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; 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.

该项目是数学家与计算机科学家之间的跨学科合作，以解决密集的研究工作，旨在解决密码学中的核心挑战，即建立了一个安全有效的代数多线性地图。 多线性图在密码学中具有显着的应用，例如多源非交互键交换，一般功能加密，完全同性恋的加密和难以区分的混淆。该项目的结果有望使新时代的加密系统和该领域的新方向开放。 该项目将通过参与计算机科学应用的深入现代数学研究来培训研究生和博士后同事。第一个候选多线性地图的实践效率低下，并且已被证明是某些所需应用的不安全。该项目与早期的方法采用了截然不同的方法。起点是观察到，算术几何形状中已经存在许多自然的多线性图，这自然源于算术品种和动机的共同体，以及来自K理论。它们提供了比有限领域的椭圆形曲线更丰富的对象，这些曲线在实践中被广泛用于加密密钥交换和公开加密。面临的挑战是找到可以有效计算多线性图的代数结构，并预计相关的加密问题（例如，离散对数问题）很难。