On Pseudorandom Generators in NC

In this paper we consider the question of whether NC0 circuits can generate pseudorandom distributions. While we leave the general question unanswered, we show • Generators computed by NC0 circuits where each output bit depends on at most 3 input bits (i.e, NC0 3 circuits) and with stretch factor greater than 4 are not pseudorandom. • A large class of “non-problematic” NC0 generators with superlinear stretch (including all NC0 3 generators with superlinear stretch) are broken by a statistical test based on a linear dependency test combined with a pairwise independence test. • There is an NC0 4 generator with a super-linear stretch that passes the linear dependency test as well as k-wise independence tests, for any constant k.

• Type: Conference
• Year: 2001
• Where: MFCS
• Authors: Mary Cryan, Peter Bro Miltersen
• Keywords: Independence Tests, Linear Dependency Test, MFCS 2001, Superlinear Stretch, Theoretical Computer Science