Testing the Strength of Chaotic Systems as Seeds in a Pseudo Random Bit Generator

Chaotic random bit generators have become an integral part of chaotic cryptography and other data protection applications, where they are used as sources of deterministic randomness, to secure an information signal. The performance of the generator though will be heavily affected by the chaotic system that is chosen. The statistical performance, key space size, operations per bit ratio, and speed, are all aspects affected by the chosen system. Thus, the same bit generator will vary in efficiency under different chaotic maps. Driven by these facts, this work studies the performance of a common modulo-based bit generator under different chaotic maps. First, the structure of the bit generator’s nonlinear hash is studied. Then, using a collection of different maps, the generator is evaluated with respect to randomness, key space size, operations per bit ratio, and execution speed. The comparison results are evaluated, to provide a series of observations regarding the use of chaotic systems in bit generators. These observations can serve as guidelines for all future chaotic encryption algorithms, and chaos-based security-related applications in general.