TWC: Small: Automorphic Forms and Harmonic Analysis Methods in Lattice Cryptology

TWC：小：格密码学中的自守形式和调和分析方法

• 批准号: 1526333
• 负责人: Stephen Miller
• 金额: $ 49.95万
• 依托单位: Rutgers University New Brunswick
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2015
• 资助国家: 美国
• 起止时间: 2015-08-15 至 2018-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1526333&HistoricalAwards=false
• 关键词: TWC; Small; Automorphic; Forms; Harmonic

Cryptography is a fundamental part of cybersecurity, both in designing secure applications as well as understanding how truly secure they really are. Traditionally, the mathematical underpinnings of cryptosystems were based on difficult problems involving whole numbers (most famously, the apparent difficulty of factoring a product of two unknown primes back into those prime factors). More recently, several completely new types of cryptography have been proposed using the mathematical properties of lattices. For example, homomorphic encryption offers the possibility of manipulating encrypted data without revealing its contents. The research funded by the project seeks to apply new mathematical techniques to understand difficult properties of lattices and hence of these proposed systems -- properties that are seen as crucial for making them practically fast, in particular. The projects in the proposal involve using tools from automorphic forms (such as Borel-Harish-Chandra reduction theory, Eisenstein series, and change of base field) to examine concrete questions about short vectors in certain families of lattices. It also includes a study of cryptosystems based on nonabelian generalizations of lattices, and the geometry of BKZ-reduced bases in Coppersmith's method (including the Boneh-Durfee attack on small exponent RSA).

密码学是网络安全的基本组成部分，既是设计安全的应用程序，又是了解它们真正安全的程度。 传统上，加密系统的数学基础是基于涉及整数的困难问题（最著名的是，将两个未知素数的产物留在这些主要因素中的明显困难）。 最近，已经提出了使用晶格的数学特性提出的几种全新类型的加密类学。 例如，同态加密提供了操纵加密数据的可能性，而无需透露其内容。 该项目资助的研究旨在应用新的数学技术来了解晶格的困难属性以及这些提议的系统的困难属性 - 这些属性对于使它们实际上是快速，尤其是至关重要的。 该提案中的项目涉及使用自动形式的工具（例如borel-harish-chandra降低理论，艾森斯坦系列和基本场的变化），以检查有关某些晶格家族中简短媒介的具体问题。 它还包括一项基于晶格的非亚伯概括的密码系统的研究，以及在Coppersmith方法中降低BKZ降低碱基的几何形状（包括对小指数RSA的Boneh-Durfee攻击）。