From Plaintext-Extractability to IND-CCA Security

We say a public-key encryption is plaintext-extractable in the random oracle model if there exists an algorithm that given access to the input/output of all queries to the random oracles can simulate the decryption oracle. We argue that the plaintext-extractability is enough to show the indistinguishably under chosen ciphertext attack (IND-CCA) of OAEP+ transform (Shoup, Crypto 2001) when the underlying trapdoor permutation is one-way. We extend the result to the quantum random oracle model (QROM) and show that OAEP+ is IND-CCA secure in QROM if the underlying trapdoor permutation is quantum one-way.