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Summary: On Pseudorandom Generators with
Linear Stretch in NC0
Benny Applebaum Yuval Ishai Eyal Kushilevitz
Computer Science Department, Technion
{abenny,yuvali,eyalk}@cs.technion.ac.il
April 16, 2007
Abstract
We consider the question of constructing cryptographic pseudorandom
generators (PRGs) in NC0
, namely ones in which each bit of the output de-
pends 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, it implies that Max3SAT is hard to approxi-
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