David Baelde

David Baelde, Stéphanie Delaune, Lucca Hirschi

Formal methods have proved effective to automatically analyze protocols. Over the past years, much research has focused on verifying trace equivalence on protocols, which is notably used to model many interesting privacy properties, e.g., anonymity or unlinkability. Many tools for checking trace equivalence rely on a naive and expensive exploration of all interleavings of concurrent actions, which calls for partial-order reduction (POR) techniques. In this paper, we present the first POR technique for protocol equivalences that does not rely on an action-determinism assumption: we recast the trace equivalence problem as a reachability problem, to which persistent and sleep set techniques can be applied, and we show how to effectively apply these results in the context of symbolic executions. We report on a prototype implementation, improving the tool DeepSec.

Lucca Hirschi, David Baelde, Stéphanie Delaune

In this paper, we consider the problem of verifying anonymity and unlinkability in the symbolic model, where protocols are represented as processes in a variant of the applied pi calculus, notably used in the ProVerif tool. Existing tools and techniques do not allow to verify directly these properties, expressed as behavioral equivalences. We propose a different approach: we design two conditions on protocols which are sufficient to ensure anonymity and unlinkability, and which can then be effectively checked automatically using ProVerif. Our two conditions correspond to two broad classes of attacks on unlinkability, i.e. data and control-flow leaks. This theoretical result is general enough that it applies to a wide class of protocols based on a variety of cryptographic primitives. In particular, using our tool, UKano, we provide the first formal security proofs of protocols such as BAC and PACE (e-passport), Hash-Lock (RFID authentication), etc. Our work has also lead to the discovery of new attacks, including one on the LAK protocol (RFID authentication) which was previously claimed to be unlinkable (in a weak sense).

David Baelde, Stéphanie Delaune, Lucca Hirschi

Security protocols are concurrent processes that communicate using cryptography with the aim of achieving various security properties. Recent work on their formal verification has brought procedures and tools for deciding trace equivalence properties (e.g., anonymity, unlinkability, vote secrecy) for a bounded number of sessions. However, these procedures are based on a naive symbolic exploration of all traces of the considered processes which, unsurprisingly, greatly limits the scalability and practical impact of the verification tools. In this paper, we overcome this difficulty by developing partial order reduction techniques for the verification of security protocols. We provide reduced transition systems that optimally eliminate redundant traces, and which are adequate for model-checking trace equivalence properties of protocols by means of symbolic execution. We have implemented our reductions in the tool Apte, and demonstrated that it achieves the expected speedup on various protocols.

David Baelde, Stéphanie Delaune, Lucca Hirschi

Many privacy-type properties of security protocols can be modelled using trace equivalence properties in suitable process algebras. It has been shown that such properties can be decided for interesting classes of finite processes (i.e., without replication) by means of symbolic execution and constraint solving. However, this does not suffice to obtain practical tools. Current prototypes suffer from a classical combinatorial explosion problem caused by the exploration of many interleavings in the behaviour of processes. Mödersheim et al. have tackled this problem for reachability properties using partial order reduction techniques. We revisit their work, generalize it and adapt it for equivalence checking. We obtain an optimization in the form of a reduced symbolic semantics that eliminates redundant interleavings on the fly.