Pseudorandomness in Number Theory, Dynamics and Cryptography

该项目的目的是调查随机性的各个方面，设计新的和分析以前已知的实际使用的随机性提取器的结构。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。该项目的意义在于大量的理论和实际应用以及将开发的新方法。预期成果包括新的密码学强哈希函数和几个著名的开放式猜想，如Sarnak猜想的进展。这些新的结果和方法将对理论数学以及密码学和信息安全等实际领域都非常有益。

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.