New public key cryptosystem based on higher residues

Abstract

This paper describes a new public-key cryptosystem based on the hardness of computing higher residues modulo a composite RSA integer. We introduce two versions of our scheme, one deterministic and the other probabilistic. The deterministic version is practically oriented: encryption amounts to a single exponentiation with respect to a modulus with at least 768 bits and a 160-bit exponent. Decryption can be suitably optimized so as to become less demanding than a couple RSA decryptions. Although slower than RSA, the new scheme is still reasonably competitive and has several specific applications. The probabilistic version exhibits an homomorphic encryption scheme whose expansion rate is much better than previously proposed such systems. Furthermore, it has semantic security, relative to the hardness of computing higher residues for suitable moduli.