  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.
