On the Quality of Random Sequences Produced with a Combined Random Bit Generator

In this paper, we prove that a combined binary generator, which combines modulo-2 bit streams produced by independent generators or by generators that can be grouped into independent pairs of dependent generators, can provide unbiased and uncorrelated bit streams. This result was obtained under the realistic assumption that each source generator produces a sequence of correlated and biased bits. The proposed theorems and formulas are useful in designing random bit generators with satisfactory properties that are robust to external manipulations or to environmental changes up to a certain degree.