In 2003

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

a third part signs a certification on an applicant’s public key or identity and sends the certification to the applicant

the applicant saves it and uses it as a partial private key (decryption key).A receiver needs the certification from the third party and his own public-private keys to decrypt a ciphertext

so CBE scheme combines the best aspects of identity-based encryption (implicit certification) and public-key encryption (no key escrow).We present an efficient and tight certificate-based public-key hybrid encryption scheme

which can be proved satisfying adaptive chosen ciphertext attack security without random oracle.