公开密钥密码编码学多项式应用研究-软件工程专业论文.docxVIP

THE STUDY AND APPLICATION ABOUT PUBLIC-KEY CRYPTOGRAPHY BASED ON MULTINOMIAL A Dissertation submitted in fulfillment of the requirements of the degree of MASTER OF ENGINEERING from Shandong University of Science and Technology by Wei Qinbing Supervisor： Professor Wu Zhehui College of Information and Science and Technology May 2006 声 明 本人呈交给山东科技大学的这篇工程硕士学位论文，除了所列参考文献和世所公认的 文献外，全部是本人在导师指导下的研究成果。该论文资料尚没有呈交于其它任何学术 机关作鉴定。 工程硕士生签名： 日 期： AFFIRMATION I declare that this dissertation, submitted in fulfillment of the requirements for the award of Master of Engineering in Shandong University of Science and Technology, is wholly my own work unless referenced of acknowledge. The document has not been submitted for qualification at any other academic institute. Signature： Date： 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 Public-key cryptography is one of the most important research field of encryption,using mathematical function to construct public-key encrypt arithmetic is the nucleus of it.This paper starts by introducing relational mathematical experience and several classical algorithm of public-key cryptography,then using number theory and algebra to create public-key cryptosystem. Concretely work include:1.put forward a public-key encrypt algorithm that based on polynomial residual-class ring in rational number field, and its derivative encrypt algorithm,and analyze their security? 2.discuss the idea of composition encrypt,put forward an encryption algorithm of iterative composition and an encryption algorithm of linear composition,then analyze their security?3.use the derivative encrypt algorithm of the public- key encrypt algorithm that based on polynomial residual-class ring in rational nu