Using the Modified Diffie–Hellman Problem to Enhance Client Computational Performance in a Three-Party Authenticated Key Agreement

Abstract

A three-party authenticated key agreement (3PAKA) scheme is a protocol that enables a pair of registered clients to establish session keys via the help of a trusted server such that each client pre-shares its secret key with the server only. This approach greatly improves the scalability of key agreement protocols and provides better user convenience. Conventionally, 3PAKA-like many other key agreement schemes are based on the classic computational Diffie–Hellman problem (CDHP) to establish the session keys, and each client requires at least two modular exponentiations. However, as more and more mobile devices with limited resources are becoming popular, it is desirable to reduce the computational load for those clients while still preserving its strong security. In this paper, based on the modified CDHP, we propose new 3PAKA schemes which require only four message steps and reduce clients’ exponentiation computations up to 50%, compared to those schemes that are based on the CDHP and provide the same functions. The security of the proposed schemes is formally proved. The excellent performance makes them very attractive to those clients with limited resources.