We study the problem of analysing the security for an unbounded number of concurrent sessions of a cryptographic protocol. Our formal model accounts for an arbitrary number of agents involved in a protocol-exchange which is subverted by a Dolev-Yao attacker. We define the parameterised model checking problem with respect to security requirements expressed in temporal-epistemic logics. We formulate sufficient conditions for solving this problem, by analysing several finite models of the system. We primarily explore authentication and key-establishment as part of a larger class of protocols and security requirements amenable to our methodology. We introduce a tool implementing the technique, and we validate it by verifying the NSPK and ASRPC protocols
