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We propose a practical scheme based on factoring and se- mantically secure (IND-CPA) in the standard model. The scheme is obtained from a modification of the so called RSA-Paillier (5) scheme. This modification is reminiscent of the ones applied by Rabin (22) and Williams (25) to the well-known RSA cryptosystem. Thanks to the spe- cial properties of such schemes, we obtain eciency similar to that of RSA cryptosystem, provably secure encryption (since recovering plain- text from ciphertext is as hard as factoring) and indistinguishability against plaintext attacks. We also construct a new trapdoor permuta- tion based on factoring, which has interest on its own. Semantic security of the scheme is based on an appropiate decisional assumption, named as Decisional Small 2e-Residues assumption. The robustness of this as- sumption is also discussed. Compared to Okamoto-Uchiyama's scheme (18), the previous IND-CPA cryptosystem in the standard model with one-wayness based on factoring, our scheme is drastically more ecient in encryption, and presents higher bandwith, achieving the same expansion factor as Paillier or El Gamal schemes. We believe the new scheme could be an interesting starting point to develop ecient IND-CCA schemes in the standard model with one-wayness based on factoring.

A Practical Public Key Cryptosystem from Paillier and Rabin Schemes