Entropy analysis on chaos excited through destabilization of semiconductor lasers at period-one nonlinear dynamics for physical random number generation
Chin-Hao Tseng, Ryo Funabashi, Kazutaka Kanno, Atsushi Uchida, Chia-Chien Wei, Sheng-Kwang Hwang
Abstract
This study analyzes entropy of broadband chaos excited in a semiconductor laser subject to intensity-modulated optical injection for random number generation with guaranteed unpredictability. It is identified that the flattening of spectral profile around the laser relaxation resonance blurs the periodicity it brings, and thus leads to a high entropy value and a high random number generation rate. The effect of measurement device noise on entropy suggests that both the power of chaos needs to be kept at a level to achieve an adequate signal-to-noise ratio, 24 dB or more, and the entropy contribution of the measurement device noise is excluded in order to assert entropy that can be extracted solely from the intrinsic property of chaos. The effect of data sampling rate on entropy shows that entropy reaches its maximum at the Nyquist rate, which is two times the standard bandwidth of chaos, and the rate of change in entropy is much slower than that in sampling rate as the sampling rate varies, which leads to the dominance of the sampling rate, not entropy, in determining the random number generation rate. It is highly likely that modest oversampling (i.e., a sampling rate modestly higher than the Nyquist rate) gives rise to a higher random number generation rate while entropy slightly decreases.