system of linear inhomogeneous equations

This paper principally reviews the identity authentication protocol and message authentication protocol based on nonhomogeneous linear equations in [1],analyzes the security defects in these two protocols in combination with [2],and modifies them by introducing in trap-door one-way function.

文中主要回顾了《基于非齐次线性方程组的认证协议的研究》一文中给出的基于具有无穷多个解的非齐次线性方程组而建立的一个身份认证协议和一个消息认证协议,结合《两个认证协议的安全缺陷》一文,对这两个认证协议中存在的安全缺陷进行具体分析;然后通过引入陷门单向函数对这两个认证协议进行改进,保障其安全缺陷和可操作性;并用RSA算法作为实例,对改进后的认证协议进行讨论分析。

The problem two fewer and one more in information hiding was transformed to find the solution vector,which had the least weight,of the nonhomogeneous linear equations whose elements amount wasn t fixed,on binary domain,built a mathematical model,and gave the solution models.

将信息隐藏中的两少一多问题转换为求二值域上变量元数不确定的非齐次线性方程组的最小权值解向量,构建了一个数学模型,对模型进行求解,作为问题模型的解给出了答案模型。

By introducing first the concept of coset in the sub-space of linear space,we have testified an im- portant property of the coset and finally give the necessary and sufficient condition for the same solution of the solva- ble nonhomogeneous linear equations.

两个n元有解的非齐次线性方程组同解的根本原因是什么?为了回答这个问题,首先引入线性空间的子空间的陪集概念,然后证明了F~n的陪集的一个重要性质,最后给出了两个n元有解非齐次线性方程组同解的充分必要条件,从而完善了线性方程组的同解性理论。

A method to solve non homogeneous and linear differential equations by homogenization high precision direct integration (HHPD P) was proposed.

根据函数分段插值逼近的思想 ,在一个积分步长内用多项式近似表示方程的非齐次项 ,提出了一种原理简单、实施容易的求解非齐次线性微分方程组的新型齐次扩容精细积分法 ,该方法不涉及矩阵的求逆运算 ,不需要计算傅里叶级数展开系数的振荡函数积分 ,且在一个积分步长内只求解一个相应的齐次扩容微分方程组 ,因而本方法和已有的同类方法相比具有更高的计算精度和效率 ,数值算例表明了该方法的有效

In this pqper we give a sufficient and necessary consistency condition of a nonhomogeneous system of linear left equations over an arbitrary skew field F, and a convenient, simple method of solving the system.

给出了任意体F上非齐次左线性方程组相容的一个充要条件和求解的简便方法,利用此法还能同时求出其导出组的基础解系,而且顺便讨论了F上一般左线性方程组的解,给出了其有解判定定理及解的结构定理。

The Explanation of the Specific Solution for the System of Linear nonhomogeneous Equation with Constant Coeficient;

常系数线性非齐次方程组特解的一个注记

nonhomogeneous linear system of differential equations

非齐次线性微分方程组

A Remark on the Solution Set of the Non-Homogenous Linear Equation;

非齐次线性方程(组)解集的一个注记

nonhomogeneous linear differential equation

非齐次线性微分方程

inhomogeneous linear ordinary differential equation

非齐次线性常微分方程

inhomogeneous linear difference equation

非齐次线性差分方程

Prerequisites for the All-Nonzero Solutions to Inhomogeneous Linear Equations;

非齐次线性方程组存在全非零解的充要条件

The C Language Programming of Solving the Inhomogeneous Linear Equation System;

解非齐次线性方程组的C语言程序设计

Java language programming of solving the general inhomogeneous system;

解非齐次线性方程组的Java Application图形界面程序设计

Primary Solution to Common Modulus Linearity Non-homogeneous Differential Coefficient Equation Groups;

常系数线性非齐次微分方程组的初等解法

Basic solutions and general solution of non-homogeneous linear differential equation

非齐次线性微分方程的基本解组与通解

Differential Operator Method in Solving the Group of Constant-coefficient Non-homogeneous Liner Differential Equations

常系数非齐次线性微分方程组的微分算子解法

A Simple Approach to General Solution for Nonhomogeneous Linear Equations

非齐次线性方程组通解的一种简便求法

On the Linear Relativity of the Solution to Factorial n Linear Equation Whose Constant Term Is Not Zero;

n阶非齐次线性方程解的线性相关性

Several Solutions of Non-homogeneous Linear First-order Differential Equation;

一阶非齐次线性微分方程的几种解法

On the analytic solution of Riccati s differential equation of first order;

一阶非线性齐次Riccati方程的解析解

FORMULA OF LIOUVILLE OF LINEAR NONHOMOGENEOUS AND ITS APPLICATIONS;

线性非齐次方程的Liouville公式及应用

On Solutions to Non-Homogeneous Differential Equations with Two Unknowns Through General Way and Laplace Transform and Discuss on Their Unification

二元非齐次线性微分方程组时域、变换域解及解的统一性探讨