Machine Learning-Based Entropy Estimation for Certifying Physical Random Number Generation Using Chaotic Dynamics of Two Mutually Coupled Semiconductor Lasers

Chin-Hao Tseng^1*, Zhan-Yu Liu¹, Sheng-Kwang Hwang^1,2

¹Department of Photonics, National Cheng Kung University, Tainan, Taiwan
²Advanced Optoelectronic Technology Center, National Cheng Kung University, Tainan, Taiwan

* Presenter:Chin-Hao Tseng, email:purep228@gmail.com

Random number generation with high entropy plays a significant role in various technological applications, including stochastic modeling, cryptography, Monte Carlo simulations, and key distribution in secure communications. Compared to conventional pseudo-random number generation approaches, such as linear congruential generators and M-sequences, which may exhibit intrinsic correlations and periodicity that can potentially be detected by machine learning algorithms, physical random number generation approaches are highly recommended. By sampling and quantizing a high-entropy physical source, the generation of high-quality random numbers is feasible. To achieve this goal for practical applications, it is essential to understand both how to produce a high-entropy physical source and how to measure its actual entropy. In this study, we utilize two semiconductor lasers with asymmetric mutual coupling for high-dimensional microwave chaos generation. To quantify the entropy of the chaotic source, we have developed an attention-based LSTM model as a machine learning-based entropy estimator. Validation with this model confirms that our proposed source achieves an entropy of 2.4 bits/sample, by excluding the contribution of the detection noise and post-processing. To the least extent, the proposed chaotic source can be considered a 2-bit true physical random bit generator, operating at a rate of 160 Gbit/s with guaranteed unpredictability.

Keywords: Random Number Generation, High-Entropy Chaos Generation, Machine Learning, Entropy Estimation, Semiconductor Lasers