Secure lightweight multi‐party key agreement based on hyperelliptic curve Diffie–Hellman for constraint networks

Abstract

AbstractWith recent developments in hyperelliptic curve cryptographic system (HECC) processing and the proposed work, the myth that HECC is not suited for practical applications in constrained networks is dispelled. This article proposes dynamic authenticated contributory group key agreement (DACGKA) protocol using HEC‐DH. The DACGKA is less costly and ideally appropriate for resource‐restricted networks such as VANETs, MANETs, and WSNs because of its lesser key sizes and advancements in operational processing. The suggested protocol is implemented across a finite field using an HEC of genus 1 (ECC), genus 2, and genus 3, with promising results, including a significant reduction in key size and exchange overhead, an increase in key safety, and a broader range of applicability. According to a comparison of the proposed approach on different genus curves, HECC over genus 2 with a suitable key length can be applied for memory and power restricted devices to increase data secrecy and system efficiency. Further, HECC can outperform ECC for low‐cost, secure group communication applications. As a part of security analysis, first, we proved that each coordinate of HEC‐DH secret value is as hard as the entire DH value, and then concrete security proofs based on the HEC‐DLP were established.