基于格的高效签名方案的设计与应用研究

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.

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。

数字签名是公钥密码学的重要组成部分，基于格困难问题设计数字签名方案是当前公钥密码学领域的一个研究热点。本项目围绕基于格的数字签名方案的高效设计及应用展开研究，申请发明专利6项，发表学术论文12篇，其中CCF推荐A类会议论文2篇，SCI源刊录用论文4篇。具体地，课题组以降低格签名方案的通信和计算复杂度，拓展格签名在云计算和大数据等新兴领域的应用为目标，通过深入了解应用需求，借鉴传统数字签名方案的设计思路并结合格密码技术，设计了一种通信有效的基于身份的格签名方案、一种更高效的基于身份的格环签名方案、一种基于格的增量签名方案、两种基于格的无秘钥泄露的变色龙哈希函数等。上述方案在实际应用中还可以采用现有技术进行进一步的优化和扩展，从而推动了相关领域的发展。此外，还对项目执行过程中发现的一些相关问题进行了拓展研究，这些研究丰富了本项目的研究内容。