Extracting Randomness from Samplable Distributions

Randomness extractors convert weak sources of randomness into an almost uniform distribution; the conversion uses a small amount of pure randomness. In algorithmic applications, the use of extra randomness can be simulated by complete enumeration (alas, at the price of a considerable slow-down), but in other applications (e.g. in cryptography) the use of extra randomness is undesirable. In this paper, we consider the problem of deterministically converting a weak source of randomness into an almost uniform distribution. Previously, deterministic extraction procedures were known only for classes of distributions having strong independence requirement. Under complexity assumptions, we show how to extract randomness from any samplable distribution, i.e. a distribution that can be generated by an efficient sampling algorithm. Assuming that there are problems in E that are not solvable by subexponential-size circuits with 5 gates, we give a polynomial-time extractor that is able to transf...

• Type: Conference
• Year: 2000
• Where: FOCS
• Authors: Luca Trevisan, Salil P. Vadhan
• Keywords: Extra Randomness, FOCS 2000, Randomness, Theoretical Computer Science, Uniform Distribution