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.

Abstract. We study the control reachability problem in the Dolev-Yao model of cryptographic protocols when principals are represented by tail recursive processes with generated names. We propose a conservative approximation of the problem by reduction to a non-standard collapsed operational semantics and we introduce checkable syntactic conditions entailing the equivalence of the standard and the collapsed semantics. Then we introduce a conservative and decidable set-based analysis of the collapsed operational semantics and we characterize a situation where the analysis is exact.

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.

We consider a new extension of the Skolem class for first-order logic and prove its decidability by resolution techniques. We then extend this class including the built-in equational theory of exclusive or. Again, we prove the decidability of the class by resolution techniques.

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

We consider arbitrary cryptographic protocols and security properties. We show that it is always sufficient to consider a bounded number of agents b (actually b = 2 in most of the cases): if there is an attack involving n agents, then there is an attack involving at most b agents.

We consider the framework of regular tree model checking where sets of configurations of a system are represented by regular tree languages and its dynamics is modeled by a term rewriting system (or a regular tree transducer). We focus on the computation of the reachability set R # (L) where R is a regular tree transducer and L is a regular tree language. The construction

Security protocols stipulate how the remote principals of a computer network should interact in order to obtain specific security goals. The crucial goals of confidentiality and authentication may be achieved in various forms, each of different strength. Using soft (rather than crisp) constraints, we develop a uniform formal notion for the two goals. They are no longer formalised as mere yes/no properties as in the existing literature, but gain an extra parameter, the security level. For example, different messages can enjoy different levels of confidentiality, or a principal can achieve different levels of authentication with different principals. The goals are formalised within a general framework for protocol analysis that is amenable to mechanisation by model checking. Following the application of the framework to analysing the asymmetric Needham-Schroeder protocol (Bella and Bistarelli 2001; Bella and Bistarelli 2002), we have recently discovered a new attack on that protocol as a form of retaliation by principals who have been attacked previously. Having commented on that attack, we then demonstrate the framework on a bigger, largely deployed protocol consisting of three phases, Kerberos.