Deciding security properties for cryptographic protocols. application to key cycles

Authors:
Hubert Comon-Lundh;Véronique Cortier;Eugen Zălinescu
Affiliations:
ENS CACHAN and Research Center for Information Security, AIST;LORIA, CNRS, Université Henri Poincaré, and INRIA Project CASSIS;MSR-INRIA Joint Centre, Orsay
Venue:
ACM Transactions on Computational Logic (TOCL)
Year:
2010

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Abstract

There is a large amount of work dedicated to the formal verification of security protocols. In this article, we revisit and extend the NP-complete decision procedure for a bounded number of sessions. We use a, now standard, deducibility constraint formalism for modeling security protocols. Our first contribution is to give a simple set of constraint simplification rules, that allows to reduce any deducibility constraint to a set of solved forms, representing all solutions (within the bound on sessions). As a consequence, we prove that deciding the existence of key cycles is NP-complete for a bounded number of sessions. The problem of key-cycles has been put forward by recent works relating computational and symbolic models. The so-called soundness of the symbolic model requires indeed that no key cycle (e.g., enc(k, k)) ever occurs in the execution of the protocol. Otherwise, stronger security assumptions (such as KDM-security) are required. We show that our decision procedure can also be applied to prove again the decidability of authentication-like properties and the decidability of a significant fragment of protocols with timestamps.