Security Analysis Of The Coupled Chaotic Systems Based On Time Delay

Optical chaotic systems with optical injection or optical feedback can produce higher dimension chaotic signals,and these systems have impressive applications in fields like secure communications,fast physical random bit generation and chaotic radar.But the chaotic output may contain time delay signature(TDS),which can be recovered by statistical analysis.The existence of TDS may pose a threat to the security of secure communication.It may also limit the choices of sampling periods and affect the statistical performance of fast physical random bit generation.As a sensitive key of these applications,TDS suppression has been a hotspot,many different approaches have been proposed to eliminate the TDS,and mutually coupled chaos systems become one of the research hotspots due to their unique advantages.This type of systems could generate two or more chaotic signals simultaneously.Meanwhile the TDS can be completely suppressed.Moreover,the synchronization scheme is relatively easier to design by utilizing such couple mechanisms.However,the TDS analyses in the literatures are focused only on the time series of a single output.The mutual statistical feature between different outputs is ignored.Are these enhanced schemes secure enough is still an open problem.Further study has been done on the issues about the security of the coupled chaotic systems,and the main works are as follows:(1)Mutual statistical analyses have been conducted to extract TD signature of this general type of coupled chaos system.More specifically,the mutually coupled semiconductor laser chaotic system,the intensity-coupled electro-optic chaotic system and the phase-coupled electro-optic chaotic system are studied by cross-correlation function(CCF)and delayed mutual information(DMI)in detail.The TDS suppression performance of the multiple outputs has been investigated numerically for a wide region of coupling strength and frequency detuning,etc.The results show that the TDS can still be extracted by mutual statistical analysis.This work has instructional significance for the chaotic system design and offers a new angle to analyse the time delay of this type of chaotic dynamic.(2)To overcome the drawbacks that the intensity-coupled electro-optic chaoticsystem is not secure enough under mutual analysis of multiple outputs,an optically coupled chaotic system involving three phase modulated electro-optic nonlinear loops and an optical coupler(OC)is proposed.The dynamical properties and the TDS suppressing performance of the system is analyzed in detail.Numerical results show that the TDS can be suppressed not only under statistical analysis of a single output,but also under mutual statistical analysis of the multiple outputs.With the introducing of frequency detuning,the proposed system can conceal the TDS by itself in a larger range.Compared with the intensity modulated electrically coupled scheme,the presented system has less interior noise due to the simpler construction and better performance.