Separate Random Number Generation from Correlated Sources

Abstract

This work studies the problem of separate random number generation from correlated general sources with side information at the tester under the criterion of statistical distance. Tight one-shot lower and upper performance bounds are obtained using the random-bin approach. A refined analysis is further performed for two important random-bin maps. One is the pure-random-bin map that is uniformly distributed over the set of all maps (with the same domain and codomain). The other is the equal-random-bin map that is uniformly distributed over the set of all surjective maps that induce an equal or quasi-equal partition of the domain. Both of them are proved to have a doubly-exponential concentration of the performance of their sample maps. As an application, an open and transparent lottery scheme, using a random number generator on a public data source, is proposed to solve the social problem of scarce resource allocation. The core of the proposed framework of lottery algorithms is a permutation, a good rateless randomness extractor, whose existence is confirmed by the theoretical performance of equal-random-bin maps. This extractor, together with other important details of the scheme, ensures that the lottery scheme is immune to all kinds of fraud under some reasonable assumptions.