Extracting the time delay signature of coupled optical chaotic systems by mutual statistical analysis

The time delay （TD） signature is a critical parameter in optical chaos-based applications. The feasi- bility of extracting the TD has been a crucial issue that significantly influences the performance of these applica- tions. In this paper, statistical analyses have been conducted to extract the TD signatures from different types of coupled optical chaos systems. More specifically, a mutually coupled semiconductor laser chaotic system, an intensity-coupled electro-optic chaotic system, and a phase-coupled electro-optic chaotic system are studied in detail. These systems are proposed to resist the attack strategies against the TD signature. They are proved to be effective under statistical analyzes, such as the self- correlation fimction （SF） and mutual information （MI）. However, only a single output has been considered for the attack process in the existing research. We demonstrated that the TD signature can still be extracted by analyzing the mutual statistical relationship between the different output signals which are generated simultaneously by the coupled system. Furthermore, we find that the extraction strategy is effective for a wide parameter range in these schemes.