Research On Lattice Based Proxy Signature

With the rapid development of internet and communication technology, digital signature schemes are becoming more and more diverse indifferent applications. In different scenarios, the traditional digital signature schemes resulted in a number of variants. Proxy signature scheme is an important part of it. The proxy signature scheme has important research value and application prospect, so it is widely concerned and studied. In recent years, with the rapid development of quantum computer, the most cryptography algorithms, which are based on the hardness of discrete logarithm and the factor decomposition and so on, will be broken. The existing lattice-based proxy signature is limited, and there are some problems in them. Hash functions play an important role in modern cryptography. As a basic structure of many encryption algorithms and protocol, it ensure the security of the algorithm. Traditional cryptographic-hash functions are generally used for string-to-string mappings. In order to facilitate the calculation, some cryptographic algorithms have mentioned the hash function that can map a string to a matrix, but they did not describe their implementation process. In addition, the post-quantum cryptography has become a research hotspots, lattice, represented after quantum cryptography has become a hot topic, build grid-based hash function possible difficulties. In addition, the post-quantum cryptography has been a hot topic. Lattice is one of them, and many schemes based on lattice assumptions have been proposed. Constructing a hash function which based on lattice problem becomes possible.In this thesis, we studied some techniques about lattice, they are discrete Gaussian distributions, preimage sampleable(trapdoor) functions, bonsai trees, rejection sampling technique, and analyze the reduction of the worst-case to average case process. The main research of our thesis are specified as follows:Research on how to construct a hash function which can map an arbitaray string to a fixed matrix. Building on the result of analyzing the reduction of the worst-case to average case process, we construct a hash function which can map an arbitrary length string to a fixed matrix. Then we proof the security of it. At last, we illustrate the parameters of our hash function.Lattice based proxy signature about basis delegation. Builiding on the result of GPV digital signature and combine with the basis delegation technique. We construct a proxy signature scheme based on the hardness assumption of the Small Integer Solution(SIS) problem on some lattice. Our scheme make the public key become shorter and the prox sign process simpler. At last, we prove its securities in the random oracle model, and compare it with the exsiting lattice based proxy signature. As a result, it degraded computational complexity.A lattice based proxy signature building on rejection sample technique. Combine with the rejection sample technique and matrix sample algorithm, we construct another lattice based proxy signature. This scheme has abandoned the exsiting delegation method which based on basis delegation. Make the delegation process more concise. In addition, our scheme requires less computation and storage. Because of this, it greatly improved the following study.