On pseudorandom generators with linear stretch in NC0

Benny Applebaum, Yuval Ishai, Eyal Kushilevitz

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

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 nontrivial hardness of approximation results without relying on PCP machinery. In particular, that Max 3SAT is hard to approximate to within some 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 [1]. We note that Alekhnovich directly obtains hardness of approximation results from the latter assumption. Thus, we do not prove hardness of approximation under new concrete assumptions. However, our first result is motivated by the hope to prove hardness of approximation under more general or standard cryptographic assumptions, and the second result is independently motivated by cryptographic applications.

Original languageEnglish
Title of host publicationApproximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques - 9th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2006 a
PublisherSpringer Verlag
Pages260-271
Number of pages12
ISBN (Print)3540380442, 9783540380443
DOIs
StatePublished - 2006
Externally publishedYes
Event9th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2006 and 10th International Workshop on Randomization and Computation, RANDOM 2006 - Barcelona, Spain
Duration: 28 Aug 200630 Aug 2006

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume4110 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference9th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2006 and 10th International Workshop on Randomization and Computation, RANDOM 2006
Country/TerritorySpain
CityBarcelona
Period28/08/0630/08/06

Fingerprint

Dive into the research topics of 'On pseudorandom generators with linear stretch in NC0'. Together they form a unique fingerprint.

Cite this