McEliece and Blum-Goldwasser group rings based probabilistic cryptosystems

Mittal, Gaurav; Kumar, Sandeep; Kumar, Sunil; Narain, Shiv

doi:10.1080/09720529.2021.2020428

Open Access Research Article

McEliece and Blum-Goldwasser group rings based probabilistic cryptosystems

^*Gaurav MittalCorresponding authorgaurav.mittaltwins@gmail.comDefense Research and Development Organisation Near Metcalfe House Civil Lines; Department of Mathematics Indian Institute of Technology RoorkeeDefence Research and Development Organization Near Metcalfe HouseCivil Lines, New Delhi, 110054, IndiaView full profile → , Sandeep Kumarsandeepkumar.hqr@gov.inDefense Research and Development Organisation Near Metcalfe House Civil LinesDefence Research and Development Organization Near Metcalfe HouseNew Delhi, New Delhi, 110054, India0009-0005-7107-3914View full profile → , Sunil Kumarsunilkumar.hqr@gov.inDefense Research and Development Organisation Near Metcalfe House Civil Lines New Delhi 110054 IndiaDefence Research and Development Organization Near Metcalfe HouseJaipur, New Delhi, 110054, IndiaView full profile → , Shiv Narainmath.shiv@gmail.comDepartment of Mathematics Arya P. G. CollegeDepartment of Mathematics Arya P.G. CollgePanipat, Haryana, 132103, IndiaView full profile →

* Corresponding author · click or hover a name for details

pp. 2229–2242Vol. 26Issue 8December 2023DOI: 10.1080/09720529.2021.2020428 Crossmark XML

Received:: 01 Jun 2021
Accepted:: 01 Nov 2021
Published Online:: 30 Mar 2022
Article type:: Research Article
Language:: EN
Article no.:: JDMSC-1534
Pages:: 2229–2242

Abstract

In this paper, we present two probabilistic public key cryptosystems (PKCs) based on the well known algebraic structure of group rings. The first cryptosystem is based on McEliece cryptosystem and we coin it as McEliece-group-ring based PKC. The second PKC is the extension of Blum-Goldwasser PKC in group rings and we name it as Blum-Goldwasser-group-ring based PKC. We carefully discuss the security analysis of the proposed PKCs and their advantages over the existing PKCs. Additionally, we consider the toy examples for both the cryptosystems in order to show the practicality of both the PKCs.

Keywords

Group ring Units Cryptography Public key cryptography

Subject Classifications

(2010) 94A6020C0520C07

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