理想格数学问题分析及隐私增强密码若干问题研究

With the fast development of quantum computing, it is crucial to study new mathematical structure and problems that are resistant to quantum analysis. Currently, lattice-based cryptography is among the main-stream technologies of post-quantum cryptography. Ideal lattice, as a special kind of lattice, enjoys better performance and becomes the foundation for the most practical lattice-based cryptographic schemes. Nevertheless, ideal lattice introduces rich mathematic structures, and brings potential vulnerabilities. As a consequence, we'll make an extensive study of the underlying mathematical structures of ideal lattice, and develop new analysis framework for ideal lattice, which can play a fundamental and instrumental basis for secure parameter selection and evaluation of lattice-based cryptography. .Privacy-enhanced cryptography, in particular identity-concealed cryptography and order-revealing encryption, plays an important role in secure message transmission over network and in secure cloud computing. We will introduce a new cryptographic primitive: identity-concealed signcryption, and study its applications to identity-concealed key exchange and secure network transmission. For order revealing encryption (ORE), we will develop file injection attacks, present framework for forward-secure ORE, introduce new game-based security model and highly practical ORE schemes that achieve much better tradeoff between security and efficiency.

随着量子计算机的快速发展，研发抗量子分析的新型数学结构变得尤为重要。格基密码是当前后量子密码主流技术之一。其中理想格由于效率的优势，成为近年来格基密码的重要数学基础。但是理想格由于引入更多代数结构，对其代数结构性质的挖掘和理想格基础数学问题的新型分析方法和框架的研究是本项目的重要研究内容。该方向的研究将丰富理想格的代数性质和分析方法，为格基密码安全参数的选取测评提供重要参考和技术支持。隐私增强密码技术，特别是身份匿藏密码技术和保序加密，是隐私保护网络传输和云计算安全的关键技术。本项目拟引入身份匿藏（公钥及标签）签密新型密码原语，研究其在身份匿藏密钥协商和网络保密通讯中的应用；发展针对保序加密的新型攻击、新型安全模型、前向安全保序加密框架和安全及效率更优平衡的高效保序加密方案。

针对量子计算带来的新威胁和隐私增强新需求，项目在后量子格基后量子密码与隐私增强密码若干关键问题上进行深入研究，取得了较为系统的研究成果。在国际和国家顶级会议和期刊发表论文25篇，申请国家发明专利3项。完成1项央行金融标准化行业标准，提交密码标准化委员会标准提案3项。

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