New probabilistic public-key encryption based on the RSA cryptosystem

We propose a novel probabilistic public-key encryption, based on the RSA cryptosystem. We prove that in contrast to the (standardmodel) RSA cryptosystem each user can choose his own encryption exponent from a more extensive set of positive integers than it can be done by the creator of the concrete RSA cryptosystem who chooses and distributes encryption keys among all users. Moreover, we show that the proposed encryption remains secure even in the case when the adversary knows the factors of the modulus n = pq, where p and q are distinct primes. So, the security assumptions are stronger for the proposed encryption than for the RSA cryptosystem. More exactly, the adversary can break the proposed scheme if he can solve the general prime factorization problem for positive integers, in particular for the modulus n = pq and the Euler functionφ(n) = (p − 1)(q − 1). In fact, theproposed encryptiondoesnot use any extra tools or functions compared to the RSA cryptosystem.