基于Tropical代数的三方密钥交换协议  

Three-party Key Exchange Protocol Based on Tropical Algebras

作　　者：邢鹏飞[1] 何明星[1] 李曦[1] 常彦妮[1] 

机构地区：[1]西华大学数学与计算机学院,四川成都610039

出　　处：《西华大学学报（自然科学版）》2014年第4期6-10,共5页Journal of Xihua University:Natural Science Edition

基　　金：国家科技部支撑计划项目(2011BAH26B00);四川省国际合作项目(2009HH0009);四川省重点学科建设项目(SZD0802-09-1);四川省信息安全创新团队建设项目(13TD0005);四川省科技厅应用基础项目(2010JY0118);西华大学创新基金项目(201315)

摘　　要：三方密钥交换协议允许3个用户在不安全信道上进行平等的密钥协商,以生成共享的安全对话密钥,从而保证公开信道上的三方保密通信。文章在D.Grigoriev等研究(Grigoriev D,Shpilrain V.Tropical Cryptography.Communications in Algebra,2014,42(6):2624-2632)的基础上,提出一种基于Tropical代数构造的三方密钥交换协议。该协议使用新的Tropical代数结构作为构造工具,将加法运算定义为取最小值运算,将乘法运算定义为一般的整数加法运算。有别于一方服务器两方用户参与的三方密钥交换协议,该协议对参与密钥交换的三方的密钥生成作用是平等的;可以抵抗线性代数攻击,提高安全性;其构造方法实施简单,可有效降低协议的计算复杂度。Three-party key exchange protocol allows three parties to agree a new secure key for communication by an contributional protocol on insecure channel, so as to ensure three-party secure communication on public channel. Based on D. Grigoriev＇s research, the three-party key exchange protocol is proposed, which is based on Tropical algebra. This protocol has following advantages. It uses new Tropical algebra as construction tool. Addition in Tropical algebra is defined as taking the minimum while multiplication is ordinary integer addition. This protocol is different from other three-party key exchange protocols which contain one trusted server and two par- ties. Three parties contribute equally in key exchange. Security of the protocol is analyzed, and it can resist linear algebra attack. This method is simple to implement and with good efficiency.

关 键 词：Tropical代数 三方密钥交换 矩阵多项式 线性代数攻击 

分 类 号：TP309.7[自动化与计算机技术—计算机系统结构]