A Novel Design of Random Number Generators Using Chaos-Based Extremum Coding

This paper proposes a new chaos-based extremum coding method to realize a true random number generator (RNG). Based on the chain rule, we innovatively introduce two parameters into the dynamics of chaotic systems to modulate the speed and amplitude of state responses. Then, by discretizing the continuous modulated chaotic system, the corresponding discrete chaotic system can be obtained, which allows the use of low-cost micro-controllers for implementation, enhancing system stability, and reducing costs. Also, a novel chaos-based extremum coding approach is proposed for generating a random extremum-coded sequence (RECS). Using this RECS to switch and decide modulation parameters significantly improves the randomness of the sequences generated by the RNGs. To highlight the contribution of this RNG design, the randomness and security of the RNGs are evaluated by statistical tests such as NIST, Diehard, and ENT. Through comparisons with recent published works, the results show that the proposed chaotic extremum-coded RNG can demonstrate superior performance with a higher level of randomness.