Computing knowledge in security protocols under convergent equational theories

Stefan Ciobaca (1) , Stéphanie Delaune (1, 2) , Steve Kremer (2, 3)

1 LSV - Laboratoire Spécification et Vérification [Cachan]
2 SECSI - Security of information systems
3 CASSIS - Combination of approaches to the security of infinite states systems

The analysis of security protocols requires reasoning about the knowledge an attacker acquires by eavesdropping on network traffic. In formal approaches, the messages exchanged over the network are modeled by a term algebra equipped with an equational theory axiomatizing the properties of the cryptographic primitives (e.g. encryption, signature). In this context, two classical notions of knowledge, deducibility and indistinguishability, yield corresponding decision problems.\par We propose a procedure for both problems under arbitrary convergent equational theories. Since the underlying problems are undecidable we cannot guarantee termination. Nevertheless, our procedure terminates on a wide range of equational theories. In particular, we obtain a new decidability result for a theory we encountered when studying electronic voting protocols. We also provide a prototype implementation.

Domaines: Cryptographie et sécurité [cs.CR]

Stefan Ciobaca, Stéphanie Delaune, Steve Kremer. Computing knowledge in security protocols under convergent equational theories. Journal of Automated Reasoning, 2012, 48 (2), pp.219-262. ⟨10.1007/s10817-010-9197-7⟩. ⟨inria-00636794⟩