毕业设计（论文）-基于混沌的椭圆曲线密码系统的研究与实现.doc

基于混沌的椭圆曲线密码系统的研究与实现
桂加睿
摘要
密码学已经有上千年的历史,一直以来,人们都用代数方法来研究密码学问题,并产生了大量的加解密算法,如DES,AES,RSA等等。同时,近年来,人们经过大量研究发现混沌系统有以下重要的特性:高度不可预测性、看似随机性、对初始条件和参数敏感性等。这些特性与密码学特性有巨大相似性,促使人们把混沌理论运用到密码学领域。
椭圆曲线加密系统(ECC)的安全性基于椭圆曲线离散对数问题的难解性。它是迄今为止每比特具有最高安全强度的密码系统。同其它非对称加密体制相比,椭圆曲线密码系统除了安全性有着高外,还具有计算负载小、密钥尺寸短、占用带宽少等优点。因此,椭圆曲线密码系统被认为是下一代最通用的公钥密码系统。
混沌系统和密码学之间有天然的联系和结构上的相似性,启示着人们把混沌理论应用于密码学领域,混沌理论与常规密码学之间的广泛联系激起了越来越多的密码学研究者的兴趣,利用混沌系统构造密码算法成为信息安全领域的一个重要研究热点。
本文以椭圆曲线加密系(ECC,elliptic curves cryptosystem)为研究对象,分析了椭圆曲线的的数学原理和工作原理,密码系统,用于数字签名的基本算法,从性能、安全性等方面分析了系统的技术优势。
关键字:混沌密码学、离散对数、群域、椭圆曲线、数字签名
Research and Implementation of Elliptic Curve Cryptography Algorithm base on Chaos
GUI,Jia-Rui
Abstract
Cryptography has been for thousands of years, people have to use algebraic methods to study the problem of cryptography, and produce a large number of cryptographic systems, such as DES, AES, RSA etc. On the other hand, in recent years, people has done a lot of research on the chaotic system, recognized some of its important features, such as: very unpredictability nature of seemingly random, on the initial conditions and parameter sensitivity. these features are great similarities with Cryptographic properties
Elliptic curve cryptography (ECC) security is based on elliptic curve discrete logarithm problem of intractability, So far, the Elliptic Curve Cryptosystem (ECC) provides the highest strength-per-bit of any cryptosystem known. In addition to its high security, ECC also has many other merits over other public-key cryptosystems such as putation overheads shorter key size, considerable bandwidth savings, and so on. Therefore, the elliptic curve cryptosystem is considered the next generation of the mon public-key cryptosystem.
Between chaos and cryptography has the natural link and structural similarity, reveals to people the chaotic field of applied cryptography, Chaos theory and conventional cryptography and extensive links between the more and more aroused interest in cryptograph