On the Quest for a PRBG Architecture with Consistent Performance Under Any 1D Chaotic Map

Chaos-based pseudo-random bit generators are among the most famous and useful applications of chaotic systems. They utilize a chaotic map as a randomness source, to generate random bits through some hash function. The main issue with such generators is that they are heavily affected by the behavior of the underlying chaotic time series. In a recent work by Moysis et al., a modulo-based hash was tested with a large collection of maps, most of which passed the NIST statistical testing. Unfortunately, not all maps were successful, which still leaves the open problem of designing a generator that has a consistent performance under any chaotic map. This is a challenging problem, which the current work tries to address, by proposing a modification of that bit generator. The proposed architecture introduces an XOR operation between two instances of the generator, where one of them has a fixed chaotic source, the logistic map, and the other uses any other map from the literature. The new generator is tested with 10 different chaotic maps, and all of them generate statistically random bitstreams. This is a highly successful result, that comes with the trade-off of increased execution cost. Guidelines for future bit generator architectures are also provided.