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Indistinguishability against adaptive chosen ciphertext attack (IND-CCA2) is the strongest notion for security of public key schemes. In this paper, we present the first IND-CCA2 schemes whose securities are equivalent to factoring n = pq under the random oracle model, where p and q are prime numbers. Our first scheme works for long messages and our second scheme is more efficient for short messages.

IND-CCA Public Key Schemes Equivalent to Factoring n =pq