Combining algorithms for deciding knowledge in security protocols

International audienceIn formal approaches, messages sent over a network are usu- ally modeled by terms together with an equational theory, axiomatiz- ing the properties of the cryptographic functions (encryption, exclusive or, . . . ). The analysis of cryptographic protocols requires a precise un- derstanding of the attacker knowledge. Two standard notions are usu- ally considered: deducibility and indistinguishability. Those notions are well-studied and several decidability results already exist to deal with a variety of equational theories. However most of the results are dedicated to specific equational theories. We show that decidability results can be easily combined for any disjoint equational theories: if the deducibility and indistinguishability relations are decidable for two disjoint theories, they are also decidable for their union. As an application, new decidability results can be obtained using this combination theorem