Sigma Identification Protocol Construction Based on MPF Defined over Non-Commuting Platform Group

Abstract

In this paper, we present the construction of a sigma identification protocol based on matrix power function (MPF) defined over a certain non-commuting platform group. We use the previously defined templates for generating public parameters of our protocol to overcome the problem that a two-sided MPF in general is not associative. We prove that the proposed sigma identification protocol is resistant to eavesdropping adversary attacks. Furthermore, relying on the asymptotic knowledge soundness property proven in this paper, we show that our protocol is also resistant against active adversary attacks with an overwhelming probability.