Research On The Encryption And Digital Signature Schemes From Bilinear Pairings

Information security is one of the most important problems in modern information society and becomes a new important subject in the information science. The basic security services a information system should provide are: Confidentiality, integrity, Authentication and Non-repudiation. At present, Confidentiality can be achieved by Encryption, and Integrity, Authentication, and Non-repudiation can be achieved by Digital Signature.The bilinear pairings, namely Weil pairing and Tate pairing of algebraic curves were used in cryptography for the MOV attack and FR attack respectively. However, the situation has changed after Joux gave a simple tripartite one-round Diffie-Hellman key agreement protocol based on Weil pairing on supersingular curves. This was one of the breakthroughs in key agreement protocols. After this, Boneh etc. presented in 2001 an identity-based encryption scheme based on properties of bilinear pairings on elliptic curves, and proposed a basic signature scheme using pairing, which has the shortest length among signature schemes in classical cryptography. Henceforth, bilinear pairing becomes one of the most important tools to construct identity-based cryptosystem and various signature schemes.To date, the bilinear pairings is still in the stage of research, and there are many problems remain to be solved. Therefore, lucubration of encryption and signature scheme from bilinear pairings is very necessary.The main contributions are as follows:From the perspective of insuring authenticity of keys, traditionalPublic Key Infrastructure, Identity-based public key cryptosystem, Certificate-based encryption and Certificateless public key cryptosystem are introduced. Furthermore, their basic thread, advantages drawbacks are analyzed and compared respectively, and some development trends in the future are outlined.Discuss several classic encryption and signature schemes from bilinear pairing.On the basis of multilinear map, D.Boneh's one round multi-party key agreement protocol and Chameleon hash, a multi-designated verifiers signature scheme was proposed. The security analysis of the proposed scheme shows that it satisfies non-transferability, unforgeability, privacy of signer's identity and has low computational cost.An Identity-based convertible limited verifier signature scheme from bilinear pairing is proposed for the first time. we also showed that the scheme satisfies the unforgeability, and non-transferability properties. The proposed scheme has the advantages of Id-based cryptosystem and can be used to resolve the conflict between authenticity and privacy in the digital signature.