Chaos-based secure communication system using logistic map Narendra Singh, Aloka Sinha à Department of Physics, Indian Institute of Technology Delhi, Hauz Khas, New Delhi-110016, India article info Article history: Received 31 July 2009 Received in revised form 30 September 2009 Accepted 1 October 2009 Available online 12 November 2009 Keywords: Opto-electronic encryption/decryption Logistic map Pulse position modulation abstract We propose a new opto-electronic secure communication system using logistic map and pulse position modulation. A modified version of the electronic circuit of the logistic map is used to generate the chaotic signal. Pulse position modulation scheme together with the logistic map has been used to encrypt the signal. Optical fiber has been used to demonstrate the proposed scheme. Eye pattern has been used to verify the noise-like nature of the encrypted signal. Opto-electronic implementation of the technique has been carried out. Experimental results are presented to verify the validity of the proposed technique. & 2009 Published by Elsevier Ltd. 1. Introduction In recent years, hacking of data has become a serious problem due to which secure communication encryption schemes [1] is becoming a fundamental need for everyone. In order to fulfill these requirements, many optical encryption techniques have been proposed. These use Fourier transform (FT) [2–3], fractional Fourier transform (FRT) [4–5], extended FRT (EFRT) [6], gyrator transform (GT) [7], Hartley transform (HT) [8], and watermarking methods [9]. Other image encryption techniques have also been proposed recently [10–12]. As the need for secure communication increases, ‘‘chaos’’ has become an important tool for the realiza- tion of such secure system. Chaos is the term used for a variety of non-linear phenomenon that occur in both discrete and contin- uous dynamical systems. Due to the attractive properties of chaos such as noise-like behavior and sensitivity to the initial condition, it has become very important for both optical encryption methods [13–18] and electronic encryption methods. Chaotic signal can be generated by using relatively simple analog hardware such as electronic hardware for logistic map [19], tent map [20] and Chua circuit [21–23]. Various chaotic modulation schemes such as differential chaos shift key (DCSK) [24] and pulse position modulation (PPM) scheme [25–29] have been proposed. Along with the development of optical telecommunications systems, there is lot of interest in secure optical transmission and in opto- electronic technique for encryption. Several opto-electronic systems have been proposed [30–35] that exploit fast chaotic dynamics as a possible alternative to classical encryption techniques based on numerical algorithms. The noisiness of the encrypted data can be analyzed by using eye pattern [36–38]. In this paper, we propose a new opto-electronic secure communication system using logistic map and PPM. The gener- ated chaotic signal is added to the input signal and a PPM scheme is performed over it. The obtained signal is the encrypted signal. The encrypted signal is communicated through an optical fiber from the transmitter side to the receiver side. At the receiver, pulse position demodulation (PPD) is performed and the same chaotic signal is subtracted from it. The obtained signal is the decrypted signal. The chaotic signal has been generated by designing the electronic circuit for implementation of the logistic map. A modified version of the electronic circuit has been designed. Optical fiber has been used as the communication channel to demonstrate the proposed technique. Eye pattern has been used to verify the noisy nature of the encrypted signal. Opto- electronic implementation of the technique has been carried out. Experimental results are presented to verify the validity of the proposed technique. 2. Logistic map Logistic map [14–19] is a chaotic map that generates chaotic signal which has a random-like appearance and is very sensitive to the initial conditions. These random iterative values are limited between bounds. After any value of iterations, convergence of the iterative values can never be seen. Logistic map is used for our study and is defined as f ðxÞ¼ lxð1  xÞ ð1Þ ARTICLE IN PRESS Contents lists available at ScienceDirect journal homepage: www.elsevier.com/locate/optlaseng Optics and Lasers in Engineering 0143-8166/$- see front matter & 2009 Published by Elsevier Ltd. doi:10.1016/j.optlaseng.2009.10.001 à Corresponding author. Tel.: +9111 2659 6003. E-mail address: aloka@physics.iitd.ernet.in (A. Sinha). Optics and Lasers in Engineering 48 (2010) 398–404