论文标题:椭圆曲线加密技术研究
Study on Elliptic Curve Cryptosystem
论文作者 张明
论文导师 钱江,论文学位 硕士,论文专业 计算机应用技术
论文单位 南京工业大学,点击次数 101,论文页数 66页File Size590k
2004-05-01论文网 http://www.lw23.com/lunwen_388370842/ 信息安全; 椭圆曲线; 椭圆曲线加密系统(ECC); 秘密共享
network security; elliptic curve; elliptic curve cryptosystem(ECC);secret sharing
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。本文首先介绍了课题的研究背景、国内外研究现状、发展动态以及椭圆曲线密码技术的历史与现状。其次介绍了ECC的数学基础,对有限域上椭圆曲线点的运算规则进行了详细描述。第三,研究了ECC体制算法实现问题,并针对关键算法作了比较研究,并优化了算法,给出了具体的实现结果。第四,我们提出了一个新的动态秘密共享方案,并对它进行了分析。分析结果表明,我们所提出的方案可以动态更新共享秘密和成员的子密钥而成员所拥有的私人密钥却无需改变,解决了传统的秘密共享方案存在的更新和复用问题。另外它还可以检测出不诚实的成员且检测方程不会泄漏秘密信息,解决了其他一些方案存在的不能防欺诈及验证方程泄密问题。与现有的一些方案相比,我们所提方案的安全性是基于求解椭圆曲线离散对数问题的困难性上的,因而具有更高的安全性。此外,我们所提出的方案的运算量不大,效率更高,适宜在支持椭圆曲线的公钥密码系统下实现。最后,对ECC的发展趋势和研究方向进行了探讨。
The security of Elliptic Curve Cryptogrphy(ECC)is based on the difficulty of elliptic curve discrete logarithm. 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, such as less computation overheads shorter key size,considerable bandwidth savings,and so on.All of these merits have made it become the best public-key cryptosystem that is suitable for use in the future.This article firstly presents some introductive materials,including public-key cryptography and the motivations and the developments of the elliptic curve cryptosystems.Then, this paper introduces the math foundation required by ECC,including the addition rule for elliptic curve point defined over finite field.Thirdly, we present an extensive study of the software implementation on PCs of the elliptic curves over prime fields.Fourthly, an elliptic curve cryptographic protocol,the dynamic secret sharing scheme based on elliptic curve cryptosystem,is designed.We also show that our proposed scheme is more secure and efficient than some other schemes. Finally,the evolutive trend and research direction are discussed.
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