Extending megrelishvili protocol for multi-party key agreement

Megrelishvili protocol is a linear algebraic-based key agreement whose security does not rely on the generic discrete logarithm problem in a particular group. Consequently, this protocol offers an alternative method for establishing a mutual key between two parties. Nevertheless, its original scheme only admits a pair of participants to construct a shared secret key. In this paper we present a generalization of the two-party Megrelishvili protocol to multiple participants. In particular, we propose two schemes of the multi-party Megrelishvili protocol and analyze their computational characteristics. Furthermore, we introduce the multi-party Megrelishvili shared key problem (MMSKP) as a mathematical problem that underlies the security of our proposed protocol. Based on this idea, we conjecture that the multi-party Megrelishvili protocol is at least as secure as its two-party counterpart.