Article

On pseudorandom generators with linear stretch in NC<Superscript>0</Superscript>

Authors:

Benny Applebaum,

Eyal KushilevitzAuthors Info & Claims

APPROX'06/RANDOM'06: Proceedings of the 9th international conference on Approximation Algorithms for Combinatorial Optimization Problems, and 10th international conference on Randomization and Computation

Pages 260 - 271

https://doi.org/10.1007/11830924_25

Published: 28 August 2006 Publication History

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 NC⁰ implies non-trivial 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.

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cover image Guide Proceedings

APPROX'06/RANDOM'06: Proceedings of the 9th international conference on Approximation Algorithms for Combinatorial Optimization Problems, and 10th international conference on Randomization and Computation

August 2006

521 pages

ISBN:3540380442

Editors:
Josep Díaz
Departament de Llenguatges i Sistemes Informatics, Universitat Politecnica de Catalunya, Campus Nord - Ed. Omega, 240 Jordi Girona Salgado, Barcelona
,
Klaus Jansen
Institute for Computer Science, University of Kiel, Olshausenstrasse 40, Kiel, Germany
,
José P. Rolim
Institute for Computer Science, Centre Universitaire d'Informatique, Battelle Bâtiment A, Route de Drize 7,, Carouge, Geneva, Switzerland
,
Uri Zwick
School of Computer Science, Tel Aviv University, Battelle Bâtiment A, Route de Drize 7,, Tel Aviv, Geneva, Israel

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Springer-Verlag

Berlin, Heidelberg

Publication History

Published: 28 August 2006

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