@inbook{019a2b98201a4941914964e1f15c1c39,
title = "On Pseudorandom Generators with Linear Stretch in NC0",
abstract = "We consider the question of constructing cryptographic pseudorandom generators in NC0 with large stretch. Our previous constructions of such PRGs were limited to stretching a seed of n bits to n + o(n) bits. This leaves open the existence of a PRG with a linear (let alone superlinear) stretch in NC0. In this chapter we study this question and obtain the following main results: (1) We show that the existence of a linear-stretch PRG in NC0 implies non-trivial hardness of approximation results without relying on PCP machinery. In particular, it implies that Max3SAT is hard to approximate to within some multiplicative constant. (2) We construct a linear-stretch PRG in NC0 under a specific intractability assumption related to the hardness of decoding {"}sparsely generated{"} linear codes. Such an assumption was previously conjectured by Alekhnovich (Proc. of 44th FOCS, pp. 298-307, 2003).",
author = "Oded Goldreich",
year = "2014",
doi = "https://doi.org/10.1007/978-3-642-17367-7_7",
language = "الإنجليزيّة",
isbn = "978-3-642-17367-7; 978-3-642-17366-0",
series = "Information Security and Cryptography Texts and Monographs",
publisher = "Springer Verlag",
pages = "123--146",
booktitle = "CRYPTOGRAPHY IN CONSTANT PARALLEL TIME",
address = "ألمانيا",
}