**Physical-Layer Encryption Using Digital Chaos for Secure OFDM Transmission**

Xuelin Yang, Adnan A.E. Hajomer and Weisheng Hu

Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/intechopen.68238

#### Abstract

Due to the broadcasting nature of passive optical network (PON), data security is challenging. For the transmission of orthogonal frequency division multiplexing (OFDM) signals, the high peak-to-average power ratio (PAPR) is considered as one of the major drawbacks. This chapter reviews the digital chaos-based secure OFDM data encryption schemes, where the transmission performance is improved via PAPR reduction. The digital chaos is incorporated into the signal scrambling approaches: selective mapping (SLM), partial transmit sequence (PTS); and precoding approaches: discrete Fourier transform (DFT) and Walsh-Hadamard transform (WHT) for PAPR reduction. Multi-fold data encryption is achieved with a huge key space provided by digital chaos, to enhance the physical-layer security for OFDM-PON, while the pseudo-random properties of digital chaos are applied for PAPR reduction, which consequently improves the transmission performance. The evidences of these encryption approaches are presented in terms of theories, simulations, as well as experimental demonstrations. The chaotic data encryption schemes could be promising candidates for next-generation OFDM-PON.

Keywords: orthogonal frequency division multiplexing (OFDM), peak-to-average power ratio (PAPR), digital chaos, passive optical network (PON)

#### 1. Introduction

Over the last decades, passive optical network (PON) has been playing a vital role in data traffic explosion driven by broadband services such as high-definition television (HDTV), cloud computing, 3D television, video on demand (VoD) [1, 2], and so on, because it offers several potential benefits such as high capacity, low cost, and energy efficiency. In fact, PON is a broadcasting structure that extends for ~20–100 km from optical line terminal (OLT) to

© 2017 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

optical network units (ONUs), in which no active component (such as Erbium-doped fiber amplifier, EDFA) is employed. The broadcasting nature in the downstream data traffic and the huge number of subscribers in PON make the data more susceptible to be eavesdropped or attacked by illegal ONUs. For instance, during the ranging process, the OLT has to broadcast the serial number and ID information of the ranged ONUs; a malicious user could make use of this information for spoofing.

Comparing with the encryption in higher layers, for instance, media access control (MAC) layer, physical-layer encryption can protect the data as well as the control and header information. If the physical-layer data encryption is implemented, this type of spoofing can be avoided since the header and ID information are all encrypted within the physical-layer; thus, it becomes desirable for security enhancement in PON. For security reasons, churning procedure of scrambling the data for downstream connection has been defined in ITU-T G.983.1 standard (Section 8.3.5.6 [3]), which is based on a key sent from ONU to OLT through a secure channel with a defined protocol; however, the key is vulnerable to be broken due to its limited short key length.

Chaos communication has been proposed to provide a huge key space for data security enhancement attributed to its unpredictable nature of randomness, noise-like nature, and broadband. However, the implementation of chaotic optical communication (i.e., fast changing of chaotic optical carriers) requires identical devices with identical parameters for transmitter and receiver, which is quite restricted from real implementation. On the other hand, digital chaos has attracted notable attention recently as a flexible alternative to avoid the implementation difficulty for device-based optical chaos [4–10]. Because it offers very appealing properties from the perspective of data encryption such as ergodicity, pseudo-randomness, and high sensitivity to the initial values, digital chaos provides a huge key space for security applications. Moreover, due to flexible digital signal processing (DSP) in electric domain, digital chaos is easier to be applied.

Optical orthogonal frequency division multiplexing (OFDM) is regarded as a promising modulation technique for next-generation PON, owing to the advantages in high spectrum efficiency, cost-effectiveness, and tolerance to fiber dispersion. High-speed data rate of OFDM signals is achieved by parallel transmission of partially overlapped spectra, lower rate frequency domain tributaries [11]. Moreover, the generation, modulation, and demodulation of OFDM signals have to be performed using DSP in electric domain, therefore it provides a natural physical-layer environment, where digital chaos can be incorporated into OFDM data encryption during transmission. However, OFDM modulation often leads to high peak-to-average power ratio (PAPR), which is one of the most detrimental factors in OFDM signal transmission, as it causes power saturation and nonlinear distortion at the optical receiver while degrading the transmission performance. The pseudo-random properties of digital chaos are helpful for PAPR reduction of OFDM signals, which consequently improves the transmission performance.

