We present characterizations of extractors and Kolmogorov extractors in terms of a combinatorial object called balanced table. These characterizations provide an alternative proof for the relation between extractors and Kolmogorov extractors, first obtained in [FHP06] and [HPV09].

Extractors are functions which are able to “extract” random bits from arbitrary distributions which “contain” sufficient randomness. Explicit constructions of extractors have many applications in complexity theory and combinatorics. This manuscript is a survey of recent developments in extractors and focuses on explicit constructions of extractors following Trevisan’s breakthrough result [Tre99].

We give an introduction to the area of “randomness extraction” and survey the main concepts of this area: deterministic extractors, seeded extractors and multiple sources extractors. For each one we briefly discuss background, definitions, explicit constructions and applications.

Computational extractors are efficient procedures that map a source of sufficiently high min-entropy to an output that is computationally indistinguishable from uniform. By relaxing the statistical closeness property of traditional randomness extractors one hopes to improve the efficiency and entropy parameters of these extractors, while keeping their utility for cryptographic applications. In ...

Fuzzy extractors have been proposed in 2004 by Dodis et al. as a secure way to generate cryptographic keys from noisy sources. In recent years, fuzzy extractors have become an important building block in hardware security due to their use in secure key generation based on Physical Unclonable Functions (PUFs). Fuzzy extractors are provably secure against passive attackers. A year later Boyen et ...