Exposure-resilient extractors

An exposure-resilient extractor is an efficient procedure that, from a random variable with imperfect min-entropy, produces randomness that passes all statistical tests including those that have bounded access to the random variable, with adaptive queries that can depend on the string being tested. More precisely, EXT : {0, 1}n times {0, 1}d rarr {0, 1}m is a (k, epsi)-exposure resilient extractor resistant to q queries if, when the min-entropy of x is at least k and y is random, EXT(x, y) looks epsi-random to all statistical tests modeled by oracle circuits of unbounded complexity that can query q bits of x. We construct, for any delta < 1, a(k, epsi)-exposure resilient extractor with query resistance ndelta, k = n - nOmega(1), epsi = n-Omega(1), m = nOmega(1) and d = O(log n)