CT-ISG: New Directions in Elliptic Curve, Pairing-Based, and Torus-Based Cryptography

CT-ISG：椭圆曲线、基于配对和基于环面的密码学的新方向

• 批准号: 0831004
• 负责人: Alice Silverberg
• 金额: $ 30万
• 依托单位: University of California-Irvine
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2009
• 资助国家: 美国
• 起止时间: 2009-03-15 至 2015-02-28
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0831004&HistoricalAwards=false
• 关键词: CT; ISG; New; Directions; Elliptic

The goal of this research is to solve some important problems in nnnntorus-based, pairing-based, multilinear, and elliptic curve and abelian variety cryptography. Elliptic curve cryptography helps to secure the Internet and is used by the U.S. and other governments and institutions to provide secure communication. Abelian variety cryptography includes elliptic and hyperelliptic curve cryptography, scales well to high security levels, and is especially advantageous in constrained environments. Pairing-based cryptography is a recent cutting-edge use of elliptic curves, with numerous useful security applications. Torus-based cryptography and compression-based abelian variety cryptography improve the efficiency of discrete log and pairing-based cryptography. Multilinear cryptography, which generalizes pairing-based cryptography, is an open question; an efficient and secure solution would give efficient and secure multi- party communication. The security of these systems and the difficulty of the number theoretic problems on which they are based are crucial for the health of the economy and for national and international security.The project focuses on the security of the elliptic curve discrete log problem and other number theoretic problems on which cryptographic security is based, and on the construction of efficient, secure, and scalable public key cryptosystems. The techniques will involve some deep and interesting mathematics.This project will educate and train a diverse workforce in cybersecurity by supporting graduate students, promoting the participation of underrepresented groups, furthering the development of new courses in cutting-edge cybersecurity, and promoting outreach that educates the public.

本研究的目的是解决基于nnntorus的、基于配对的、多线性的、椭圆曲线和交换变种密码系统中的一些重要问题。椭圆曲线密码技术有助于保护互联网的安全，被美国和其他国家的政府和机构用来提供安全的通信。Abelian变种密码体制包括椭圆和超椭圆曲线密码体制，可很好地扩展到高安全级别，并且在受限环境中特别具有优势。基于配对的密码学是椭圆曲线最近的一种前沿应用，具有许多有用的安全应用。基于环面的密码学和基于压缩的阿贝尔变体密码学提高了离散对数和基于配对的密码学的效率。多线性密码学是基于配对的密码学的推广，它是一个悬而未决的问题；一个有效和安全的解决方案将提供高效和安全的多方通信。这些系统的安全性和作为其基础的数论问题的难度对经济的健康和国家和国际安全至关重要。该项目的重点是椭圆曲线离散对数问题和其他作为密码安全基础的数论问题的安全性，以及高效、安全和可扩展的公钥密码系统的构建。这些技术将涉及一些深入和有趣的数学。这个项目将通过支持研究生、促进代表不足的群体的参与、进一步开发尖端网络安全的新课程以及促进教育公众的外展来教育和培训一支多元化的网络安全队伍。