The reachability problem for cryptographic protocols with nonatomic keys can be solved via a simple constraint satisfaction procedure.

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.

We propose a constraint-based system for the verification of security protocols that improves upon the one developed by Millen and Shmatikov [30]. Our system features (1) a significantly more efficient implementation, (2) a monotonic behavior, which also allows to detect flaws associated to partial runs and (3) a more expressive syntax, in which a principal may also perform explicit checks. In this paper we also show why these improvements yield a more effective and practical system.

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In experiments with a resolution-based verification method for cryptographic protocols, we could enforce its termination by tagging, a syntactic transformation of messages that leaves attack-free executions invariant. In this paper, we generalize the experimental evidence: we prove that the verification method always terminates for tagged protocols.

Abstract. 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. 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, andxor, with a bounded number of role instances, but without imposing any bounds on the size of terms created by the attacker. 1

Abstract. Properties of security protocols such as authentication and secrecy are often verified by explictly generating an operational model of the protocol and then seeking for insecure states. However, message exchange between the intruder and the honest participants induces a form of state explosion that makes the model infinite in principle. Building on previous work on symbolic semantics, we propose a general framework for automatic analysis of security protocols that make use of a variety of crypto-functions. We start from a base language akin to the spi-calculus, equipped with a set of generic cryptographic primitives. We propose a symbolic operational semantics that relies on unification and provides finite and effective protocol models. Next, we give a method to carry out trace analysis directly on the symbolic model. Under certain conditions on the given cryptographic primitives, our method is proven complete for the considered class of properties. 1