The Design And Implementation Of Signature And Signcryption Scheme Based On Lattice

Now and in the future life, the main participant of information exchange will gradually replace paper documents by electronic documents. And signature will also translate from handwriting to a characteristic data, the electronic signature. Digital signature is mainly used to solve the problem of certification and approval of electronic documents . At present, secure signature schemes include three fields:schemes based on mathematics, physics and biology, and the first category is the most common.Lattice signature has been developed since modern times, which belong to schemes based on mathematics. Most of the traditional signature schemes are based on bilinear pairings that could unable to resist the quantum attack, so the existing signature schemes encountered potential security threat. The cryptosystem based on lattice could resist quantum attacks effectively for there is no effective polynomial time algorithm to solve difficult problems based on lattice. Furthermore, the operations in lattice are simple, especially the operations in the ideal lattice, which could help to reduce the length of the public key, private key, signature and signcryption length, reduce the computational complexity, thus it's one focus of research scholars at home and abroad.In this paper, there is a exploratory research of signature and signcryption schemes based on the difficult problem of small integer solution (SIS) in ideal lattice, and the major achievements are as follows:1. Introduce the basic theory of lattice, and its special structure and mathematical characteristics, analyze various difficult problems in lattice and their value. Introduce the research status of signature schemes based on lattice, analyze the advantages and disadvantages of each of them,analyze its research value and security on the basis of their practical value.2. In order to improve the capability to resist quantum attack and other security function, there is an identity based ring signature scheme based on the difficult assumption of SIS, and provably unforgrable in the standard model by using the ideal lattice technology that presented by Ducas, and then analyzed its effectiveness and efficiency.3. Aiming the secrecy of the signature data, the application of the signature scheme above in signcryption, identity-based signcryption scheme is proposed in this chapter, which achieved both signature and encryption operation at the same time, and realized the function of authentication and secrecy. It reduced the computational complexity without cutting down its security.4. In view of the security problem of the original signature will sign the right to entrust to proxy signature, further extend application, the identity-based proxy ring signcryption scheme, is given in this chapter based on ideal lattice, which realized the security features of the unabuse,anonymity, unforgrable and others, which also simplifying the operation steps of the scheme to improve the operation efficiency.