The authors show that two well-known and widely employed public-key encryption schemes - RSA optimal asymmetric encryption padding (RSA-OAEP) and Diffie-Hellman integrated encryption scheme (DHIES), instantiated with a one-time pad, - are secure under (the strong, simulation-based security notion of) selective opening security against chosen-ciphertext attacks in the random oracle model. Both schemes are obtained via known generic transformations that transform relatively weak primitives (with security in the sense of one-wayness) to indistinguishability (IND)-CCA secure encryption schemes. The authors also show a similar result for the well-known Fujisaki-Okamoto transformation that can generically turn a one-way secure public key encryption system and a one-time pad into a IND-CCA-secure public-key encryption system. The authors prove that selective opening security comes for free in these transformations. Both DHIES and RSA-OAEP are important building blocks in several standards for public key encryption and key exchange protocols. The Fujisaki-Okamoto transformation is very versatile and has successfully been utilised to build efficient lattice-based cryptosystems. The considered schemes are the first practical cryptosystems that meet the strong notion of simulation-based selective opening (SIM-SO-CCA) security.