文档介绍：摘 要
公开密钥密码编码学是密码编码学的一个重要研究方向,其核心就是利用数学函数构造公钥加密算法。本文首先简要介绍有关数学知识和公钥密码学的几个经典算法。在此基础上将数论与代数学知识应用于公钥加密体制的生成。本文具体工作主要包括:(1) 给出了一个基于有理系数域多项式剩余类环的加密算法,并在此基础上派生出一个特例算法,分析了它们的安全性;(2)探讨了复合加密的思想,给出了一个迭代复合加密算法和一个线性复合加密算法,分析了它们的安全性;(3)结合多项式剩余类环加密算法所派生出的特例算法、一次不定方程、公钥证书管理系统,给出了一个单向鉴别协议。
关键词:公钥加密算法,多项式环,不定方程,零次多项式,迭代复合,线性复合,单向鉴别
Abstract
Public­key cryptography is one of the most important research field of encryption,using mathematical function to construct public­key encrypt arithmetic is the nucleus of paper starts by introducing relational mathematical experience and several classical algorithm of public­key cryptography,then using number theory and algebra to create public­key cryptosystem. Concretely work include: forward a public­key encrypt algorithm that based on polynomial residual­class ring in rational number field, and it's derivative encrypt algorithm,and analyze their security; the idea position encrypt,put forward an encryption algorithm of position and an encryption algorithm of position,then analyze their security; the derivative encrypt algorithm of the public­ key encrypt algorithm that based on polynomial residual­class ring in rational number field, linear indeterminate equation,key distribution center(KDC),then put forward an unidirectional discrimination­protocol.
Keywords:public­key encrypt algorithm, polynomialring, indeterminate equation, zeroth polynomial,position,position, unidirectional discrimination
目 录
1绪论...........................................................1
密码学的起源和发展............................................... 1
密码学的若干基本概念............................................. 2
本文所作工作与内容安排........................................... 4
2相关的数学基础.................................................6
相关的数论知识................................................... 6
相关的代数学知识................................................. 9
多项式.......................................................... 13
3经典的公钥加密算法....................