An Efficient and Secure Group Key Transfer Protocol based on Linear Secret Sharing Scheme

Abstract

Recently, many group key transfer(GKT) protocols based on Shamir’s secret sharing(SSS) have been proposed. In the traditional GKT protocols, all the group members shall register themselves into a key generation center (KGC) and also at the time of registration they had to share there long-term secret password with KGC. Then KGC would randomly select a group key and would securely distribute it to all the authorized group members. But in many conventional GKT protocols, to generate and to recover the secret group key, key generation centre (KGC) and each group member needs to compute a t-degree interpolating polynomial. In 2016, Hsu et al. gave a new and efficient group key transfer(GKT) protocol. In their scheme, the information related to group keys is hidden using Vandermonde
matrix and to distribute the group key efficiently they employed linear secret sharing scheme(LSSS) on Vandermonde matrix. But they adopted a common model where
group keys are issued and transmitted by an untrustworthy key generation center(KGC). In this paper, we propose an efficient and secure GKT protocol that has no mutually trusted KGC. To design our protocol we adopted the advantages of Diffie-Hellman(DH) scheme and to distribute the group key efficiently and securely we employed linear secret sharing scheme(LSSS) on alternant matrix. The security analysis shows that the proposed protocol can resist all the potential attacks. In addition, the comparison between the proposed scheme and other recent GKT protocols are also given in this article.