Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  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 )a nd Williams (25) to the ll-known RSA cryptosystem. Thanks to the spe- cial properties of such schemes,  obtain efficiency 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.  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 assump- tion 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 efficient in encryption, and presents higher bandwith, achieving the same expansion factor as Paillier or El Gamal schemes.  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.
['David Galindo', 'Sebastiá Martýn', 'Paz Morillo', 'Jorge L. Villar']
I am writing a research paper on a idea A Practical Public Key Cryptosystem from Paillier and Rabin Schemes
[{"from": "human", "value": "I am writing a research paper on a idea A Practical Public Key Cryptosystem from Paillier and Rabin Schemes"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  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 )a nd Williams (25) to the ll-known RSA cryptosystem. Thanks to the spe- cial properties of such schemes,  obtain efficiency 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.  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 assump- tion 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 efficient in encryption, and presents higher bandwith, achieving the same expansion factor as Paillier or El Gamal schemes.  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."}]