@article{111965ea7e60439794ce35518353f201,
title = "On pseudorandom generators with linear stretch in NC0",
abstract = "We consider the question of constructing cryptographic pseudorandom generators (PRGs) in NC0, namely ones in which each bit of the output depends on just a constant number of input bits. 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 work we study this question and obtain the following main results: 1. We show that the existence of a linear-stretch PRG in NC 0 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 (FOCS 2003).",
keywords = "Constant depth circuits, Cryptography, Pseudorandom generators, nc0",
author = "Benny Applebaum and Yuval Ishai and Eyal Kushilevitz",
note = "Funding Information: We thank Eli Ben-Sasson, Amir Shpilka and Amnon Ta-Shma for helpful discussions. WealsothankOdedGoldreichformanyusefulsuggestionswhichim-proved the presentation of this paper. Research supported by grants 1310/06 and 36/03 from the Israel Science Foundation.",
year = "2008",
month = apr,
doi = "10.1007/s00037-007-0237-6",
language = "אנגלית",
volume = "17",
pages = "38--69",
journal = "Computational Complexity",
issn = "1016-3328",
publisher = "Birkhauser Verlag Basel",
number = "1",
}