Paper 2005/285 Original: eprint.iacr.org/2005/285 ↗

Generalizations of RSA public key cryptosystems

Abstract

In this paper, for given $N=pq$ with $p$ and $q$ different primes and a unimodular polynomial with coefficients in ${\Bbb Z}$ mod $N$, we give a public key cryptosystem. When the degree of the polynomial is $1$, the system is just the famous RSA system. And when the degree bigger than $1$, the system is usually more secure than the original RSA systems. Some part-correct systems are introduced so that the period of any message in these systems under the Simmons attack are bigger than that of any message in the RSA system.