您的位置:山东大学 -> 科技期刊社 -> 《山东大学学报(理学版)》

J4 ›› 2013, Vol. 48 ›› Issue (05): 1-13.

• 前沿进展 •    下一篇

椭圆曲线在密码中的应用:过去,现在,将来…

张方国   

  1. 中山大学信息科学与技术学院, 广东 广州 510006
  • 收稿日期:2013-03-07 出版日期:2013-05-20 发布日期:2013-05-10
  • 作者简介:张方国(1972- ),教授,博士生导师,研究兴趣为密码学理论及其应用.Email:isszhfg@mail.sysu.edu.cn
  • 基金资助:

    国家自然科学基金资助项目(61070168,U1135001);高等学校博士学科点专项科研基金资助项目

Elliptic curves in cryptography: past, present and future…

ZHANG Fang-guo   

  1. School of Information Science and Technology, Sun Yatsen University, Guangzhou 510006, Guangdong, China
  • Received:2013-03-07 Online:2013-05-20 Published:2013-05-10

摘要:

 从19世纪开始,数学家们就把椭圆曲线的算术性质作为代数、几何和数论的一个研究目标进行深入研究。至今,椭圆曲线的理论不仅应用在数学领域,还被广泛应在计算科学、信息安全、物理学等领域。本文主要综述一下椭圆曲线理论在密码学领域的应用,从最早的素性检测、整数分解到椭圆曲线密码体制,以及双线性对密码体制和最近的抗击量子计算的椭圆曲线同种密码体制,对这些应用的基本原理和研究及应用现状逐一介绍。最后对这一领域的一些公开问题和可能的未来进展作了简单探讨。

关键词: 椭圆曲线;密码学;离散对数;双线性对;同种

Abstract:

 From the beginning of the nineteenth century, mathematicians have put the elliptic curves as a research objective of algebra, geometry and number theory to study in-depth. So far, the theory of elliptic curves applied not only in the field of mathematics, and also widely in computing science, information security, physics and other fields. In this paper, we reviewed the application of elliptic curves in cryptography, from the primality testing, integer factorization to elliptic curve cryptosystem, bilinear pairing based cryptosystem and the quantum-resistant cryptosystems from elliptic curve isogenies. We introduced the basic principles and the status of these applications. Finally, we briefly discussed some open questions and possible future progress in this area.

Key words:  elliptic curve; cryptography; discrete logarithm problem (DLP); bilinear pairing; isogenies

No related articles found!
Viewed
Full text


Abstract

Cited

  Shared   
  Discussed   
No Suggested Reading articles found!