On pseudorandom generators with linear stretch in NC0

Benny Applebaum

doi:10.1007/978-3-642-17367-7_7

On pseudorandom generators with linear stretch in NC⁰

Benny Applebaum

School of Physics and Astronomy

Tel Aviv University

Research output: Chapter in Book/Report/Conference proceeding › Chapter

Abstract

We consider the question of constructing cryptographic pseudorandom generators in NC ⁰ with large stretch. Our 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 chapter we study this question and obtain the following main results: (1) We show that the existence of a linear-stretch PRG in NC ⁰ implies non-trivial hardness of approximation results without relying on PCP machinery. In particular, it implies that Max3SAT is hard to approximate to within some multiplicative constant. (2) We construct a linear-stretch PRG in NC ⁰ under a specific intractability assumption related to the hardness of decoding “sparsely generated” linear codes. Such an assumption was previously conjectured by Alekhnovich (Proc. of 44th FOCS, pp. 298–307, 2003).

Original language	English
Title of host publication	Information Security and Cryptography
Publisher	Springer Verlag
Pages	123-146
Number of pages	24
DOIs	https://doi.org/10.1007/978-3-642-17367-7_7
State	Published - 2014

Publication series

Name	Information Security and Cryptography
Volume	19
ISSN (Print)	1619-7100

All Science Journal Classification (ASJC) codes

Safety, Risk, Reliability and Quality
Computer Networks and Communications
Computational Theory and Mathematics
Information Systems and Management

Access to Document

10.1007/978-3-642-17367-7_7

Cite this

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