Group ring based public key cryptosystems

TL;DR

This paper introduces two new public key cryptosystems based on group rings, claiming enhanced security over existing elliptic curve and ElGamal cryptosystems, with practical examples provided.

Contribution

It presents novel cryptosystems based on group rings that offer greater security than traditional elliptic curve and ElGamal cryptosystems.

Findings

Proposed elliptic ElGamal type group ring cryptosystem with higher security

ElGamal type group ring cryptosystem with improved security

Examples demonstrating the cryptosystems' implementation

Abstract

In this paper, we propose two cryptosystems based on group rings and existing cryptosystem. First one is Elliptic ElGamal type group ring public key cryptosystem whose security is greater than security of cryptosystems based on elliptic curves discrete logarithmic problem (ECDLP). Second is ElGamal type group ring public key cryptosystem, which is analogous to ElGamal public key cryptosystem but has comparatively greater security. Examples are also given for both the proposed cryptosystems.