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

doi:10.1007/s12200-017-0706-8

Front. Optoelectron.

2017, Vol. 10

Issue (4) : 378-387 https://doi.org/10.1007/s12200-017-0706-8

RESEARCH ARTICLE

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

Xinhua ZHU, Mengfan CHENG(

), Lei DENG, Xingxing JIANG, Deming LIU

Next Generation Internet Access National Engineering Laboratory (NGIA), School of Optical and Electronic Information, Huazhong University of Science and Technology, Wuhan 430074, China

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Abstract

The time delay (TD) signature is a critical parameter in optical chaos-based applications. The feasibility of extracting the TD has been a crucial issue that significantly influences the performance of these applications. 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 function (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.

Keywords optical chaotic system chaos electro-optic nonlinear system time delay (TD) concealment

Corresponding Author(s): Mengfan CHENG

Just Accepted Date: 10 August 2017 Online First Date: 14 September 2017 Issue Date: 21 December 2017

Cite this article:

Xinhua ZHU,Mengfan CHENG,Lei DENG, et al. Extracting the time delay signature of coupled optical chaotic systems by mutual statistical analysis[J]. Front. Optoelectron., 2017, 10(4): 378-387.

URL:

https://academic.hep.com.cn/foe/EN/10.1007/s12200-017-0706-8
https://academic.hep.com.cn/foe/EN/Y2017/V10/I4/378

Fig.1 Configuration of the capture system

Fig.2 (a) SF curve of E₁; (b) MI curve of E₁; (c) CCF between E₁ and E₂; (d) DMI between E₁ and E₂. Parameters are chosen at h = 7.5 ns^-¹ and D f = 0 GHz

Fig.3 Maps of TD signature in parameter space of h, Df under CCF and DMI analyses. (a) CCF; (b) DMI. The insets show the CCF and DMI curves at h = 0.04, Df = 12 GHz and h = 0.08, D f = 0 GHz, respectively

Fig.4 System configuration built on the intensity-coupled electro-optic chaotic system

Fig.5 SF(x₁), MI(x₁), CCF (x₁, x₂) and DMI(x₁, x₂) curve when b = 4. (a) SF curve; (b) MI curve; (c) CCF curve; (d) DMI curve

Fig.6 Peak values of the CCF and DMI curves while b ranges from 2 to 9. The insets show the CCF and DMI curves while b = 6, 7.5, 9

Fig.7 System configuration built on the phase-coupled electro-optic chaotic system

Fig.8 Fig. 8 SF, MI curve of x₁(t) and CCF, DMI curve of x₁(t), z₁(t), while the bit rate of PRBS is 3 Gb/s and the amplitude is p/2. (a) SF curve; (b) MI curve; (c) CCF curve; (d) DMI curve

Fig.9 Absolute value of the peaks in CCF and DMI at T₁' and T₂' while the bit rate of PRBS increases. (a) CCF; (b) DMI. The insets show the CCF and DMI curves while the bit rate of PRBS is 3 and 10 Gb/s, respectively

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