热带Linde-de-la Puente矩阵的密码应用  

Cryptographic applications of the tropical Linde-de-la Puente matrix

作　　者：潘戈洋 黄华伟 姜鑫 PAN Ge yang;HUANG Hua wei;JIANG Xin(College of Mathematical Sciences,Guizhou Normal University,Guiyang,550025,China)

机构地区：[1]贵州师范大学数学科学学院,贵州贵阳550025

出　　处：《长江信息通信》2023年第6期24-28,共5页Changjiang Information & Communications

基　　金：国家自然科学基金资助项目(61462016);贵州省科学技术基金资助项目(黔科合基础-ZK[2021]一般313号)。

摘　　要：近年来,一些密码学研究者提出了基于热带代数半环的公钥密码,例如Grigoriev和Shpilrain提出了几个有关热带半环密码方案,但他们设计的方案都存在安全缺陷。为了解决有关他们设计方案中存在的缺陷,将采用一种新的热带Linde-de-la Puente矩阵的形式,设计一类新的热带半环密钥交换协议和公钥加密系统。该协议的安全性可归约为求解热带非线性整数方程组的NP困难问题。由于私钥矩阵不能用已知矩阵线性表示,因此可以抵抗KU攻击,该密码系统没有使用热带矩阵加法运算,因此同样也可以抵抗RM攻击,在抵御敌手攻击方面要优于Grigoriev和Shpilrain的方案。In recent years,some cryptographic researchers have proposed public key cryptography based on tropical algebraic semirings.For example,Grigoriev and Shpilrain have proposed several schemes concerning tropical semirings,but the schemes they designed have security flaws.In order to address the shortcomings concerning their design scheme,a new class of tropical semiring key exchange protocols and public key cryptosystems will be designed in the form of a new tropical Linde-de-la Puente matrix.The security of this protocol can be reduced to the NP-hard problem of solving tropical nonlinear systems of integer equ ations.Since the private key matrix cannot be represented linearly by a known matrix and is therefore resistant to KU attacks,the cryptosystem does not use tropical matrix addition operations and is therefore similarly resistant to RM attacks,outperforming Grigoriev and Shpilrain's scheme in terms of resistance to adversary attacks.

关 键 词：公钥密码 密钥交换协议 公钥加密方案 热带代数半环 热带Linde-de-la Puente矩阵 

分 类 号：TP309[自动化与计算机技术—计算机系统结构]