We present positive and negative results of fuzzy extractors with computational security. As a negative result, we show that, under a certain computational condition, the existence of a computational fuzzy extractor implies the existence of an information-theoretic fuzzy extractor with slightly weaker parameters. The condition is that the generation procedure of the fuzzy extractor is efficient...

Trevisan has shown that constructions of pseudo-random generators from hard functions (the Nisan-Wigderson approach) also produce extractors. We show that constructions of pseudo-random generators from one-way permutations (the Blum-Micali-Yao approach) can be used for building extractors as well. Using this new technique we build extractors that do not use designs and polynomial-based error-co...

Extractors are Boolean functions that allow, in some precise sense, extraction of randomness from somewhat random distributions, using only a small amount of truly random bits. Extractors, and the closely related ``dispersers,'' exhibit some of the most ``random-like'' properties of explicitly constructed combinatorial structures. In this paper we do two things. First, we survey extractors and ...

We give the first construction of a family of quantum-proof extractors that has optimal seed length dependence O(log(n/ǫ)) on the input length n and error ǫ. Our extractors support any min-entropy k = Ω(log n+ log(1/ǫ)) and extract m = (1− α)k bits that are ǫ-close to uniform, for any desired constant α > 0. Previous constructions had a quadratically worse seed length or were restricted to very...

Since its introduction by Nisan and Zuckerman (STOC ‘93) nearly a decade ago, the notion of a randomness extractor has proven to be a fundamental and powerful one. Extractors and their variants have found widespread application in a variety of areas, including pseudorandomness and derandomization, combinatorics, cryptography, data structures, and computational complexity. Equally striking has b...

Preface Roughly speaking, a deterministic extractor is a function that 'extracts' almost perfect random bits from a 'weak random source'-a distribution that contains some entropy but is far from being truly random. In this book we explicitly construct deterministic extractors and related objects for various types of sources. A basic theme in this book is a methodology of recycling randomness th...