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On Pseudorandom Generators with Linear Stretch in NC0
 

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 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 as-
sumption related to the hardness of decoding "sparsely generated" linear

  

Source: Applebaum, Benny - Faculty of Mathematics and Computer Science, Weizmann Institute of Science

 

Collections: Computer Technologies and Information Sciences