Abstract

We give explicit constructions of extractors which work for a source of any min-entropy on strings of length n. These extractors can extract any constant fraction of the min-entropy using O(log² n) additional random bits, and can extract all the min-entropy using O(log³ n) additional random bits. Both of these constructions use fewer truly random bits than any previous construction which works for all min-entropies and extracts a constant fraction of the min-entropy. We then improve our second construction and show that we can reduce the entropy loss to 2 log(1=") +O(1) bits, while still using O(log³ n) truly random bits (where entropy loss is defined as [(source min-entropy) + (# truly random bits used) (# output bits)], and " is the statistical difference from uniform achieved). This entropy loss is optimal up to a constant additive term. our...

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