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

Aleksejus Mihalkovich, Kestutis Luksys and Eligijus Sakalauskas
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Aleksejus Mihalkovich: Department of Applied Mathematics, Faculty of Mathematics and Natural Sciences, Kaunas University of Technology, 44249 Kaunas, Lithuania
Kestutis Luksys: Department of Applied Mathematics, Faculty of Mathematics and Natural Sciences, Kaunas University of Technology, 44249 Kaunas, Lithuania
Eligijus Sakalauskas: Department of Applied Mathematics, Faculty of Mathematics and Natural Sciences, Kaunas University of Technology, 44249 Kaunas, Lithuania

Mathematics, 2022, vol. 10, issue 15, 1-15

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.

Keywords: sigma identification protocol; matrix power function; non-commuting cryptography (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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