密码格中行列式的若干定义及性质比较研究  

A comparative study of some definitions and properties of determinants in cryptographic lattices

作　　者：杨军[1] 李庆[1] YANG Jun;LI Qing(School of Computer Science anil Technology,Southwest Minzu University,Chengdu 610041,P.R.C.)

机构地区：[1]西南民族大学计算机科学与技术学院

出　　处：《西南民族大学学报（自然科学版）》2019年第6期598-602,共5页Journal of Southwest Minzu University(Natural Science Edition)

基　　金：西南民族大学中央高校基本科研业务费专项资金项目(2014NYB04);国家自然科学基金青年科学基金项目(11401493)

摘　　要：格密码学近年被认为是抗量子计算攻击的新型公钥密码系统之一.首先在前人工作的基础上,证明"满秩整数格的行列式必为正整数"的较强结果.其次给出"实数格的行列式是一个与基选择无关的格不变量"的完整证明.最后站在集合论、高等代数及抽象代数的交叉视角下指出国内外信息安全专业流行教材及文献中6处相关概念的描述不足之处,并给出具体改进建议.Lattice cryptography has recently been recognized as one of the new public-key cryptosystems against quantum computing attacks.This paper first proves a stronger result that the determinant of any full rank integer lattice is always a positive integer based on the work of predecessors.Secondly,a complete proof that the determinant of any real lattice is a lattice invariant independent of the base selection is given.Finally,from the cross perspective of set theory,advanced algebra and abstract algebra,it points out six defective descriptions of six related concepts in popular textbooks and literature on information security major at home and abroad,and makes specific suggestions for improvements.

关 键 词：抗量子计算密码 满秩格 整数格 等价基 格行列式 格不变量 幺模矩阵 

分 类 号：O15[理学—数学] TN918.91[理学—基础数学]