Time Delay Signature Extraction of Optical Time-Delay Chaos Systems From Short and Noisy Time Series

The optical chaos communication (OCC) can provide physical layer security for high-speed data transmission. In these OCC systems, the time delay signature (TDS) serves as a crucial encryption key. We propose a method based on reservoir computing (RC) network for TDS extraction of OCC systems. The output weight matrix of the RC network provides a numerical representation of nonlinear correlation between a chaotic time series and its time-delayed variants. Then, we can extract TDS by quantifying the features of the weight matrix. The effectiveness is verified by extracting TDS of the two main types of optical time-delay feedback chaos systems. The results demonstrate that, even in cases of strong nonlinearity, noise, and external random disturbance, the TDS can be successfully extracted from time series. Moreover, the required amount of data is significantly reduced in our method.