A Novel Cryptosystem Based on General Linear Group

Abstract

In this article, we have developed a novel public-key cryptosystem that uses large abelian subgroup of general linear group over residue ring. The merit of this proposed public key cryptosystem is that we can select session key in abelian subgroup of general linear group which reduces exponentiations and performed encryption effectively in a simple way. Our algorithm doesn't use matrix modular exponentiation which leads us to problem in implementing. The aim of this article is to decrease the number of these exponentiations and consequently to accelerate the execution of encryption algorithm. A discussion about the security of built modifications made in the article shows that the level of security is high enough for an appropriate choice of parameters of the cryptosystems.