隐子群量子算法设计及其在密码分析中的应用

With the rapid development of quantum computation, especially hidden subgroup quantum algorithm, some classical cryptosystems are under severe threats. Therefore, the quantum cryptanalysis based on hidden subgroup algorithm is of great theoretical and practical significance. By far, lots of outstanding designs of quantum algorithms have emerged, only a few of which can be applied to quantum cryptanalysis though. This project study quantum algorithm for cryptography related mathematics problem, including the principal ideal, discrete logarithm and its extension problem. Meanwhile, algorithm optimization and resource estimates of quantum algorithms will be considered. Moreover, this project researches on the theory of quantum cryptanalysis against classical cryptosystems, mostly based on the hidden subgroup model, with the help of classical differential and linear cryptanalysis skills. Furthermore, we design quantum-safe cryptography. It is expected to make some breakthroughs in accelerating classical cryptanalysis based on quantum computation, which will provide theoretical and technical support for the quantum cryptanalysis and post-quantum cryptography.

随着量子计算，尤其是隐子群量子算法的快速发展，部分密码算法的安全性受到威胁。开展基于隐子群模型的量子密码分析研究具有重要的理论价值和现实意义。当前，隐子群算法设计取得了许多优秀的研究成果，但是适用于密码分析的有效量子算法较少。课题重点研究求解密码相关数学问题，包括主理想、离散对数及其拓展问题的量子算法，探索相关算法的优化与资源分析；同时，基于隐子群量子算法模型，结合差分、线性分析等经典分析方法，研究针对经典密码体制的量子密码分析理论；研究量子安全的密码方案。期望在经典密码分析方法的量子加速方面有所突破，为量子密码分析与抗量子密码设计提供理论和技术支持。

开展基于隐子群算法的量子密码分析研究具有重要的理论价值和现实意义。本课题围绕求解密码相关数学问题的量子算法优化与资源分析、量子安全的密码方案开展研究，取得了一系列研究成果。学术成果和人才培养均达到预期目标。在CRYPTO2018, PKC2019、IEEE IT、Scientific Reports等国内外知名会议及期刊上发表学术12篇（3篇已录用待发表），其中SCI检索6篇，中国密码学会A类会议1篇，B类会议1篇。申报发明专利5项，出版译著1部。培养博士生5人，其中已毕业博士3人，培养硕士3人，其中已毕业硕士1人，2人次获得大学优秀博士学位论文，1人次获评全军优秀博士学位论文。