基于格的公钥密码体制不仅是后量子时代最有前途的公钥密码体制之一，也为全同态加密体制的构造提供了重要的解决途径，因此受到了国际密码学界的极大关注。众所周知，密码体制的安全性是决定该体制能否应用的最根本因素之一。因此，对格密码体制的安全性进行分析就是一项十分必要且重要的工作。本项目拟从构造普遍的格算法和实施具体的密码攻击两个方面对一些格密码的安全性进行分析。项目预期将提出新的格基约化算法，提出更有效的针对理想格的随机筛法，实现对某些重要格密码体制更有效的攻击。项目的研究成果将对了解格密码的安全性产生十分重要的理论意义, 对格密码的参数选取、现实中的合理应用有着重要的现实意义，并有助于提出新的密码分析工具，促进格密码的进一步发展。

Lattice-based public-key cryptosystems have drawn considerable attention for these years, since they are not only one of the main post-quantum public-key cryptosystems, but also the main way to construct fully homomorphic encryption. It is well known that the security decides the practicality of a cryptosystem essentially, so it is necessary and important to analyze the security of lattice-based public-key cryptosystems. In this project, we will analyze their security by studying both the general lattice algorithm and the concrete cryptographic attack. We plan to propose a new lattice basis reduction algorithm, a more efficient random sieve algorithm for ideal lattice, and more efficient attacks against some important lattice-based public-key cryptosystems. These results will help us understand the security of lattice-based public-key cryptosystems better, choose more appropriate parameters for them, apply them more reasonably in practice, develop new cryptanalytic tools and improve the lattice-based public-key cryptosystems.