In this paper, we present a new methodology, called a random oracle (RO) transformation, for designing IND-CCA secure PKE schemes in the standard model from schemes in the RO model. Unlike the RO methodology [3], [19], the security of the original scheme in the RO model does not necessarily have to be identical with that of the scheme resulting from the RO transformation. We then introduce a new notion, IND-INS-CCA security, and show how to obtain IND-CCA secure PKE schemes by instantiating ROs in IND-INS-CCA secure PKE schemes. Furthermore, we introduce another new notion, a strong pseudorandom function (PRF) family associated with a trapdoor one-way permutation generator (briefly, -SPRF family), which can be regarded as an enhanced PRF family, so that the resulting PKE scheme becomes quite practical.