TWC: Small: Algorithms for Number-Theoretic Problems Arising in Cryptography

TWC：小：密码学中出现的数论问题的算法

• 批准号: 1617802
• 负责人: Kirsten Eisentraeger
• 金额: $ 50万
• 依托单位: Pennsylvania State Univ University Park
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2016
• 资助国家: 美国
• 起止时间: 2016-08-01 至 2020-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1617802&HistoricalAwards=false
• 关键词: TWC; Small; Algorithms; Number; Theoretic

This project studies several questions that have applications to cryptography. One goal is to develop classical cryptosystems that are secure against quantum computers. In particular, the project explores the security of some of the recently proposed lattice-based systems. Another goal is to make systems that are currently being used more efficient. The project aims to improve some of the algorithms for constructing curves that can be used in cryptosystems. This project will have implications for understanding which cryptosystems should be used now or in the future. Some lattice-based cryptosystems were recently broken by use of quantum algorithms. The investigators are exploring whether other lattice-based systems, such as systems based on Ring-LWE, can be broken by quantum computers as well. The Ring-LWE problem is important because a number of cryptographic constructions, including fully homomorphic encryption, can be based on it. The PI and the co-PI are also investigating other post-quantum key-exchange, signature and encryption schemes. In a different direction, the investigators work on more efficient algorithms for constructing curves that can be used in discrete-log based cryptosystems. The investigators involve their graduate students in many parts of these research projects. Through her involvement in various mentoring activities the PI aims to increase the number of women who will pursue a career in science or mathematics. She also teaches middle school and high school students about cryptography.

这个项目研究了几个在密码学中有应用的问题。目标之一是开发出能够抵御量子计算机攻击的经典密码系统。特别是，该项目探讨了一些最近提出的基于网格的系统的安全性。另一个目标是使目前正在使用的系统更有效。该项目旨在改进一些用于构造可用于密码系统的曲线的算法。该项目将对理解现在或将来应该使用哪些密码系统产生影响。最近，一些基于格的密码系统被量子算法破解。研究人员正在探索其他基于晶格的系统，例如基于Ring-LWE的系统，是否也可以被量子计算机打破。Ring-LWE问题是一个重要的密码学问题，包括全同态加密在内的许多密码学构造都可以基于它。PI和co-PI也在研究其他后量子密钥交换、签名和加密方案。在另一个方向上，研究人员致力于更有效的算法，用于构建可用于离散对数密码系统的曲线。 研究人员让他们的研究生参与这些研究项目的许多部分。 通过参与各种辅导活动，PI旨在增加将在科学或数学领域从事职业的妇女人数。她还教初中和高中学生密码学。