Authenticated Distributed Group Key Agreement Protocol Using Elliptic Curve Secret Sharing Scheme

Abstract

One of the fundamental construction blocks in safeguarding group communications is group key establishment protocols. Group key agreement protocols are more suitable for distributed environments where the participant from various places can agree upon the group key. Group key related information is distributed to various group participants, mostly using techniques such as using polynomials, bilinear pairing, and secret sharing scheme (SSS). Out of these, secret sharing schemes are more efficient compared to other techniques. Recent growth in Internet of things (IoT) related applications stresses the need for such key agreement protocols in resource-constrained environments. Elliptic curves are quite popular in resource-constrained environments to produce enough security with smaller key sizes. Elliptic curve secret sharing scheme (ECSSS) is proposed in this paper for resource-constrained environments. Using the same scheme, Authenticated distributed group key agreement protocol using Elliptic curve secret sharing scheme (ADGKAP) is proposed, which can be used as a group key agreement protocol, and the group key related information is shared using ECSSS. To the best of our knowledge, we know no group key agreement protocol in the literature that uses ECSSS in a distributed environment. Our proposed ADGKAP provides equal security with less key size, storage space, faster computation, and less computational cost without compromising on the number of rounds compared to existing schemes. This scheme security relies on the Elliptic curve discrete logarithm problem (ECDLP), and the security analysis of the scheme is discussed.

Keywords

• Secret sharing scheme (SSS)
• key agreement protocol (KAP)
• group key agreement protocol (GKAP)
• elliptic curve (EC)
• elliptic curve discrete logarithm (ECDLP)