Fundamental Performance Limits of Chaotic-Map Random Number Generators

A chaotic-map random number generator (RNG) is defined using a chaotic map and a bit-generation function. When the map function is exactly known, for a given bit-generation function, the entropy-rate of the generated output bit sequence is asymptotically the highest rate at which truly random bits can be generated from the map. The supremum of the entropy-rate amongst all bit-generation functions is called the binary metric entropy, which is the highest rate at which information can be extracted from any given map using the optimal bit-generation function. In this paper, we provide converse and achievable bounds on the binary metric entropy. The achievability is based on a sequence of universal bit-generation functions in the sense that the bit-generation function is not dependent on the specific map. The proposed sequence of bit-generation functions offers a fairly simple implementation which can easily be realized on hardware for practical purposes.