early as 500 B.C.. With the rise of Internet, electronic auctions have been a great success and are increasingly used. Many cryptographic protocols have been proposed to address the various security requirements of these electronic transactions. We propose a formal framework to analyze and verify security properties of e-Auction protocols. We model protocols in the Applied π-Calculus and define privacy notions, which include secrecy of bids, anonymity of the participants, receipt-freeness and coercion-resistance. We also discuss fairness, non-repudiation and non-cancellation. Additionally we show on two case studies how these properties can be verified automatically using ProVerif, and discover several attacks

Soundness of Symbolic Equivalence for Modular Exponentiation

In this paper, we study the Dynamic Decisional Diffie-Hellman (3DH) problem, a powerful generalization of the Decisional Diffie-Hellman (DDH) problem. Our main result is that DDH implies 3DH. This result leads to significantly simpler proofs for protocols by relying directly on the more general problem. Our second contribution is a computationally sound symbolic technique for reasoning about protocols that use symmetric encryption and modular exponentiation. We show how to apply our results in the case of the Burmester & Desmedt protocol

Probabilistic Opacity for a Passive Adversary and its Application to Chaum\u27s Voting Scheme

A predicate is opaque for a given system, if an adversary will never be able to establish truth or falsehood of the predicate for any observed computation. This notion has been essentially introduced and studied in the context of transition systems whether describing the semantics of programs, security protocols or other systems. In this paper, we are interested in studying opacity in the probabilistic computational world. Indeed, in other settings, as in the Dolev-Yao model for instance, even if an adversary is $99\%$ sure of the truth of the predicate, it remains opaque as the adversary cannot conclude for sure. In this paper, we introduce a computational version of opacity in the case of passive adversaries called cryptographic opacity. Our main result is a composition theorem: if a system is secure in an abstract formalism and the cryptographic primitives used to implement it are secure, then this system is secure in a computational formalism. Security of the abstract system is the usual opacity and security of the cryptographic primitives is IND-CPA security. To illustrate our result, we give two applications: a short and elegant proof of the classical Abadi-Rogaway result and the first computational proof of Chaum\u27s visual electronic voting scheme

Automated Security Proofs for Almost-Universal Hash for MAC verification

Message authentication codes (MACs) are an essential primitive in cryptography. They are used to ensure the integrity and authenticity of a message, and can also be used as a building block for larger schemes, such as chosen-ciphertext secure encryption, or identity-based encryption. MACs are often built in two steps: first, the `front end\u27 of the MAC produces a short digest of the long message, then the `back end\u27 provides a mixing step to make the output of the MAC unpredictable for an attacker. Our verification method follows this structure. We develop a Hoare logic for proving that the front end of the MAC is an almost-universal hash function. The programming language used to specify these functions is fairly expressive and can be used to describe many block-cipher and compression function-based MACs. We implemented this method into a prototype that can automatically prove the security of almost-universal hash functions. This prototype can prove the security of the front-end of many CBC-based MACs (DMAC, ECBC, FCBC and XCBC to name only a few), PMAC and HMAC. We then provide a list of options for the back end of the MAC, each consisting of only two or three instructions, each of which can be composed with an almost-universal hash function to obtain a secure MAC

Defining Privacy for Weighted Votes, Single and Multi-voter Coercion

Most existing formal privacy definitions for voting protocols are based on observational equivalence between two situations where two voters swap their votes. These definitions are unsuitable for cases where votes are weighted. In such a case swapping two votes can result in a different outcome and both situations become trivially distinguishable. We present a definition for privacy in voting protocols in the Applied Pi-Calculus that addresses this problem. Using our model, we are also able to define multi-voter coercion, i.e. situations where several voters are attacked at the same time. Then we prove that under certain realistic assumptions a protocol secure against coercion of a single voter is also secure against coercion of multiple voters. This applies for Receipt-Freeness as well as Coercion-Resistance

Formal Verification of e-Auction Protocols

Auctions have a long history, having been recorded as early as 500 B.C.. With the rise of Internet, electronic auctions have been a great success and are increasingly used. Many cryptographic protocols have been proposed to address the various security requirements of these electronic transactions. We propose a formal framework to analyze and verify security properties of e-Auction protocols. We model protocols in the Applied Pi-Calculus and define privacy notions, which include secrecy of bids, anonymity of the participants, receipt-freeness and coercion-resistance. We also discuss fairness, non-repudiation and non-cancellation. Additionally we show on two case studies how these properties can be verified automatically usingProVerif, and discover several attacks

