论文标题:超椭圆曲线密码体制的研究
Research of Some Intelligent Mining Algorithms Based on Knowledge Roughness and Extended Reducts of Rough Sets
论文作者 瞿芳
论文导师 刘传才,论文学位 硕士,论文专业 计算机系统结构
论文单位 福州大学,点击次数 77,论文页数 60页File Size2281k
2004-12-01论文网 http://www.lw23.com/lunwen_223810937/ 超椭圆曲线;Jacobian群;离散对数问题;公钥密码体制;公钥证书
Hyperelliptic curve;Jacobian group;Discrete Logorithm problem;public-key cryptosystem; public-key certificate
超椭圆曲线是一类特殊的代数曲线，它可以看成是椭圆曲线的推广，亏格为1的超椭圆曲线就是椭圆曲线。与椭圆曲线密码体制(ECC)相比，超椭圆曲线密码体制(HCC)具有明显的安全性优势，因而，近几年来超椭圆曲线密码理论备受密码学界的重视。目前对它的研究主要还是停留在理论阶段，存在大量未解决的问题。本文以二进制有限域上的超椭圆曲线为主要研究对象，从HCC的数学基础以及协议两方面对该类密码体制进行了深入的研究。 建立有限域上安全超椭圆曲线密码体制的基础是构造有限域上安全的超椭圆曲线，因而应当首先选择适于建立密码体制的超椭圆曲线。现有的研究表明，用于构造密码体制的超椭圆曲线必须是低亏格的，且它的Jacobian基数中必须至少含有一个160bit的大素因子。从该安全前提出发，作者提出一种安全曲线的生成算法，该算法是对Weil算法的一个改进，具有曲线生成速度快、安全性高等特点。为提高系统的实现速度，作者主要研究了有限域和Jacobian群中基本运算的快速实现问题，在参考大量有关文献的基础上，分别给出这些运算的有效实现算法，并在系统中予以实现。此外，作者还对实现过程中的一些关键问题，如基点的选取、明文的嵌入等，进行了深入的探讨，分别给出相应的解决方案。 在对密码协议的研究过程中，作者提出了一种基于公钥证书的超椭圆曲线密码体制方案，该方案有效地解决了传统密码体制中的一些安全问题，具有安全强度高、通信量小、计算速度快等优点，特别适合用于解决资源受限系统的安全问题。该方案除了具有信息加密、数字签名等功能之外，稍作修改后，还能用于系统和用户之间身份的双向认证。但由于时间上的关系，方案还未能得以实现。
The hyperelliptic curve is a kind of special algebra curve, it can be regarded as the popularization of the elliptic curve, elliptic curve is a kind of special hyperelliptic curve whose genus equals to 1. Compared with Elliptic Curve Cryptosystems (ECC), Hyperelliptic Curve Cryptosystems(HCC) has obvious security advantages , therefore the theory of HCC has caused the crypto circle"s extensive attention in recent years. The study on it mainly remains at theory stage at present, and a large amount of problems await to solve further. This paper regards the Hyperelliptic curve based on the binary finite field as the main research object, has carried on deep research to this kind of cryptosystems from two respects which are the mathematics foundation and agreement of HCC.The basis of building secure hyperelliptic curve cryptosystems is constructing secure hyperelliptic curve over finite field, therefore firstly must select an hyperelliptic curve suitable to build cryptosystem. Research on hand shows that the genus of an secure hyperelliptic curve should be small and the cardinality of its Jacobian group should contain a 160bit big prime factor at least. Proceeding from this safe prerequisite, this paper presents a method to construct safe curve, it is an improvement to Weil algorithm. In order to improve the HCC speed of realization, the fast problem of implementation which are connected with basis operation on the finite field and the jacobian group is studied, and the corresponding algorithms are presents in this paper. In addition, some important problems, such as the choice of a base point and the embedding problem of plain text etc, also are studied in this paper. In the course of study on the agreements, this paper provides a kind of hyperelliptic cryptosystem scheme based on public key certificate, this scheme solves some safe problems in the traditional cryptosystem effectively, have the small communication amount, safe intensity and computation speed, especially suitable for solving the security problem existing in some systems with limited resource. Except for some basic functions, such as data encrypting and figures signing, this cryptosystems still can be used in the two-way authentication between the system and the users. But because of the relation on time, it fails to can be realized.
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