基于格的高效签名方案的设计与应用研究

项目名称： 基于格的高效签名方案的设计与应用研究

项目编号： No.61502443

项目类型： 青年科学基金项目

立项/批准年度： 2016

项目学科： 自动化技术、计算机技术

项目作者： 田苗苗

作者单位： 安徽大学

项目金额： 20万元

中文摘要： 数字签名是公钥密码学的重要组成部分，是许多安全协议的一个基础构件。基于格问题设计数字签名方案是公钥密码领域的一个研究热点。当前，基于格的签名方案效率总体较差，难以满足大多数应用的需求，且种类也很少，无法适应一些特殊的应用场景。针对这些问题，本项目拟研究基于格的签名方案的高效设计及其应用问题，主要研究内容包括：(1)改进的格签名压缩技术；(2)简化格签名生成算法的新方法；(3)设计基于身份的高效格签名方案；(4)新型格签名的设计及其应用。我们拟从选择更好的概率分布入手，研究新概率分布和理想格等紧致格的融合问题，大幅缩短格签名的长度；同时从增量和可复用的角度，研究设计基于格的增量签名和高效陷门哈希函数，简化格签名的生成算法；在此基础上，将这些技术进一步推广到基于身份的环境下，设计基于身份的高效格签名方案，提高格签名的实用效率；最后研究一些特殊格签名的设计及其在移动网络、大数据等领域的应用。

中文关键词： 基于格的公钥密码学；数字签名；基于身份的签名

英文摘要： Digital signature is an important component of public key cryptography and is often used as a building block of numerous cryptographic protocols. Currently, constructing digital signature schemes on lattice problems is a hot topic in public key cryptography community. However, most of the existing lattice-based signature schemes are inefficient and thus cannot meet the needs of most real applications. In addition, there are no corresponding lattice signature schemes in some special scenarios. To address these issues, this project intends to study the efficient constructions and applications of lattice-based signature schemes. Its main research contents include: (1) the improved compression methods for lattice signatures, (2) the newly simplified technologies of lattice signature generation algorithms, (3) designing efficient identity-based signatures over lattices, and (4) the realizations and applications of new types of lattice signatures. Starting from selecting better probability distributions, we would study the integration problem of the new probability distributions and the compact lattices like ideal lattice for largely reducing the length of lattice signatures. At the same time, from the incremental and reusable perspectives we would design lattice-based incremental signatures and efficient trapdoor hash functions to simplify the generation algorithms of lattice signatures. After that, we would like to further generalize these technologies to the identity-based setting, and construct efficient identity-based lattice signature schemes to improve the practical efficiency of lattice signatures. Finally, we will also design several special lattice signature schemes and study their applications in mobile network, big data, etc.

英文关键词： lattice-based public key cryptography;digital signature;identity-based signature