In this paper, we propose a new “full public verifiability” concept for hybrid public-key encryption schemes. We also present a new hybrid public-key encryption scheme that has this feature, which is based on the decisional bilinear Diffie–Hellman assumption. We have proven that the new hybrid public-key encryption scheme is secure against adaptive chosen ciphertext attack in the standard model. The “full public verifiability”feature means that the new scheme has a shorter ciphertext and reduces the security requirements of the symmetric encryption scheme. Therefore, our new scheme does not need any message authentication code, even when the one-time symmetric encryption scheme is passive attacks secure. Compared with all existing publickey encryption schemes that are secure to the adaptive chosen ciphertext attack, our new scheme has a shorter ciphertext, efficient tight security reduction, and fewer requirements(if the symmetric encryption scheme can resist passive attacks). We also present a new hybrid public-key encryption scheme that has this feature, which is based on the decisional bilinear Diffie-Hellman We have proven that the new hybrid public-key encryption scheme is secure against adaptive chosen ciphertext attack in the standard model. The “full public verifiability” feature means that the new scheme has a shorter ciphertext and reduces the security requirements of Thus, our new scheme does not need any message authentication code, even when the one-time symmetric encryption scheme is passive attacks secure, compared with all existing public -key encryption schemes that are secure to the adaptive chosen ciphertext attack, our new scheme has a shorter ciphertext, efficient tight security reduction, and fewer requirements (if the symmetric encryption scheme can resist passive attacks).