This paper focuses on the instantiation of random oracles in public key encryption schemes. A misunderstanding in the former instantiations is pointed out and analyzed. A method of using this primitive as a substitution of random oracles is also proposed. The partial and full instantiations of random oracles in optimal asymmetric encryption padding (OAEP) implemented by pseudorandom functions are described and the resulted schemes are proven to be indistinguishable secure against adaptive chosen ciphertext attack (IND-CCA2) secure. Using this method, one can transform a practical public key encryption scheme secure in the random oracle model into a standard-model secure scheme. The security of the scheme is based on computational assumptions, which is weaker than decisional assumptions used in CramerShoup like schemes.
