Programming with rewrite rules and strategies has been already used for describing several computational logics. This paper describes the way the Needham-Schroeder Public-Key protocol is specified in ELAN, the system developed in Nancy to model and compute in the rewriting calculus. The protocol aims to establish a mutual authentication between an initiator and a responder that communicate via an insecure network. The protocol has been shown to be vulnerable and a correction has been proposed. The behavior of the agents and of the intruders as well as the security invariants the protocol should verify are naturally described by conditional rewrite rules whose application is controlled by strategies. Similar attacks to those already described in the literature have been discovered. We show how different strategies using the same set of rewrite rules can improve the efficiency in finding the attacks and we compare our results to existing approaches.