SaTC: CORE: Medium: Collaborative: An Algebraic Approach to Secure Multilinear Maps for Cryptography

SaTC：核心：媒介：协作：保护密码学多线性映射的代数方法

• 批准号: 1701567
• 负责人: Dan Boneh
• 金额: $ 40万
• 依托单位: Stanford University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2017
• 资助国家: 美国
• 起止时间: 2017-08-01 至 2022-03-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1701567&HistoricalAwards=false
• 关键词: SaTC; CORE; Medium; Collaborative; Algebraic

The project is an interdisciplinary collaboration between mathematicians and computer scientists in an intensive focused research effort to solve a central challenge in cryptography, namely constructing a family of secure and efficient algebraic multilinear maps. Multilinear maps have remarkable applications in cryptography, such as multiuser non-interactive key-exchange, general functional encryption, fully-homomorphic encryption, and indistinguishability obfuscation. The results of the project are expected to enable a new age of cryptographic systems and open new directions in the field. The project will train graduate students and postdoctoral associates through involvement in deep modern mathematics research with applications in computer science.The first candidate multilinear maps are inefficient in practice, and have been shown to be insecure for some of the desired applications. This project takes a very different approach from earlier ones. The starting point is the observation that there already exist many natural multilinear maps in arithmetic geometry, arising naturally from the cohomology of arithmetic varieties and motives, and from K-theory. They give a richer class of objects than elliptic curves over finite fields, whose groups of points are widely used in practice for cryptographic key exchange and public-key encryption. The challenge is to find such algebraic structures for which the multilinear maps can be efficiently computed, and for which the associated cryptographic problems (e.g., discrete logarithm problems) are expected to be hard.

该项目是数学家和计算机科学家之间的跨学科合作，集中进行密集的研究工作，以解决密码学中的一个核心挑战，即构建一系列安全和高效的代数多线性映射。多线性映射在密码学中有着重要的应用，如多用户非交互密钥交换、一般泛函加密、全同态加密、不可分辨混淆等。该项目的结果预计将使密码系统进入新时代，并在该领域开辟新的方向。该项目将通过参与深度现代数学研究和计算机科学应用来培训研究生和博士后助理。第一个候选多线型地图在实践中效率低下，而且已被证明对一些预期的应用程序不安全。这个项目采取了与早期项目截然不同的方法。本文的出发点是观察到，在算术几何中已经存在许多自然的多线性映射，这些映射自然地产生于算术种类和动机的上同调，以及K理论。它们给出了比有限域上的椭圆曲线更丰富的对象类别，其点群在实践中被广泛用于密码密钥交换和公钥加密。挑战是找到这样的代数结构，对于这种代数结构，可以有效地计算多线性映射，并且对于其相关的密码问题(例如，离散对数问题)预计是困难的。

项目成果

Supersingular curves with small noninteger endomorphisms

具有小的非整数自同态的超奇异曲线

• DOI: 10.2140/obs.2020.4.7
• 发表时间: 2020
• 期刊: Open Book Series
• 作者: Love, Jonathan;Boneh, Dan
• 通讯作者: Boneh, Dan