On the Generalizations of Megrelishvili Protocol for Group Key Distribution

Abstract

This article presents an extension of our previous research in <cite>AW17</cite> where we propose two variants of Megrelishvili key distribution schemes and investigate some of their elementary theoretical security analysis. We briefly discuss the two protocols in <cite>AW17</cite> and propose another two schemes which are more efficient than the preceding ones. Additionally, we also devise efficient procedures for constructing a new mutual key if the group membership is altered. Furthermore, we discuss the security of the protocols rigorously and we provide a sufficient condition for breaking the protocols by way of solving several instances of Megrelishvili vector-matrix problems (MVMP). We prove that the secret group key can be recovered easily if an attacker can express the sum of the secret exponents of the participants as a linear combination of the secret exponents excerpted from the transmission. Based on this result, we reason that our Megrelishvili key distribution schemes are theoretically at least as secure as the standard two-party Megrelishvili key exchange procedure.