 
Summary: On Pseudorandom Generators with
Linear Stretch in NC 0 #
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 NC 0 , 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
NC 0 . In this work we study this question and obtain the following main
results:
1. We show that the existence of a linearstretch PRG in NC 0 implies
nontrivial hardness of approximation results without relying on PCP
machinery. In particular, it implies that Max3SAT is hard to approxi
mate to within some multiplicative constant.
2. We construct a linearstretch PRG in NC 0 under a specific intractabil
ity assumption related to the hardness of decoding ``sparsely gener
