Research On Lattice-based Proxy Signature

With the rapid development of computer network and communication technology, the applications of digital signature schemes are becoming increasingly diverse. The general digital signature schemes resulted in a number of variants. Proxy signature scheme is an important one of those schemes. It has important research values and applied fields (e.g. electronic payment systems, electronic voting and so on). In recent years, lattice-based public key cryptography has been become a research hotspot by many cryptographers. However, lattice-based proxy signature schemes are rarely proposed.In this paper, we studied the relevant notions of lattice:discrete Gaussian distributions, preimage sampleable functions, bonsai tree, basis delegation without increasing the dimension of the lattice. we discuss the signature schemes and hierarchical identity based encryption by using these theories we talked before. We analyzed a lattice-based proxy signature which was constructed by using bonsai tree as well. Our results are as follows:1) We first proposed a new tree-based signature scheme in lattice. Our new scheme was based on Cash’s signature scheme by using basis delegation without increasing dimension technology. The advantage of the improved signature scheme is that the length of the generated signature does not increase as the message size does. It reduced storage and computation cost. As a result, it degraded computational complexity.2) By using basis delegation without increasing dimension technology, we constructed an improved lattice-based proxy signature scheme which is based on Xia’s proxy signature scheme. The scheme keeps efficient in the same context, and optimized the length of proxy signature which results degrading the cost of storage.3) We constructed a proxy signature scheme by using the new trapdoor generation algorithm and trapdoor delegation algorithm which is proposed by Micciancio and Peikert. Compared with several known lattice-based proxy signatures, the operation speed of the scheme is the fastest one as far as we know. Because of this, it greatly improved the operation efficiency of proxy signature scheme.