Pseudorandomness in Number Theory, Dynamics and Cryptography

数论、动力学和密码学中的伪随机性

• 批准号: DP230100530
• 负责人: A/Prof Alina Ostafe
• 金额: $ 30.34万
• 依托单位: The University of New South Wales
• 依托单位国家: 澳大利亚
• 项目类别: Discovery Projects
• 财政年份: 2023
• 资助国家: 澳大利亚
• 起止时间: 2023-07-01 至 2026-06-30
• 项目状态: 未结题
• 来源: https://dataportal.arc.gov.au/RGS/Web/Grants/DP230100530
• 关键词: Pseudorandomness; Number; Theory; Dynamics; Cryptography

The aim of the project is to investigate various aspects of randomness, design new and analyse previously known constructions of randomness extractors of practical use. As a dual aim, we will also investigate the pseudorandomness of some classical number-theoretic objects. The significance of this project is in a large number of theoretical and practical applications and in new methods which will be developed. Expected outcomes include new cryptographically strong hash functions and progress towards several famous open conjectures such as Sarnak’s conjecture. These new results and methods will be highly beneficial for both theoretical mathematics and also for such practical areas as cryptography and information security.

该项目的目的是调查随机性的各个方面，设计新的并分析以前已知的实际使用的随机性抽取器的结构。作为一个双重目标，我们还将研究一些经典数论对象的伪随机性。本项目的意义在于大量的理论和实际应用，以及将被开发的新方法。预期的结果包括新的密码强哈希函数和几个著名的公开猜想的进展，如Sarnak猜想。这些新的结果和方法不仅对理论数学，而且对密码学和信息安全等实用领域都有很大的帮助。