In this chapter, OFDM data encryption schemes are reviewed in detail for physical-layer security enhancement based on digital chaos during transmission, while jointly the transmission performances are significantly improved because of the effective reduction in PAPR of OFDM signals. The rest of the chapter is organized as follows. In Section 2, the fundamental theory of PAPR reduction of OFDM signals is shown. The properties of digital chaos are presented in Section 3. In Section 4, the encryption schemes are illustrated in details. Conclusions are given in Section 5.

## 2. PAPR of OFDM signals

optical network units (ONUs), in which no active component (such as Erbium-doped fiber amplifier, EDFA) is employed. The broadcasting nature in the downstream data traffic and the huge number of subscribers in PON make the data more susceptible to be eavesdropped or attacked by illegal ONUs. For instance, during the ranging process, the OLT has to broadcast the serial number and ID information of the ranged ONUs; a malicious user could make use of

Comparing with the encryption in higher layers, for instance, media access control (MAC) layer, physical-layer encryption can protect the data as well as the control and header information. If the physical-layer data encryption is implemented, this type of spoofing can be avoided since the header and ID information are all encrypted within the physical-layer; thus, it becomes desirable for security enhancement in PON. For security reasons, churning procedure of scrambling the data for downstream connection has been defined in ITU-T G.983.1 standard (Section 8.3.5.6 [3]), which is based on a key sent from ONU to OLT through a secure channel with a defined

protocol; however, the key is vulnerable to be broken due to its limited short key length.

Chaos communication has been proposed to provide a huge key space for data security enhancement attributed to its unpredictable nature of randomness, noise-like nature, and broadband. However, the implementation of chaotic optical communication (i.e., fast changing of chaotic optical carriers) requires identical devices with identical parameters for transmitter and receiver, which is quite restricted from real implementation. On the other hand, digital chaos has attracted notable attention recently as a flexible alternative to avoid the implementation difficulty for device-based optical chaos [4–10]. Because it offers very appealing properties from the perspective of data encryption such as ergodicity, pseudo-randomness, and high sensitivity to the initial values, digital chaos provides a huge key space for security applications. Moreover, due to flexible digital signal processing (DSP) in electric domain, digital chaos is easier to be applied.

Optical orthogonal frequency division multiplexing (OFDM) is regarded as a promising modulation technique for next-generation PON, owing to the advantages in high spectrum efficiency, cost-effectiveness, and tolerance to fiber dispersion. High-speed data rate of OFDM signals is achieved by parallel transmission of partially overlapped spectra, lower rate frequency domain tributaries [11]. Moreover, the generation, modulation, and demodulation of OFDM signals have to be performed using DSP in electric domain, therefore it provides a natural physical-layer environment, where digital chaos can be incorporated into OFDM data encryption during transmission. However, OFDM modulation often leads to high peak-to-average power ratio (PAPR), which is one of the most detrimental factors in OFDM signal transmission, as it causes power saturation and nonlinear distortion at the optical receiver while degrading the transmission performance. The pseudo-random properties of digital chaos are helpful for PAPR reduction

In this chapter, OFDM data encryption schemes are reviewed in detail for physical-layer security enhancement based on digital chaos during transmission, while jointly the transmission performances are significantly improved because of the effective reduction in PAPR of OFDM signals. The rest of the chapter is organized as follows. In Section 2, the fundamental theory of PAPR reduction of OFDM signals is shown. The properties of digital chaos are presented in Section 3. In Section 4, the encryption schemes are illustrated in details. Conclu-

of OFDM signals, which consequently improves the transmission performance.

this information for spoofing.

318 Optical Fiber and Wireless Communications

sions are given in Section 5.

OFDM modulation is the superposition of many independent signals modulated onto individual subcarriers with equal-spaced bandwidth. Figure 1 shows the overlapping of the subcarriers in frequency domain. High PAPR could be inevitable especially when a large number of subcarriers are in phase. As a result, the optical receiver with a wide linear range is required to accommodate a large dynamic range of PAPR [12].

