Vincent Cheval

Trace equivalence decision: negative tests and non-determinism

We consider security properties of cryptographic protocols that can be modeled using the notion of trace equivalence. The notion of equivalence is crucial when specifying privacy-type properties, like anonymity, vote-privacy, and unlinkability. In this paper, we give a calculus that is close to the applied pi calculus and that allows one to capture most existing protocols that rely on classical cryptographic primitives. First, we propose a symbolic semantics for our calculus relying on constraint systems to represent infinite sets of possible traces, and we reduce the decidability of trace equivalence to deciding a notion of symbolic equivalence between sets of constraint systems. Second, we develop an algorithm allowing us to decide whether two sets of constraint systems are in symbolic equivalence or not. Altogether, this yields the first decidability result of trace equivalence for a general class of processes that may involve else branches and/or private channels (for a bounded number of sessions).

Deciding equivalence-based properties using constraint solving☆

Formal methods have proved their usefulness for analyzing the security of protocols. Most existing results focus on trace properties like secrecy or authentication. There are however several security properties, which cannot be defined (or cannot be naturally defined) as trace properties and require a notion of behavioural equivalence. Typical examples are anonymity, privacy related properties or statements closer to security properties used in cryptography. In this paper, we consider three notions of equivalence defined in the applied pi calculus: observational equivalence, may-testing equivalence, and trace equivalence. First, we study the relationship between these three notions. We show that for determinate processes, observational equivalence actually coincides with trace equivalence, a notion simpler to reason with. We exhibit a large class of determinate processes, called simple processes, that capture most existing protocols and cryptographic primitives. While trace equivalence and may-testing equivalence seem very similar, we show that may-testing equivalence is actually strictly stronger than trace equivalence. We prove that the two notions coincide for image-finite processes, such as processes without replication. Second, we reduce the decidability of trace equivalence (for finite processes) to deciding symbolic equivalence between sets of constraint systems. For simple processes without replication and with trivial else branches, it turns out that it is actually sucient to decide symbolic equivalence between pairs of positive constraint systems. Thanks to this reduction and relying on a result first proved by M. Baudet, this yields the first decidability result of observational equivalence for a general class of equational theories (for processes without else branch nor replication). Moreover, based on another decidability result for deciding equivalence between sets of constraint systems, we get decidability of trace equivalence for processes with else branch for standard primitives.

Automating security analysis: symbolic equivalence of constraint systems

We consider security properties of cryptographic protocols, that are either trace properties (such as confidentiality or authenticity) or equivalence properties (such as anonymity or strong secrecy). Infinite sets of possible traces are symbolically represented using deducibility constraints. We give a new algorithm that decides the trace equivalence for the traces that are represented using such constraints, in the case of signatures, symmetric and asymmetric encryptions. Our algorithm is implemented and performs well on typical benchmarks. This is the first implemented algorithm, deciding symbolic trace equivalence.