Normal Proofs in Intruder Theories

Given an arbitrary intruder deduction capability, modeled as an inference system S and a protocol, we show how to compute an inference system b S such that the security problem for an unbounded number of sessions is equivalent to the deducibility of some message in b S. Then, assuming that S has some subformula property, we lift such a property to b S, thanks to a proof normalisation theorem. In general, for an unbounded number of sessions, this provides with a complete deduction strategy. In case of a bounded number of sessions, our theorem implies that the security problem is co-NP-complete. As an instance of our result we get a decision algorithm for the theory of blind-signatures, which, to our knowledge, was not known before.