Finite models for formal security proofs

Abstract

First-order logic models of security for cryptographic protocols, based on variants of the Dolev–Yao model, are now well-established tools. Given that we have checked a given security protocol π using a given first-order prover, how hard is it to extract a formally checkable proof of it, as required in, e.g., common criteria at the highest evaluation level (EAL7)? We demonstrate that this is surprisingly hard in the general case: the problem is non-recursive. Nonetheless, we show that we can instead extract finite models $\mathcal{M}$ from a set S of clauses representing π, automatically, and give two ways of doing so. We then define a model-checker testing $\mathcal{M}\vDash \mathit{S}$ , and show how we can instrument it to output a formally checkable proof, e.g., in Coq. Experience on a number of protocols shows that this is practical, and that even complex (secure) protocols modulo equational theories have small finite models, making our approach suitable.