有限域上多变量线性代数方程求解密码学分析  

Cryptanalysis of Multivariate Linear Algebraic Equations in Finite Fields

作　　者：石红岩[1] 王江涛[2] Shi Hongyan;Wang Jiangtao(Department of Mathematics,Yang-En University,Quanzhou 362014,China;College of Engineering Technology,Yang-En University,Quanzhou 362014,China)

机构地区：[1]仰恩大学数学系,福建泉州362014 [2]仰恩大学工程技术学院,福建泉州362014

出　　处：《科技通报》2017年第4期195-198,218,共5页Bulletin of Science and Technology

基　　金：福建省中青年教师教育科研项目(科技)(JA15581)

摘　　要：针对加密学中有限域上多变量线性代数方程求解中的问题,提出一种有限域上多变量线性代数方程求解密码学分析方法。在有限域上的多项式环上建立一种多变量线性代数公钥密码系统,求解出关于MQ公钥密码体制的公钥和私钥的结构,在此基础上通过采用中心映射的特殊对应关系,得到关于明密文域上的一组多变量线性代数方程,并通过构造具有良好密码性质的多变量线性可逆变换,求解出多变量的线性代数公钥密码体制。实验结果表明,所提方法能够有效提高公钥密码的实现效率和安全性,且易于硬件的实现。For cryptography of multivariable linear algebraic equations in finite field is the problem,putforward a kind of multivariable linear algebraic equations in finite field analysis method of cryptography.Polynomial ring in finite field to build a multivariate linear algebra public key cryptosystem,find outabout the MQ public key cryptosystems of the structure of the public and private keys,on the basis ofthis center mapping through the use of special corresponding relation,get about a group of Ming cipherdomain on multivariable linear algebraic equations,and by constructing a good cryptographic propertiesof multivariate linear invertible transform,solving the multivariable linear algebra public keycryptosystems.The experimental results show that the proposed method can effectively improve theefficiency of the implementation of public key cryptography and security,and easy to implement inhardware.

关 键 词：有限域 多变量 线性代数方程 密码学分析 

分 类 号：TN918[电子电信—通信与信息系统]