We consider the problem of constructing public-key encryption (PKE) schemes that are resilient to a-posteriori chosen-ciphertext and key-leakage attacks (LR-CCA2). In CTYPTO'09, Naor and Segev proved that the Naor-Yung generic construction of PKE which is secure against chosen-ciphertext attack (CCA2) is also secure against key-leakage attacks. They also presented a variant of the Cramer-Shoup cryptosystem, and showed that this PKE scheme is LR-CCA2-secure under the decisional Diffie-Hellman assumption. In this paper, we apply the generic construction of “Universal Hash Proofs and a Paradigm for Adaptive Chosen Ciphertext Secure Public-Key Encryption” (EUROCRYPT'02) to generalize the above work of Naor-Segev. In comparing to the first construction of Naor-Segev, ours is more efficient because of not using simulation-sound NIZK. We also extend it to stateful PKE schemes. Concretely, we present the notion of LR-CCA2 attack in the case of stateful PKE, and a generic construction of stateful PKE that is secure against this attack.