The Research On Digital Signature Schemes And Signcryption Schemes Based On Elliptic Curves

With the rapid development of information technique and the large-scale application of network technique, information security is becoming more and more important, and is becoming a generally concerned research topic in domestic and international computer and network application field. As the main means of the authentication, the digital signature has provided an important technique for information security.In 1985, Koblitz and Miller independently proposed using the group of points on an elliptic curve defined over a finite field to construct cryptosystem, which is elliptic curves cryptosystems(ECC). The signcryption scheme based on elliptic curves combines encryption,decryption> digital signature technology, which needs less communication and computation than encryption,decryptions digital signature separately. In this paper, the certificate-based digital signature scheme and identity-based digital signature scheme are discussed. The main works are as follows:The public key cryptosystems and the certificate-based digital signature scheme and identity-based digital signature scheme on elliptic curve are introduced.Among the certificate-based digital signcryption schemes based on elliptic curves , as a example of Zhao's digital signcryption scheme ,the paper describes that Zhao's scheme does not all satisfy secure requirements of digital signcryption schemes .To get over the drawbacks of Zhao's scheme ,the paper proposed an ideal digital signcryption scheme which satisfies the confidentiality,integrality,unforgeability signature,authentications non-repudiations forward security,public verification of ciphers resist Bob's evil forge signature scheme.The paper proposes a new digital signature scheme based on the properties of bilinear pairing, the scheme satisfies security of digital signcryption simultaneously, such as public verification and forward security, which does not need double private keys. And then, applying this technology to identity-based threshold signcryption scheme, security of scheme is same.Comparing identity-based cryptosystems with certificate-based cryptosystems, the advantages and inherent drawbacks of existent identity-based cryptosystems are analyzed . And then, a new secure key issuing protocol based on the difficult problem of ellipse (CDLP, CDHP) and the properties of bilinear pairing are proposed, which doesn't require certificates to guarantee the authenticity of public keys and doesn't require key escrow. At last, a security and performance analyses of new Chan-Cheon signature scheme are given.