Verifiable Public Key Certificateless Public Key Cryptosystem

In 1976,Diffie and Hellman first proposed the concept of public key cryptosystem.It can be said that the public key cryptosystem is the most revolutionary achievement in the history of cryptography.However,there are public key authentication in public key cryptosystem.In public key infrastructure,the problem of public key authentication is solved by dig-ital certificate.Although a public key can be authenticated by a certificate,the certificate also brings some problems such as how to send the certificate,the storage of the certifi-cate and the abolishment or revocation of the certificate.In order to solve the problem of certificate management,Shamir proposed a identity-based public key cryptosystem.In the system,a user's public key is derived through its unique identity information,so no authentication.However,the user's private key is generated by the secret key genera-tor center,with secret key escrow problem.In order to solve the problems of certificate management and key escrow,Al-Riyami and Paterson propose a certificateless public key encryption scheme,and prove its security in the random oracle model.For a long time,a large number of certificateless public key encryption schemes have been developed,but many of them have security problems.Therefore,The focus of cryptographers is propose an efficient and provably secure certificateless public key encryption scheme.In this paper,we further study and discuss certificateless public key encryption,and obtain the following results:? Baek,Safavi-Naini and Susilo proposed a certificateless public key cryptosystem with-out bilinear pairings.In the process of proving that the CLPKE scheme is IND-CCA secure against the Type I attacker in the random oracle model,there are some theo-retical errors,and the security proof is not given against the Type II attacker.In this paper,we first point out and solve the problems in the process of security proof,and prove the CLPKE scheme is also IND-CCA secure against the Type two attacker in the random oracle model.? Al-Riyami and Paterson give a certificateless public key cryptosystem based on bilin-ear pairings.In this paper,we propose a certificateless public key encryption scheme without bilinear operation by using Schnorr signature.The public key of the scheme can only be verified by the sender.According to the trust level defined by Girault for the third party trust institution TTP,the scheme achieves the same level as the pub-lic key infrastructure PKI,with the level of third.In addition,our scheme is IND-CCA secure in the random oracle model,assuming the CDH problem is intractable.