摘要： 格(Lattice)是多维空间中点的规则排列,对它的研究最早出现在19 世纪的数论和晶体学研究中。由于20 多年前出现的LLL 格归约算法,格在密码学中才有了非常广泛的应用。在1996 年以前,格的应用还只是局限于攻击各种已有加密系统,基于格的公钥密码系统是从这年之后才出现并开始深入研究的。该文主要介绍了3 个较著名的基于格的PKCS,并讨论了它们的安全性和实际应用效率。

关键词: 格, LLL归约算法, 归约基, 公钥加密系统, 安全性

Abstract: Lattice is a regular alignment of points in multi-dimensional space. The research on it appeared in both number-theory and crystallography in 19th century. Because of the appearance of the famous LLL lattice reduction algorithm, lattices have had surprisinsg applications in cryptology. Before 1996, applications of lattices were restricted in attacking the existing cryptosystems; public-key cryptosystems based on lattice appeared in 1996 and have been studied further more. This paper mainly introduces three celebrated public-key cryptosystems based on lattice and discusses their security and practical efficiency.

中图分类号: 

• TN918.1