Time delay estimation from the time series for optical chaos systems using deep learning

Abstract

We propose a model-free time delay signature (TDS) extraction method for optical chaos systems. The TDS can be identified from time series without prior knowledge of the actual physical processes. In optical chaos secure communication systems, the chaos carrier is usually generated by a laser diode subject to opto-electronic/all-optical time delayed feedback. One of the most important factors to security considerations is the concealment of the TDS. So far, statistical analysis methods such as autocorrelation function (ACF) and delayed mutual information (DMI) are usually used to unveil the TDS. However, the effectiveness of these methods will be reduced when increasing the nonlinearity of chaos systems. Meanwhile, certain TDS concealment strategies have been designed against statistical analysis. In our previous work, convolutional neural network shows its effectiveness on TDS extraction of chaos systems with high loop nonlinearity. However, this method relies on the knowledge of detailed structure of the chaos systems. In this work, we formulate a blind identification method based on long short-term memory neural network (LSTM-NN) model. The method is validated against the two major types of optical chaos systems, i.e. opto-electronic oscillator (OEO) chaos system and laser chaos system based on internal nonlinearity. Moreover, some security enhanced chaotic systems are also studied. The results show that the proposed method has high tolerance to additive noise. Meanwhile, the data amount needed is less than existing methods.

Time-Delay Identification Using Multiscale Ordinal Quantifiers

“…Chaotic solutions are obtained in such a case for all τ 0 ≥ 1 [45,46]. We first explore the capability of the ACF, WPE, PE and OTA quantifiers to identify the presence of a time-delay in the time series generated by the time-delayed Hénon map of Equation (10). In nonlinear systems with time-delay, it is often of importance to estimate the precise value of the time-delay from the time series [7,10].…”

“…We first explore the capability of the ACF, WPE, PE and OTA quantifiers to identify the presence of a time-delay in the time series generated by the time-delayed Hénon map of Equation (10). In nonlinear systems with time-delay, it is often of importance to estimate the precise value of the time-delay from the time series [7,10]. Thus, we present in Figure 7 the estimated delay for all the analyzed quantifiers as a function of the true time-delay, τ 0 , of the generating chaotic model.…”

“…But what is more important for our present concerns is the fact that the success of this optical chaos-based cryptosystems strongly depends on the ability to conceal the time-delay signature, and much effort has been focused on designing new schemes able to hide it [7][8][9]. Consequently, tools specially developed to unveil this supposedly hidden information are crucial to realize how effective the concealment strategies can actually be [10].…”

“…Moreover, several heterogeneous scientific fields could benefit from advances along this research line. Even though several methods have been introduced for time-delay estimation from time series [12] (and references therein) [10,13], the general question about which is the optimal approach or strategy remains open. Trying to give a step forward in this direction, in this paper, we analyze the ability of three quantifiers based on ordinal patterns to unveil delay dynamics.…”

An Enhanced Electro-Optic Chaos Secure Communication System Immune to Time Delay Signature Extraction

“…Unfortunately, it is recently discovered that there is still some security vulnerability from the perspective of dynamics. Based on the strong nonlinear inversion capability of deep learning, a TDS identification method has been proposed [23], which brings new threats to optical chaos communication. The method can identify the TDS of some security enhanced systems, even when statistical analysis loss their effectiveness.…”