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.
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