公钥密码学是信息安全中现代密码学的重要组成部分，RSA类型算法则是其中的典型代表，至今仍被广泛应用于网络空间中。格方法是当前热点密码分析技术之一，是公钥密码分析领域的高效数学工具。本项目在已有RSA类型算法理论分析的基础上，针对网络空间中密钥信息极易泄露的问题，基于格方法开展RSA类型算法实际应用时的密码分析研究。通过探索部分密钥信息的可能泄露情形，构建完善的部分密钥泄露模型，应用格方法进行安全性分析。本项目计划系统性地研究CRT-RSA算法与素数幂RSA算法的部分密钥泄露攻击，拟提出工具箱式安全性分析结果，并利用模拟仿真实验与真实算法实例对所提攻击的正确性与有效性进行验证。本项目的预期结果将会对RSA类型算法，特别是其中的CRT-RSA算法与素数幂RSA算法的实际应用安全性构成威胁。系统性分析结论将给出任意部分密钥泄露情形下的算法安全性分析结果，具有一定的理论指导意义和深刻的实用价值。

The public-key cryptography is an important part of modern cryptography in information security. The RSA-type algorithms are typical representatives of public-key algorithms, which are still widely used in cyberspace. The lattice-based method is one of the most popular cryptanalytic techniques, which is a highly efficient mathematical tool in the field of public-key cryptanalysis. In this project, based on the theoretical analyses of RSA-type algorithms, we focus on the problem that the key information in cyberspace is easy to leak, and carry out the research on cryptanalysis of practical RSA-type algorithms using the lattice-based method. By exploring the possible situations of key information leakage, we construct sound partial key exposure models and apply the lattice-based method to analyze the security. We plan to systematically study the partial key exposure attacks of CRT-RSA algorithm and Prime-Power RSA algorithm, propose the security analysis results in a toolkit, and verify the correctness and effectiveness of the proposed attacks by simulated experiments and real algorithm instances. The expected results of this project will pose a threat to the practical security of RSA-type algorithms, especially CRT-RSA and Prime-Power RSA. The systematic analytic conclusion will show the security analysis results of RSA-type algorithms under any partial key leakage cases, which has certain theoretical guidance significance and profound practical value.