If a block of N symbols is denoted as the vector X =[X0, X1, …, XN-1] for OFDM signals, the vector X is oversampling by g (i.e., g(N-1) zero-padding, ZP), where g is an integer greater than or equal one. Therefore, the complex envelop of OFDM signals is

$$\mathbf{x}[n] = \frac{1}{\sqrt{N}} \sum\_{i=0}^{Ng-1} \mathbf{X}\_i e^{\frac{2\pi i}{Ng}},\\ 0 \le n \le \mathbf{Ng} - 1 \tag{1}$$

By definition, the PAPR of OFDM signals is

$$PAPR = 10\log(\max(|\mathbf{x}[n]|^2)/E(|\mathbf{x}[n]|^2))\tag{2}$$

From Eqs. (1) and (2), the oversampling factor must be greater than one for sufficient accuracy of PAPR calculation [13]. To evaluate the PAPR performance, the complementary cumulative distribution function (CCDF) is commonly simulated, which is defined as the PAPR probability exceeding a given threshold for a certain OFDM data block. Based on the central limit theorem, the real and imaginary parts of the complex OFDM signals after inverse fast Fourier transformation (IFFT) have Gaussian distribution in the case of sufficient large number of subcarriers, thus the amplitudes follow the Rayleigh distribution. For instance, if the CDF of the amplitude of a signal sample is given by

$$F(z) = 1 - e^{-z} \tag{3}$$

Figure 1. Spectrum of equal-spaced subcarriers in OFDM signals.

and N is a large number of samples, the CCDF of PAPR of the signal is [14]

$$P(PAPR > z) = 1 - P(PAPR \le z) = 1 - F(z)^N = 1 - \left(1 - e^{-z}\right)^N \tag{4}$$

#### 3. Characteristics of digital chaos

Digital chaos has recently attracted numerous applications in OFDM-PONs [4–9], especially for data encryption, which is mainly due to the chaotic characteristics including pseudorandomness, ergodicity, and high sensitivity to the initial values. Secure optical OFDM transmission is achieved by digital chaos, in which a huge key space is generated and predetermined by chaotic equations. Since the initial values and the other control parameters are utilized as the secure keys between OLT and ONUs, it provides a huge key space, which guarantees the physical-layer confidentiality. At ONUs, the same chaotic sequences are generated using the same keys for data recovering after reception.

The fundamental properties of digital chaos can be described, for example, via a 4-dimensional (4D) hyper chaos [15]

$$\begin{cases} \dot{\mathbf{x}} = a(-\mathbf{x} + \mathbf{y}) + yzu \\ \dot{\mathbf{y}} = b(\mathbf{x} + \mathbf{y}) - \mathbf{x}zu \\ \dot{\mathbf{z}} = cy - u + dxyu \\ \dot{u} = -\varepsilon u + \mathbf{x}yz \end{cases} \tag{5}$$

where a, b, c, d, and e are constant parameters. When a = 35, b = 10, c = 80, d = 0.5, and e = 10, these appropriate initial values bring the system into chaotic zones. Eq. (5) can be solved by Runge-Kutta method with a time step of h = 0.001. The solutions of Eq. (5) output the attractor diagrams of the 4D chaos, as plotted in Figure 2, where excellent chaotic behaviors in terms of pseudo-randomness and phase dynamics are illustrated.

In digital chaos, the chaotic state is very sensitive with respect to the initial values, thus even a tiny change or modification of the original initial values will let it enter into another different chaotic state. In Figure 3(a), the variation curve is illustrated for the digital chaotic sequence {yi}, under a slight change (1 · 10�15) in the initial value of y0. The auto- and cross-correlation functions Rac(τ) and Rcc(τ) are plotted in Figure 3(b) and (c) respectively, which reveal the high sensitivity associated with the chaotic initial values, where τ is the time lag. The good quality of randomness observed in Figure 3 is essential to guarantee high-level security reliability for data encryption.

Figure 2. Chaotic attractor diagrams in phase planes of (x, y), (x, z), and (x, u).

Figure 3. (a) Chaotic sequence of {yi} under tiny change of the initial values; (b) autocorrelation for y0 =1.428121243912452; (c) cross-correlation for y0 =1.428121243912452 and y0 =1.428121243912453.

For a conservative estimate, a tiny change (~1 · 1015) of the initial values leads to a totally different chaotic state, as shown in Figure 3, therefore, the key space of 4D digital hyper chaos is ~1060 (10<sup>15</sup> · 10<sup>15</sup> · 1015 · 1015).

Furthermore, the iteration times of chaotic differential equations and even the equations themselves can be served as the additional secure keys as well, so the actual key space will be >>1060. Currently, the fastest computing speed is about 2.5 · 1013s 1 , thus it will take ~1.3 · 1039 years to work out the possible initial keys of the 4D chaos via brutal-force trials [16]. Consequently, the chaotic data encryption provides a huge key space, which is large enough to resist exhaustive attacks.
