Abstract. We propose a practical scheme based on factoring and semantically secure (IND-CPA) in the standard model. The scheme is obtained from a modification of the so called RSA-Paillier  scheme. This modification is reminiscent of the ones applied by Rabin  and Williams  to the well-known RSA cryptosystem. Thanks to the special properties of such schemes, we obtain efficiency similar to that of RSA cryptosystem, provably secure encryption (since recovering plaintext from ciphertext is as hard as factoring) and indistinguishability against plaintext attacks. We also construct a new trapdoor permutation 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 assumption is also discussed. Compared to Okamoto-Uchiyama’s scheme , the previous IND-CPA cryptosystem in the standard model with one-wayness based on factoring, our scheme is drastically more efficient 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 efficient IND-CCA schemes in the standard model with one-wayness based on factoring
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