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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

基本信息

批准号：
1703321
负责人：
Alice Silverberg
金额：
$ 20万
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：
2017
资助国家：
美国
起止时间：
2017-08-01 至 2022-07-31
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=1703321&HistoricalAwards=false
关键词：
SaTC CORE Medium Collaborative Algebraic

项目摘要

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，旨在解决密码学中的一个核心挑战，即构建一个安全有效的代数多线性映射家族。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、一般函数加密、全同态加密、不可否认性混淆等。该项目的成果有望开启密码系统的新时代，并开辟该领域的新方向。该项目将培养研究生和博士后助理通过参与深入的现代数学研究与计算机科学中的应用。第一个候选多线性映射在实践中是低效的，并已被证明是不安全的一些所需的应用。这个项目采取了与以前非常不同的方法。出发点是观察到算术几何中已经存在许多自然的多重线性映射，这些映射自然地产生于算术簇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一类对象，椭圆曲线的点群在实践中广泛用于密钥交换和公钥加密。挑战在于找到这样的代数结构，对于该代数结构，可以有效地计算多线性映射，并且对于该代数结构，相关联的密码学问题（例如，离散对数问题）预计是困难的。

项目成果

期刊论文数量（5）

专著数量（0）

科研奖励数量（0）

会议论文数量（0）

专利数量（0）

Mathematics and Cryptography: A Marriage of Convenience?

数学和密码学：方便的结合？

DOI：
10.1007/978-3-030-45721
发表时间：
2020
期刊：
Advances in Cryptology – EUROCRYPT 2020
影响因子：
0
作者：
Silverberg, Alice
通讯作者：
Silverberg, Alice

Universal gradings of orders

订单通用分级

DOI：
10.1007/s00013-018-1228-3
发表时间：
2018
期刊：
Archiv der Mathematik
影响因子：
0.6
作者：
Lenstra, H. W.;Silverberg, A.
通讯作者：
Silverberg, A.

Multiparty Non-Interactive Key Exchange and More From Isogenies on Elliptic Curves

DOI：
10.1515/jmc-2015-0047
发表时间：
2018-07
期刊：
Journal of Mathematical Cryptology
影响因子：
1.2
作者：
D. Boneh;D. Glass;D. Krashen;K. Lauter;Shahed Sharif;A. Silverberg;Mehdi Tibouchi;Mark Zhandry
通讯作者：
D. Boneh;D. Glass;D. Krashen;K. Lauter;Shahed Sharif;A. Silverberg;Mehdi Tibouchi;Mark Zhandry

Algebraic maps constant on isomorphism classes of unpolarized abelian varieties are constant

非极化阿贝尔簇的同构类上的代数映射常数是常数