Abstract not found

We provide a method for deciding the insecurity of cryptographic protocols in presence of the standard Dolev-Yao intruder (with a finite number of sessions) extended with so-called oracle rules, i.e., deduction rules that satisfy certain conditions. As an instance of this general framework, we obtain that protocol insecurity is in NP for an intruder that can exploit the properties of the XOR operator. This operator is frequently used in cryptographic protocols but cannot be handled in most protocol models. We also apply our framework to an intruder that exploits properties of certain encryption modes such as cipher block chaining (CBC).

We present decidability results for the verification of cryptographic protocols in the presence of equational theories corresponding to xor and Abelian groups. Since the perfect cryptography assumption is unrealistic for cryptographic primitives with visible algebraic properties such as xor, we extend the conventional Dolev-Yao model by permitting the intruder to exploit these properties. We show that the ground reachability problem in NP for the extended intruder theories in the cases of xor and Abelian groups. This result follows from a normal proof theorem. Then, we show how to lift this result in the xor case: we consider a symbolic constraint system expressing the reachability (e.g., secrecy) problem for a finite number of sessions. We prove that such constraint system is decidable, relying in particular on an extension of combination algorithms for unification procedures. As a corollary, this enables automatic symbolic verification of cryptographic protocols employing xor for a fixed number of sessions.

The history of the application of formal methods to cryptographic protocol analysis spans over 20 years and recently has been showing signs of new maturity and consolidation. Not only have a number of specialized tools been developed, and generalpurpose ones been adapted, but people have begun applying these tools to realistic protocols, in many cases supplying feedback to designers that can be used to improve the protocol’s security. In this paper, we will describe some of the ongoing work in this area, as well as describe some of the new challenges and the ways in which they are being met.

Abstract not found

We demonstrate that for any well-defined cryptographic protocol, the symbolic trace reachability problem in the presence of an Abelian group operator (e.g., multiplication) can be reduced to solvability of a decidable system of quadratic Diophantine equations. This result enables complete, fully automated formal analysis of protocols that employ primitives such as Diffie-Hellman exponentiation, multiplication, andxor, with a bounded number of role instances, but without imposing any bounds on the size of terms created by the attacker. 1

Abstract. We consider the following problem: Given a term t, a rewrite system R, a finite set of equations E ′ such that R is E ′-convergent, com-pute finitely many instances of t: t1,..., tn such that, for every substi-tution σ, there is an index i and a substitution θ such that tσ ↓ =E ′ tiθ (where tσ ↓ is the normal form of tσ w.r.t. →E ′ \R). The goal of this paper is to give equivalent (resp. sufficient) conditions for the finite variant property and to systematically investigate this property for equational theories, which are relevant to security protocols verification. For instance, we prove that the finite variant property holds for Abelian Groups, and a theory of modular exponentiation and does not hold for the theory ACUNh (Associativity, Commutativity, Unit, Nilpotence, homomorphism).

Abstract. Most of the decision procedures for symbolic analysis of protocols are limited to a fixed set of algebraic operators associated with a fixed intruder theory. Examples of such sets of operators comprise XOR, multiplication/exponentiation, abstract encryption/decryption. In this paper we give an algorithm for combining decision procedures for arbitrary intruder theories with disjoint sets of operators, provided that solvability of ordered intruder constraints, a slight generalization of intruder constraints, can be decided in each theory. This is the case for most of the intruder theories for which a decision procedure has been given. In particular our result allows us to decide trace-based security properties of protocols that employ any combination of the above mentioned operators with a bounded number of sessions. 1

We demonstrate that for any well-defined cryptographic protocol, the symbolic trace reachability problem in the presence of an Abelian group operator (e.g., multiplication) can be reduced to solvability of a decidable system of quadratic Diophantine equations. This result enables complete, fully automated formal analysis of protocols that employ primitives such as Diffie-Hellman exponentiation, multiplication, and xor, with a bounded number of role instances, but without imposing any bounds on the size of terms created by the attacker. 1

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. 1