journal-of-discrete-mathematical-sciences-and-cryptography Journal of Discrete Mathematical Sciences and Cryptography 2169-0065 0972-0529 Taru Publications 10.1080/09720529.2021.2020428 McEliece and Blum-Goldwasser group rings based probabilistic cryptosystems Mittal Gaurav Defense Research and Development Organisation, Near Metcalfe House, Civil Lines, New Delhi , 110054, India Department of Mathematics, Indian Institute of Technology Roorkee, Roorkee, India Kumar Sandeep Defense Research and Development Organisation, Near Metcalfe House, Civil Lines, New Delhi, 110054, India Kumar Sunil Defense Research and Development Organisation, Near Metcalfe House, Civil Lines, New Delhi 110054, India Narain Shiv Department of Mathematics, Arya P. G. College, Panipat, Haryana, India 26 8 2229 2242 30 03 2022

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.

 Group ring Units Cryptography Public key cryptography access open retracted no