Database encryption is essential for cloud database systems. For a large database, decryption could take a lot of computational time. Therefore, verifying an encryption that contains a correct plaintext without decryption becomes significant for a large database system. Plaintext-checkable encryption (PCE) is a potential tool for such database systems, which is first proposed by Canard et al. in CT-RSA 2012. Although the generic PCE in the random oracle model has been studied intensively, the generic PCE in the standard model and its efficient implementation are still challenging problems. This paper presents the first generic PCE in the standard model using smooth projective hash function (SPHF) and prove its s-priv1-cca security, which is independent of current unlink security. Based on the instantiated SPHF from DDH assumption, we obtain the most efficient PCE in the standard model, without any pairing operation. Finally, we improve two existing generic constructions in the random oracle model so that they are secure under chosen ciphertext attack.