Sigma Identification Protocol Construction Based on MPF

Abstract

A new sigma identification protocol (SIP) based on matrix power function (MPF) defined over the modified medial platform semigroup and power near-semiring is proposed. It is proved that MPF SIP is resistant against direct and eavesdropping attacks. Our security proof relies on the assumption that MPF defined in the paper is a candidate for one-way function (OWF). Therefore, the corresponding MPF problem is reckoned to be a difficult one. This conjecture is based on the results demonstrated in our previous studies, where a certain kind of MPF problem was proven to be NP-complete.

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

“…There, MPF was defined over the non-commuting medial semigroup, which by nature, is almost commuting. This property implies that the main MPF identity necessary to construct a SIP is valid together with the two-sided associativity of MPF [9]. In that paper, we have shown that the proposed SIP is resistant to passive impersonation attacks by demonstrating that our protocol is a special honest Verifier zero knowledge.…”

“…Our previous attempt to construct a SIP using MPF defined over a non-commuting semigroup was presented in [9]. There, MPF was defined over the non-commuting medial semigroup, which by nature, is almost commuting.…”

“…Our first attempt to present a working SIP based on MPF was made in [9]. Though it was a rather successful idea, our proposal lacked the proof of knowledge soundness property.…”