Descripción del proyecto
Un estudio aborda problemas inveterados en la teoría de los extractores de aleatoriedad
La aleatoriedad de alta calidad es fundamental para la informática. Por ejemplo, en criptografía, los extractores de aleatoriedad se utilizan para generar claves secretas y aleatorias a partir de fuentes que son semisecretas. En general, los extractores de aleatoriedad son algoritmos que convierten una fuente aleatoria débil y una semilla verdaderamente aleatoria en una distribución uniforme de números aleatorios. El proyecto EXT, financiado con fondos europeos, prevé estudiar algunos de los problemas sin resolver más importantes en la teoría de los extractores de aleatoriedad. El proyecto, que se basa en los buenos resultados de anteriores investigaciones en este campo, aplicará técnicas de la teoría de extractores de aleatoriedad a tres problemas elegidos cuidadosamente: la desaleatorización de la computación delimitada en el espacio, las construcciones de grafos de Ramsey y los códigos descodificables localmente.
Objetivo
"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."
Ámbito científico
Programa(s)
Régimen de financiación
ERC-STG - Starting GrantInstitución de acogida
69978 Tel Aviv
Israel