Adaptively-Secure Authenticated Key Exchange Protocol in Standard Model

Design a Secure Authenticated Key Exchange (AKE) protocol is a wide research area. Many works have been done in this field and remain few open problems. Design an AKE-secure without NAXOS approach is remaining as an open problem. NAXOS approach [18] is used to hide the ephemeral secret key from an adversary even if the adversary in somehow may obtain the ephemeral secret key. Using NAXOS approach will cause two main drawbacks, (1) leaking of the static secret key which will be used in computing the exponent of the ephemeral public key. (2) Maximize of using random oracle when applying to the exponent of the ephemeral public key and session key derivation. Another open problem is designing an AKE-secure in the standard model without relying on Pseudo-Random Function with Pairwise-Independent Random Sources. In this paper, we present a general construction for AKE-secure protocol from the projective hash family secures under hard subset membership problem in the standard model. We also give an instantiation of our protocol from DDH with a novel security proof from games sequences tool introduced by [24]. We show the efficiency of our protocol compares to other similar AKE protocol.