CT-ISG: The Foundational Security of Elliptic Curve Cryptography

CT-ISG：椭圆曲线密码学的基础安全性

• 批准号: 0627458
• 负责人: Ming-Deh Huang
• 金额: $ 30万
• 依托单位: University of Southern California
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2006
• 资助国家: 美国
• 起止时间: 2006-09-01 至 2010-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0627458&HistoricalAwards=false
• 关键词: CT; ISG; Foundational; Security; Elliptic

In the ever expanding cyber community public-key cryptography isdeployed at various platforms and gateways to ensure authenticity,confidentiality, and integrity in all kinds of communication andtransaction. Therefore the security of public-key cryptography isfoundational to the security of the cyberspace. Elliptic curvecryptography has risen in recent years to meet the challenge ofconstraints in bandwidth, power, and size in wireless and mobilecommunication, and is likely to become the mainstay for public-keycryptography in the wireless arena. This research focuses oncritical issues concerning the foundational security of ellipticcurve cryptography. A unified approach using the theory of globalduality is developed to study the discrete logarithm problem uponwhich elliptic curve cryptosystems are based. This research seeks toidentify and classify weak cases of elliptic curve groups beyondwhat is currently known. The findings of this research will deepenunderstanding of the security of the elliptic curve cryptosystems ingeneral, and relative cryptographic strength of specific classes ofelliptic curves in particular. The techniques and methodologydeveloped in the proposed research will provide the basis for futureresearch on similar issues in curve-based cryptography. Along-term goal of this research is to explore the prospect of usingalgebraic groups for building future generations of public-keycryptosystems. Elliptic Curve Cryptography is also an excellentsubject to integrate research and education in mathematics andengineering. Part of this project is to introduce students at alllevels and across disciplinary boundaries to research in this areathrough well-designed courses, seminars and workshops.

在不断扩大的网络社区中，公钥密码被部署在各种平台和网关上，以确保各种通信和交易的真实性、保密性和完整性。因此，公钥密码体制的安全性是网络空间安全的基础。椭圆曲线密码体制是近年来为应对无线和移动通信中带宽、功率和大小的限制而兴起的，很可能成为无线领域公钥密码体制的中流砥柱。本文主要研究椭圆曲线密码体制基础安全的关键问题。利用整体对偶理论，发展了一种统一的方法来研究椭圆曲线密码体制所基于的离散对数问题。这项研究试图识别和分类椭圆曲线群的弱情况，而不是目前所知的情况。这一研究结果将加深对椭圆曲线密码体制安全性的一般理解，特别是对特定类型椭圆曲线的相对密码强度的理解。所提出的技术和方法将为今后研究基于曲线的密码学中的类似问题提供基础。这项研究的长期目标是探索使用代数群来构建下一代公钥密码系统的前景。椭圆曲线密码学也是数学和工程研究与教育相结合的一门优秀学科。该项目的一部分是通过精心设计的课程、研讨会和讲习班，向所有水平和学科边界的学生介绍这一领域的研究。