On The Geometry Of Cyclic Lattices

At present,lattice-based cryptography system attracts much attention as a kind of public key cryptosystem against quantum computing attack.As a kind of lattice,the cyclic lattice has been more and more discussed in recent years.The cyclic lattice is not only used in the NTRU cryptosystem,but also be widely discussed and studied in the post-quantum cryptography.The geometry of the cyclic lattice has also been extensively studied.In this paper,by reading a great deal of literature about lattice,cyclic lattice and geometrical cyclic lattice,we can get a certain understanding of the geometric properties of cyclic lattice.By taking full advantage of the characteristics of lattice and cyclic lattice,the nature and its corresponding proof are given in this paper.The content of this paper is as follows:The first chapter is introduction.It tells the background and significance of the cyclic lattice,and it also introduces the research status of the lattice theory,concludes with a brief description of the main content of this article.The second chapter is preliminary.The basic algebra and basic lattice theory are used in it.This knowledge provides theoretical support for the subsequent study of the geometric properties of the cyclic lattice.The third chapter is the main content.It gives the geometry of the cycle of the specific geometry,and gives the corresponding proof.The fourth chapter is about the summary and prospect.The main content of this article is summarized,and the application and research of the cycle lattice raises new problems.