Hierarchical combination of intruder theories

International audienceRecently automated deduction tools have proved to be very effective for detecting attacks on cryptographic protocols. These analysis can be improved, for finding more subtle weaknesses, by a more accurate modelling of operators employed by protocols. Several works have shown how to handle a single algebraic operator (associated with a fixed intruder theory) or how to combine several operators satisfying disjoint theories. However several interesting equational theories, such as exponentiation with an abelian group law for exponents remain out of the scope of these techniques. This has motivated us to introduce a new notion of hierarchical combination for non-disjoint intruder theories and to show decidability results for the deduction problem in these theories. We have also shown that under natural hypotheses hierarchical intruder constraints can be decided. This result applies to an exponentiation theory that appears to be more general than the one considered before

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

Heuristic Methods for Security Protocols

Model checking is an automatic verification technique to verify hardware and software systems. However it suffers from state-space explosion problem. In this paper we address this problem in the context of cryptographic protocols by proposing a security property-dependent heuristic. The heuristic weights the state space by exploiting the security formulae; the weights may then be used to explore the state space when searching for attacks

Hierarchical Combination of Intruder Theories

Abstract. Recently automated deduction tools have proved to be very effective for detecting attacks on cryptographic protocols. These analysis can be improved, for finding more subtle weaknesses, by a more accurate modelling of operators employed by protocols. Several works have shown how to handle a single algebraic operator (associated with a fixed intruder theory) or how to combine several operators satisfying disjoint theories. However several interesting equational theories, such as exponentiation with an abelian group law for exponents remain out of the scope of these techniques. This has motivated us to introduce a new notion of hierarchical combination for intruder theories and to show decidability results for the deduction problem in these theories. Under a simple hypothesis, we were able to simplify this deduction problem. This simplification is then applied to prove the decidability of constraint systems w.r.t. an intruder relying on exponentiation theory.

Knowledge Flow Analysis for Security Protocols

Knowledge flow analysis offers a simple and flexible way to find flaws in security protocols. A protocol is described by a collection of rules constraining the propagation of knowledge amongst principals. Because this characterization corresponds closely to informal descriptions of protocols, it allows a succinct and natural formalization; because it abstracts away message ordering, and handles communications between principals and applications of cryptographic primitives uniformly, it is readily represented in a standard logic. A generic framework in the Alloy modelling language is presented, and instantiated for two standard protocols, and a new key management scheme.Comment: 20 page

Computing Knowledge in Equational Extensions of Subterm Convergent Theories

International audienceWe study decision procedures for two knowledge problems critical to the verification of security protocols, namely the intruder deduction and the static equivalence problems. These problems can be related to particular forms of context matching and context unification. Both problems are defined with respect to an equational theory and are known to be decidable when the equational theory is given by a subterm convergent term rewrite system. In this work we extend this to consider a subterm convergent term rewrite system defined modulo an equational theory, like Commutativity. We present two pairs of solutions for these important problems. The first solves the deduction and static equivalence problems in systems modulo shallow theories such as Commutativity. The second provides a general procedure that solves the deduction and static equivalence problems in subterm convergent systems modulo syntactic permutative theories, provided a finite measure is ensured. Several examples of such theories are also given

Toward an Automatic Analysis of Web Service Security

Web services send and receive messages in XML syntax with some parts hashed, encrypted or signed, according to the WS-Security standard. In this paper we introduce a model to formally describe the protocols that underly these services, their security properties and the rewriting attacks they might be subject to. Unlike with usual security protocols, we have to address here the facts that: (1) The Web service receive/send actions are nondeterministic to accommodate the XML format and the lack of normalization in parsing XML messages. Our model is designed to permit non-deterministic operations. (2) The Web service message format is better modelled with multiset constructors than with fixed arity symbols. Hence we had to introduce an attacker model that handles associativecommutative operators. In particular we present a decision procedure for insecurity of Web services with messages built using encryption, signature, and other cryptographic primitives