We study the interaction of the "new" construct with a rich but common form of (first-order) communication. This interaction is crucial in security protocols, which are the main motivating examples for our work; it also appears in other programming-language contexts. Specifically, we introduce a simple, general extension of the pi calculus with value passing, primitive functions, and equations among terms. We develop semantics and proof techniques for this extended language and apply them in reasoning about some security protocols.

We investigate the complexity of the protocol insecurity problem for a finite number of sessions (fixed number of interleaved runs). We show that this problem is NP-complete with respect to a Dolev-Yao model of intruders. The result does not assume a limit on the size of messages and supports non-atomic symmetric encryption keys. We also prove that in order to build an attack with a fixed number of sessions the intruder needs only to forge messages of linear size, provided that they are represented as dags.

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

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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).

A cryptographic protocol can be described as a system of concurrent processes, and analysis

We introduce a class of tree automata that perform tests on a memory that is updated using function symbol application and projection. The language emptiness problem for this class of tree automata is shown to be in DEXPTIME.

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.

Abstract. 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. 1

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.