Research On Certificate-based Verifiably Encrypted Signature Andmessage Recovery Signature

Certificate-based public key cryptography combines the merits of traditional public key cryptography(PKC) and identity-based cryptography(IBC). It not only simplifies the certificate management problem in traditional public key cryptology, but also overcomes the key escrow problem in identity-based cryptography. So it becomes a new direction of research in public key cryptography.Verifiably encrypted signature(VES) system consists of three parties: the signer, the verifier, the trusted third party(the adjudicator). The signer generates the VES by encrypting an ordinary signature under a third party’s public key and proved that the resulting ciphertext do contains such a signature. The verifier can verify that the signer has signed the message, but cannot deduce any information about his signature. Later in the protocol, if the signer is unable or unwilling to reveal his signature, the verifier can ask the third party to reveal the signer’s signature.In networks with limited bandwidth and lightweight mobile devices, long digital signatures will obviously be a drawback. A digital signature with message recovery is a signature that the message itself is not required to be transmitted together with the signature. Comparing with other digital signatures, it has the advantage of small data size. So message recovery signature can be used for the bandwidth restricted areas.In this paper, a new certificate-based verifiably encrypted signature(CBVES) scheme is proposed by combining the VES with certificate-based signature(CBS). It can solve the unfairness exposed on online transaction effectively. Firstly, the security model of certificate-based verifiably encrypted signature scheme is defined, and a new efficient CBVES scheme is proposed based on the hardness of collision attack algorithm with k traitors problem and Square Computational Differ-Hellman problem, its safety is proved under the random oracle model. Secondly, we combine the advantages of verifiably encrypted signature and the certificateless signature(CLS) scheme proposed by Chen et al., construct a strong secure certificateless verifiably encrypted signature(CLVES) scheme which security is analyzed. We build a CBVES scheme from a CLVES scheme based on the property that the CLS scheme and CBS scheme can transform into each other in certain circumstances. Finally, a new certificate-based with message recovery signature scheme is proposed based on the hardness of Computational Differ-Hellman problem, and its safety is proved under the random oracle model.