Summary: This paper proposes a generic construction that yields encryption schemes that are secure against adaptive chosen ciphertext attacks. In particular, we focus on combining weak encryption schemes with proofs of knowledge made non-interactive through the use of a hash function. This type of conversion yields encryption schemes that allow anybody to verify the integrity of the ciphertexts. A typical example is a combination of ElGamal encryption with the Schnorr proof of knowledge, but a straightforward combination requires a stronger assumption than the random oracle assumption to prove the security. We first generalize a class of encryption schemes and proofs of knowledge to key-encapsulation schemes and signature schemes, and then present a secure way of combining them so that the security of the resulting scheme can be proven solely in the random oracle model.