Shannon Entropy Estimation Based on Chaotic Attractor Reconstruction for a Semiconductor Laser

State-space reconstruction of chaotic attractors is investigated for deducing the randomness generated by an optically injected semiconductor laser. The attractors are reconstructed using the intensity time series from both simulations
and experiments. The time-dependent exponent is adopted for estimating the divergence between nearby trajectories, thereby verifying the effective noise amplification by chaotic dynamics. After discretization for obtaining the output bits, the Shannon entropies continually generated by the laser are estimated. Here, the effect of postprocessing on the randomness of the output bits is investigated by evaluating the Shannon entropies. The role of a delayed exclusive-or operation is investigated, where the time-dependent exponents as well as the Shannon entropies are affected. The results fundamentally confirm the provision of non-deterministic randomness by the chaotic lasers. Practical tests for randomness at a combined output bit rate of 200 Gbps are successfully conducted.