SaTC: CORE: Small: Lattices, number theory, and distribution questions in cryptography

SaTC：核心：小：密码学中的格、数论和分布问题

• 批准号: 2124692
• 负责人: Stephen Miller
• 金额: $ 50万
• 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: 2021
• 资助国家: 美国
• 起止时间: 2021-07-01 至 2024-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2124692&HistoricalAwards=false
• 关键词: SaTC; CORE; Small; Lattices; number

Modern cryptography faces the serious concern that quantum computers will one day break most of our presently-used cryptosystems. This would have catastrophic consequences to internet security and privacy. As a result, it is very important to develop and understand newer types of potentially quantum-resistant cryptosystems. Cryptosystems based on the mathematical notion of Euclidean lattices are presently the leading candidates for post-quantum cryptography. The proposal studies the mathematical underpinnings of these systems, as well as possible attacks on them.Specifically, the PI and collaborators will study distribution questions (such as biased outputs) related to the behavior of the LLL lattice basis reduction algorithm, one of the basic tools for attacking lattice-based cryptosystems. Estimating the security of lattice-based cryptosystems requires understanding the actual, average-case performance of the LLL algorithm and its variants, hence the interest in such an analysis. The PI and collaborators also plan to develop machinery from analytic number theory and automorphic forms to study the size of the smallest basis of a random lattice, which is also important for understanding average-case key sizes. Finally, the PI and collaborators will systematically study various practical aspects of implementations of elliptic curve cryptosystems, such as unusual biases in timings or other side-channel information.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

现代密码学面临着一个严重的关注，即量子计算机有一天会破坏我们目前使用的大多数加密系统。 这将对互联网安全和隐私产生灾难性的影响。 结果，开发和理解较新类型的潜在抗量子的密码系统非常重要。 基于欧几里得格子的数学概念的密码系统目前是量词后加密术的主要候选者。 该建议研究这些系统的数学基础以及对它们的可能攻击。特别是，PI和合作者将研究与LLL Lattice降低算法的行为相关的分发问题（例如有偏见的输出），这是攻击基于Lattice Crypteposystems的基本工具之一。 估计基于晶格的密码系统的安全性需要了解LLL算法及其变体的实际平均案例性能，从而对这种分析产生兴趣。 PI和合作者还计划开发从分析数理论和自动形式的机械，以研究随机晶格的最小基础的大小，这对于理解平均案例键键的大小也很重要。 最后，PI和合作者将系统地研究椭圆曲线密码系统实施的各个实践方面，例如时间安排中的异常偏见或其他侧向通道信息。该奖项反映了NSF的法定任务，并已通过评估该基金会的知识分子优点和广泛的影响来评估NSF的法定任务。