For construction a public cryptosystem that requiring fewer infrastructures than public key infrastructure（PKI）

a certificate-based public-key encryption（CBE） scheme was proposed by Gentry.In CBE scheme

a certification was signed by a third part on an applicant’s public key or identity and sent to the applicant

the applicant saved it and used it as partial private key（decryption key）.A receiver wanted to decrypt a ciphertext

the certification was needed from the third party and his own public-private keys

so CBE combined the best aspects of identity-based encryption（implicit cer-tification） and public key encryption（no escrow）.A new efficient certificate-based hybrid encryption scheme with short public key was proposed

which based on Gentry’s identity-based encryption scheme

the new scheme can be proved re-sistance adaptive chosen ciphertext attack in the standard model（without random oracle）.