@MISC{_onpseudorandom, author = {}, title = {On pseudorandom generators in NC0?}, year = {} }

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Abstract

Abstract. 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, NC03 circuits) and with stretch factor greater than 4 are not pseudorandom. * A large class of "non-problematic " NC0 generators with superlinear stretch (including all NC03 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 NC04 generator with a super-linear stretch that passes the linear dependency test as well as k-wise independence tests, for any constant k. 1 Introduction The notion of deterministically expanding a short seed into a long string thatlooks random to efficient observers, i.e., the notion of a pseudorandom generator, has been a fundamental idea in complexity as well as cryptography. Nevertheless,the question of whether strong pseudorandom generators actually exist is a huge open problem, as their existence (at least with cryptographic parameters) impliesthat P 6 = NP: One can prove that a generator G is not pseudorandom bypresenting a polynomial-time algorithm to decide range(