Provable secure lightweight multiple shared key agreement based on hyper elliptic curve Diffie-Hellman for wireless sensor networks

摘要

In this paper, we propose a new protocol in which 2~(m~2) - 1 session keys can be generated when m public keys are exchanged in a one run of the aforesaid protocol based on the difficulty of the hyper elliptic curve discrete logarithm problem. In this work, we are implementing the proposed protocol using an hyper elliptic curve of genus 2 over a finite field and the results are very encouraging. The main advantages of the proposed protocol are a considerable decrease in keys exchange overhead, a further increase in the safety of the keys and broadening of applicability. A relative study among the proposed and existing protocols is made and acceptable results have been obtained. The proposed protocol is immune to known-key attack, replay attack, key compromise impersonation, forgery attack and key control. Further, an upper limit for the quantity of shared keys is obtained in terms of the number of keys exchanged and, in fact, we find a formula for the minimal required number of keys to be exchanged for a given number shared keys. Further we can easily provide session key authentication for various wireless users/ sessions on proposed protocol by integrating lightweight three-factor authentication scheme in the back ground.