【作者】 黄宇；

【导师】 周福才；

【作者基本信息】 东北大学 ， 计算机软件与理论， 2005， 硕士

【摘要】 随着信息社会的到来,保证信息的安全可靠的传输成为一个日益紧迫和重要的问题,所以密码系统的研究与应用成为计算机科学领域的一个热点。现在的密码系统主要分为两种:对称密码系统和公钥密码系统。当今普遍应用的一些密码系统存在着很多问题,比如密钥过长,比如计算速度比较缓慢等等。另外,在无线环境或者智能卡的应用中,由于带宽、计算能力和存储能力都受到了限制,使得传统的密码系统不适合应用于这些领域。 本文针对这些问题,介绍了一种新的公钥密码系统。这种密码系统是基于椭圆曲线的,它的安全性是基于椭圆曲线离散对数问题的难解性上。椭圆曲线密码系统与其他公钥系统相比,在密钥长度增加程度一样的情况下,安全性却有较大增长。所以在计算能力和存储能力受限的环境下,椭圆曲线密码系统的这个优势尤其显得突出。另外,以椭圆曲线为基础的安全体系结构具有低功耗,代价小等优点。椭圆曲线的这些优点使之在很多场合都适合应用,比如无线环境和智能卡等等。 本文所作的工作包括: (1) 介绍了椭圆曲线密码系统的基本原理和基本算法,包括它所基于的数学理论、有限域上的运算以及一些诸如密钥交换算法、加密算法和数字签名算法等一些基本算法。 (2) 介绍了如何构造一个安全的椭圆曲线密码系统,包括随机产生一条椭圆曲线,并通过计算曲线的阶来判断该曲线是否安全。 (3) 利用NIST推荐的五条曲线,编程实现了一个基于二元域的椭圆曲线密码系统,包括密钥交换算法、加密解密算法以及数字签名算法(ECDSA),并探讨了将椭圆曲线密钥交换算法应用到CDMA环境中的问题,最后针对其性能与RSA密码系统进行了比较。更多还原

【Abstract】 Because of the coming of information times,the safe transfer of information becomes more important. So the research and application of cryptosystems have become very important in computer science.There are two kinds of cyptosystems at prensent:symmetric cryptosystems and public key cryptosystems. But there are many disadvantages in current public cyptosystems:the too long keys and the slow computation speed.Except, there are some enviroments of those fields are special such as intelligence card or mobile environment,in which the bindwidth,computation ablity and store ablity are limited,so the traditional public key cryptosystems are not fit for those new fields.To solve those above problems,this paper illustrates a new public key crypto-system,which is based on elliptic curve,and whose security is based on the elliptic curve discreet logarithm problem(ECDLP).In contrast with those wellknown public key cryptosystems,the Elliptic Curve Cryptosystems(ECC) maintain reliable security with key lengths that are shorter(therefore more practical).So in the enviroment whose computation ablity, bindwidth and store ablity are limited,the advantage of ECC is more important.And the security scheme based on ECC have less energy cost.Those advantages of the ECC lead itselt to wider application in more fields such as mobile commerce,cell phone systems,e-cash,notebook PC and intelligent card.The following are the points of this paper:(l)The illustration of the basic theories and algoithms of ECC,including those mathematic theory,compuation in infinite field and some basic algorithms such as key exchange algorithms,encyption algorithms and digital signature algorithms.(2)The illustration about how to construct a new elliptic curve cryptosystem including obtaining an elliptic curve random and judging it safe or not by computing its order.(3)Using the five elliptic curve which NIST recommend to construct an Elliptic Curve Cryptosystem on binary field, implementing the Elliptic Curve Diffie-Hellman key exchange algorithm,the Elliptic Eurve ElGamal algorithm and the Elliptic Curve Sigital Signature Algorithm,and trying to apply elliptic curve Diffie-Hellman to CDMA更多还原