Pseudorandom number generators with balanced Gray codes

In this article, it is shown that a large class of truly chaotic Pseudorandom Number Generators can be constructed. The generators are based on iterating Boolean maps, which are computed using balanced Gray codes. The number of such Gray codes gives the size of the class. The construction of such generators is automatic for small number of bits, but remains an open problem when this number becomes large. A running example is used throughout the paper. Finally, first statistical experiments of these generators are presented, they show how efficient and promising the proposed approach seems.