Space lower-bounds for pseudorandom-generators

Abstract

Pseudorandom generation is a fundamental notion with many applications such as cryptography and deterministic simulation of random computation. A strong pseudorandom generator w.r.t. a tester class C is one that will "fool" any Turing-test in C to "believe" its output is truly random. We establish the first lower-bounds on the space complexity of general pseudorandom generators (namely, generators with no restrictions on their access to the input seed) which are strong w.r.t the typical time-/space-bounded classes of testers.<>