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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 w.r.t. a modulus with at least 768 bits and a 160-bit exponent. Decryption can be suitably opti- mized so as to become less demanding than a couple RSA decryptions. Although slower than RSA, the new scheme is still reasonably compet- itive and has several specific applications. The probabilistic version ex- hibits an homomorphic encryption scheme whose expansion rate is much better than previously proposed such systems. Furthermore, it has se- mantic security, relative to the hardness of computing higher residues for suitable moduli.

A new public key cryptosystem based on higher residues