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In this paper, we study some RSA-based semantically secure encryption schemes (IND-CPA) in the standard model. We first derive the exactly tight one-wayness of Rabin-Paillier encryption scheme which assumes that factoring Blum integers is hard. We next propose the first IND-CPA scheme whose one-wayness is equivalent to factoring generaln=pq (not factoring Blum integers). Our reductions of one-wayness are very tight because they require only one decryption-oracle query.

Some RSA-Based Encryption Schemes with Tight Security Reduction