A Formal Taxonomy of Privacy in Voting Protocols

International audiencePrivacy is one of the main issues in electronic voting. We propose a family of symbolic privacy notions that allows to assess the level of privacy ensured by a voting protocol. Our definitions are applicable to protocols featuring multiple votes per voter and special attack scenarios such as vote-copying or forced abstention. Finally we employ our definitions on several existing voting protocols to show that our model allows to compare different types of protocols based on different techniques, and is suitable for automated verification using existing tools

Vérification relationnelle pour des programmes avec des données entières

Les travaux présentés dans cette thèse sont lies aux problèmes de vérification de l'atteignabilité et de la terminaison de programmes qui manipulent des données entières non-bornées. On décrit une nouvelle méthode de vérification basée sur une technique d'accélération de boucle, qui calcule, de manière exacte, la clôture transitive d'une relation arithmétique. D'abord, on introduit un algorithme d'accélération de boucle qui peut calculer, en quelques secondes, des clôtures transitives pour des relations de l'ordre d'une centaine de variables. Ensuite, on présente une méthode d'analyse de l'atteignabilité, qui manipule des relations entre les variables entières d'un programme, et applique l'accélération pour le calcul des relations entrée-sortie des procédures, de façon modulaire. Une approche alternative pour l'analyse de l'atteignabilité, présentée également dans cette thèse, intègre l'accélération avec l'abstraction par prédicats, afin de traiter le problème de divergence de cette dernière. Ces deux méthodes ont été évaluées de manière pratique, sur un nombre important d'exemples, qui étaient, jusqu'a présent, hors de la portée des outils d'analyse existants. Dernièrement, on a étudié le problème de la terminaison pour certaines classes de boucles de programme, et on a montré la décidabilité pour les relations étudiées. Pour ces classes de relations arithmétiques, on présente un algorithme qui s'exécute en temps au plus polynomial, et qui calcule l'ensemble d'états qui peuvent générer une exécution infinie. Ensuite on a intégré cet algorithme dans une méthode d'analyse de la terminaison pour des programmes qui manipulent des données entières.This work presents novel methods for verification of reachability and termination properties of programs that manipulate unbounded integer data. Most of these methods are based on acceleration techniques which compute transitive closures of program loops. We first present an algorithm that accelerates several classes of integer relations and show that the new method performs up to four orders of magnitude better than the previous ones. On the theoretical side, our framework provides a common solution to the acceleration problem by proving that the considered classes of relations are periodic. Subsequently, we introduce a semi-algorithmic reachability analysis technique that tracks relations between variables of integer programs and applies the proposed acceleration algorithm to compute summaries of procedures in a modular way. Next, we present an alternative approach to reachability analysis that integrates predicate abstraction with our acceleration techniques to increase the likelihood of convergence of the algorithm. We evaluate these algorithms and show that they can handle a number of complex integer programs where previous approaches failed. Finally, we study the termination problem for several classes of program loops and show that it is decidable. Moreover, for some of these classes, we design a polynomial time algorithm that computes the exact set of program configurations from which non-terminating runs exist. We further integrate this algorithm into a semi-algorithmic method that analyzes termination of integer programs, and show that the resulting technique can verify termination properties of several non-trivial integer programs.SAVOIE-SCD - Bib.électronique (730659901) / SudocGRENOBLE1/INP-Bib.électronique (384210012) / SudocGRENOBLE2/3-Bib.électronique (384219901) / SudocSudocFranceF

Mind the Gap: Modular Machine-checked Proofs of One-Round Key Exchange Protocols

Using EasyCrypt, we formalize a new modular security proof for one-round authenticated key exchange protocols in the random oracle model. Our proof improves earlier work by Kudla and Paterson (ASIACRYPT 2005) in three significant ways: we consider a stronger adversary model, we provide support tailored to protocols that utilize the Naxos trick, and we support proofs under the Computational DH assumption not relying on Gap oracles. Furthermore, our modular proof can be used to obtain concrete security proofs for protocols with or without adversarial key registration. We use this support to investigate, still using EasyCrypt, the connection between proofs without Gap assumptions and adversarial key registration. For the case of honestly generated keys, we obtain the first proofs of the Naxos and Nets protocols under the Computational DH assumption. For the case of adversarial key registration, we obtain machine-checked and modular variants of the well-known proofs for Naxos, Nets, and Naxos+