 
Summary: On Pseudorandom Generators with
Linear Stretch in NC0
Benny Applebaum, Yuval Ishai, and Eyal Kushilevitz
Computer Science Department, Technion, Haifa 32000, Israel
{abenny,yuvali,eyalk}@technion.ac.il
Abstract. We consider the question of constructing cryptographic pseudoran
dom 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 linearstretch 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 linearstretch PRG in NC0
under a specific intractability as
sumption related to the hardness of decoding "sparsely generated" linear
