Project description
Study addresses long-standing problems in randomness extractor theory
High-quality randomness is central to computer science. For example, in cryptography randomness extractors are used to generate secret and random keys from sources that are semi-secret. In general, random extractors are algorithms that convert a weakly random source and a truly random seed into a uniform distribution of random numbers. The EU-funded EXT project plans to study some of the most important open problems in randomness extractor theory. Building on successful outcomes of previous research on the field, the project will apply techniques from randomness extract theory to three carefully chosen problems: derandomisation of space-bounded computation, Ramsey graph constructions, and locally decodable codes.
Objective
"Randomness extractors are central in theoretical computer science and have a huge impact in complexity theory, error correcting codes, and cryptography to name a few. Informally, a randomness extractor is an algorithm that ""purifies"" the randomness of an imperfect random source by extracting from it a sequence of uniform and independent random bits. The myriad of applications make randomness extractor theory a vibrant and exciting research field with a major impact. Over the last few years, there has been a flurry of progress on deep long-standing open problems in the field and the PI's work played a key role in this development. Several novel ideas were introduced which give hope that other long-standing open problems in the field can be resolved. Moreover, the new techniques raise new and intriguing questions. In this research, we propose to study some of the most important open problems in randomness extractor theory: classic as well as the new challenges that arise. Moreover, we propose to apply results and techniques from randomness extract theory to three carefully chosen problems with a huge impact on their respective fields: (1) derandomization of space-bounded computation; (2) Ramsey graph constructions; and (3) locally decodable codes. Progress on any of these problems would be ground breaking. Despite the significant challenge, we believe that we are in a unique place to pursue these long-standing open problems both within randomness extractors theory and beyond. Indeed, as mentioned, the PI's work on randomness extractors was pivotal to the exciting progress in the field. Moreover, the PI obtained a breakthrough result on Ramsey graphs construction and the first improvement in 25 years on a problem related to derandomization of space-bounded computation. Both results were obtained using machinery from randomness extractor theory."
Fields of science
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Funding Scheme
ERC-STG - Starting GrantHost institution
69978 Tel Aviv
Israel