Analysis Of Digital Signature Scheme Based On Lattice

Digital signature is widely applied in military, communications,e-commerce and other fields because of its unique data integrity,non-repudiation and unforgeability security properties. Currently, mostdigital signature schemes’ security are built on the hardness of traditionalnumber theory problems, such as large integer factoring problem, discretelogarithm problem and so on. But these problems have been shown to beunable to resist quantum attack. In order to avoid the cryptography crisisin quantum era, it’s very urgent to research on new type of digitalsignature scheme which is anti-quantum attack. And digital signaturescheme based on lattice is one of the most important research directions.This thesis mainly focuses on digital signature schemes based onlattice, especially the group signatures and blind signatures with specialnature, and its applications in e-cash. The following are the main researchresults:(1) Research and mounted on the first group signature scheme basedon lattice. It shows the group signature scheme is vulnerable totrap attacks and without reversibility. Using statisticalzero-knowledge proofs and time parameters, an improved schemeis proposed. The improved scheme is anti-trap attacks and candynamic increase or deletes group members.(2) In-depth research and analyze the blind signature scheme basedon lattice. It introduces the construction process of the scheme andgives a complete analysis and proves on the security properties,such as completeness, blindness and unforgeability etc.(3) The first fair e-cash scheme based on lattice is presented. Appliedthe blind signature scheme based on lattice to e-cash and usingtrusted third party, statistical zero-knowledge proofs and the mainidea of member join protocol in group signatures, the first faire-cash scheme based on lattice is proposed. It not only protects theuser’s consume privacy, but also ensures the fairness of the electronic trading.