An elliptic curve analogue of McCurley's key agreement scheme

Abstract

McCurley's key agreement scheme is a variation on the well known Diffie-Hellman scheme with enhanced security. In McCurley's scheme a successful attacker must be able to break the ordinary Diffie-Hellman scheme and also factorise large numbers. This paper presents an analogue of McCurley's scheme using elliptic curves. A consequence is that a method to break ordinary Diffie-Hellman would not be applicable to our scheme. An advantage of our scheme over McCurley's is that much smaller key lengths can be used.