The Research And Design Of The Lattice-based Blind Signature Schenes From Bonsai Trees

Nowadays, as one of the most famous cryptosystems in Post-QuantumCryptography, the public-key cryptosystem on lattice is widely accepted and accededin the cryptography. Compared with some other cryptosystems, this one is higher onefficiency, and better on encryption. A lot of good publications are proposed in thisstage, most of them are mainly about signature schemes and encryptions. As a kind ofspecial digital signatures, blind signature can ensure signing requester’s anonymity andnon-traceability. Thus it has a wide prospect in the electronic commerce and electronicgovernment systems. In this paper, we mainly discuss blind signature’s theory, securityand its application. We have done some works in blind signature by reading manyliteratures. Our research and results are listed as follows:(1)We give the concept of lattice and some other theories based on lattice,especially these three things: bonsai trees, the technique called basis delegation andpreimage sampleable functions. At the same time, we introduce and analyze a blindsignature scheme based on lattice. Our works lay a good foundation of theory for thenew blind signature schemes.(2)As none of the proxy blind signature schemes based on lattice have beenproposed, we give a new method of proposing proxy blind signature scheme andmultiple-grade proxy blind signature scheme, which are based on small integersolution problems (SIS). The basis delegation technique in bonsai tree model is used togenerate proxy blind signing keys in our schemes. Compared with those proxy blindschemes which are based on Integer Factoring Problem (IFP) and Discrete LogarithmProblem (DLP), our schemes can resist the quantum algorithms. Both designing andusing are very easy. But they also have defects with large dimensions and hugestorages.