变形Diffie-Hellman问题的等价性

发布时间：2018-05-02 07:39

本文选题：离散对数问题 + Diffie-Hellman问题　；参考：《华南理工大学》2014年硕士论文

【摘要】：解决变形Diffie-Hellman问题的等价性对密码学的研究具有重要的意义，本文正是基于这点展开研究分析的。首先，，本文对密码学的基本原理、应用和特点、主要研究方法和国内外研究现状进行了介绍，随后介绍有限域上离散对数问题和Diffie-Hellman问题的定义。还介绍了公钥密钥系统、数字签名、零知识证明等基于有限域上离散对数问题计算困难性的实际应用，此外，我们还简单介绍和讨论了目前解决有限域上离散对数问题的几种有效算法。 Diffie-Hellman问题是密码学中的一个重要研究课题，受到越来越多的重视。该问题与计算循环群上离散对数问题的困难性紧密关联。已有研究表明4个变形Diffie-Hellman问题：平方Diffie-Hellman问题、逆Diffie-Hellman问题、除Diffie-Hellman问题、平方根Diffie-Hellman问题基于预言机的计算上与计算性Diffie-Hellman问题是等价的。此外，我们还考虑了与判定性Diffie-Hellman问题相关的问题。计算性Diffie-Hellman问题是著名的问题，它有许多各种各样的变形。如果我们对每一种变形都去证明其等价性是非常耗费时间的。本文主要工作是，使用有效和抽象的方法，在满足一定条件下可以直接证明某些变形Diffie-Hellman问题的等价性。其后，我们还将给出一个建立在有限域的离散对数问题上的等价类及其猜想。目前，还没有得知其是否成立，它是一个有趣的问题。最后，对全文进行了总结，并对未来的研究方向进行了展望。
[Abstract]:The equivalence of solving the deformed Diffie-Hellman problem is of great significance to the study of cryptography. Firstly, this paper introduces the basic principles, applications and characteristics of cryptography, the main research methods and the current research situation at home and abroad, and then introduces the definitions of discrete logarithm problem and Diffie-Hellman problem over finite fields. It also introduces the practical applications of public key key system, digital signature, zero knowledge proof and so on based on the discrete logarithm problem over finite fields. We also briefly introduce and discuss some effective algorithms for solving the problem of discrete logarithm over finite fields. Diffie-Hellman problem is an important research topic in cryptography, which has been paid more and more attention. The problem is closely related to the difficulty of computing the discrete logarithm problem on a cyclic group. It has been shown that four deformed Diffie-Hellman problems: square Diffie-Hellman problem, inverse Diffie-Hellman problem, except Diffie-Hellman problem, the square root Diffie-Hellman problem is equivalent to the computational Diffie-Hellman problem based on prophecy. In addition, we also consider the problems related to the deterministic Diffie-Hellman problem. Computational Diffie-Hellman problem is a famous problem, it has many kinds of deformation. It would be time consuming if we proved the equivalence of each variant. The main work of this paper is to prove the equivalence of some deformed Diffie-Hellman problems directly under certain conditions by using effective and abstract methods. After that, we also give an equivalent class and its conjecture based on the discrete logarithm problem in finite fields. At present, it is not yet known whether it holds, it is an interesting question. Finally, the paper summarizes the whole paper and looks forward to the future research direction.
【学位授予单位】：华南理工大学
【学位级别】：硕士
【学位授予年份】：2014
【分类号】：TN918.1

【共引文献】