Summary: Cryptography in NC 0
(EXTENDED ABSTRACT) 
Benny Applebaum Yuval Ishai
Computer Science Department, Technion
fabenny,yuvali,eyalkg@cs.technion.ac.il
Eyal Kushilevitz
Abstract
We study the parallel time­complexity of basic crypto­
graphic primitives such as one­way functions (OWFs) and
pseudorandom generators (PRGs). Specifically, we study
the possibility of computing instances of these primitives
by NC 0 circuits, in which each output bit depends on a
constant number of input bits. Despite previous efforts in
this direction, there has been no significant theoretical ev­
idence supporting this possibility, which was posed as an
open question in several previous works.
We essentially settle this question by providing over­
whelming positive evidence for the possibility of cryptog­
raphy in NC 0 . Our main result is that every ``moderately
easy'' OWF (resp., PRG), say computable in NC 1 , can

Source: Applebaum, Benny - Faculty of Mathematics and Computer Science, Weizmann Institute of Science
Ishai, Yuval - Department of Computer Science, Technion, Israel Institute of Technology

Collections: Computer Technologies and Information Sciences