Physical Layer Encryption for CO-OFDM Systems Enabled by Camera Projection Scrambler

Abstract

In this paper, we propose a camera projection approach to enhance the physical layer security of coherent optical orthogonal frequency division multiplexing (CO-OFDM) systems. The data are converted to the new location by the camera projection module in the encryption system, where the 5D hyperchaotic system provides the keys for the camera projection module. The simulated 16QAM CO-OFDM security system over 80 km SSMF is shown to provide a key space of about 9 × 10⁹⁰ through the five-dimensional (5D) hyperchaotic system, making it impossible for eavesdroppers to obtain valid information, and the peak-to-average power ratio (PAPR) is reduced by about 0.8 dB.

1. Introduction

Coherent optical orthogonal frequency division multiplexing (CO-OFDM) systems are widely used in high-speed and long-distance transmission [1,2,3,4,5], and the importance of solving security problems in the transmission process has emerged. The physical layer is at the bottom of the open system interconnect (OSI) model, and to completely secure the transmitted data, the advantages of research methods for encryption of the physical layer are highlighted [6].

Various physical layer encryption methods, such as quantum key distribution (QKD) [7], optical steganography [8], optical code division multiple access (OCDMA) [9], hardware chaos encryption [10,11,12,13], and digital chaos encryption [14,15,16,17,18,19,20,21,22,23,24], etc., have all made significant contributions to securing data. Zhang et al. used an implementation of high-speed QKD in an SiP QKD encoder using a pass-block architecture and a dedicated SiP decoder based on the polarization-based decoy state Bennett–Brassard 1984 protocol [7]. Su et al. used a multi-user optical steganography transmission system based on filtered amplified spontaneous emission (ASE) noise, in which stealth signals can be hidden in time and frequency domains of a common channel to increase the capacity of the stealth channel [8]. Lu et al. used an electro-optical chaotic system with phase modules for time delay signature elimination through deep learning to enhance nonlinearity. Long short-term memory (LSTM) networks are trained with specially designed loss functions to enhance the nonlinear effects [10]. Digital chaotic encryption with digital signal processing (DSP) technology saves a lot of components and is easy to operate, and many researchers have invested in the work. Zhang et al. enhanced the security of orthogonal frequency-division multiple access passive optical network (OFDMA-PON) systems by deoxyribonucleic acid (DNA) encoding and operational cryptographies through chaotic systems [14]. Liang et al. used chaotic Hilbert motion encryption, and Hilbert motion on the key and used the hash value generated from the encryption result as a digital signature to effectively secure the OFDM-PON system [15]. Bai et al. used Chua’s circuit model to realize an OFDM-PON security system with polarity-coded chaotic encryption [16].

In this paper, a scrambling method based on camera projection is proposed to offer a low-complexity and novel design idea for enhancing the security of CO-OFDM systems. The transmitted data are encrypted by the principle of camera projection mapping, in which the camera projection matrix is controlled by keys generated by a five-dimensional (5D) hyperchaotic system. Data in the subcarrier domain, symbol domain, and complex domain of the three-domain coordinates are visualized in real-world three-dimensional space, and the three-dimensional coordinates are projected through the camera to obtain homogeneous coordinates so that the positional transformation of the coordinates reaches the role of data perturbation. The feasibility and security of the encryption scheme are verified by running back-to-back (BTB) and 80 km standard single-mode fiber (SSMF) computer simulations of the CO-OFDM system. The results show that the encryption scheme has a decrease of 0.8 dB in peak-to-average power ratio (PAPR) and a key space size of about 9 × 10⁹⁰ and the analysis of the bit error rate (BER) shows that the encryption scheme does not incur an additional BER cost. These are good indications that the encryption scheme can effectively secure the CO-OFDM system.

2. Proposed Algorithm

Figure 1 demonstrates the physical layer encryption method to obtain the CO-OFDM system employing camera projection. Firstly, the raw data are mapped into QAM symbols after a serial-parallel (S/P) transformation such that the QAM symbols are arranged in the subcarrier domain N = {1, 2,..., N}, the symbol domain S = {1, 2,..., S}, and the complex number domain Q = {Re, Im}. Then, 5 keys are generated using the 5D hyperchaotic system to participate in the encryption process. The projected homogeneous coordinates are obtained by the method of camera projection of the three-dimensional coordinates of the original data to realize the effect of data scrambling in the three domains. Finally, encrypted data are passed through fast Fourier inverse transform (IFFT) and the cyclic prefix (CP) is added to obtain the encrypted OFDM.

2.1. Camera Skewed Projection

The camera coordinate system is a three-dimensional coordinate system established at the position of the aperture. The P point under the camera coordinate system is mapped to the P^′ point in the two-dimensional image plane and according to the principle of small-hole imaging to attain $P=(x, y, z)$, then $P^{\prime }=(fx/z, fy/z)$, where $f$ is the focal length. The origin of the coordinate system of the pixel plane is at the lower left corner, while the origin of the coordinate system of the image plane is at the center, and an offset of the origin is required, i.e., $P^{\prime }=(fx/z+c_x, fy/z+c_y)$. Since the image plane is measured in m and the pixel plane is measured in pixels, the pixel-to-meter conversion quantities k and l need to be decided on for the characteristics of the imaging components to obtain $P^{\prime }=(fkx/z+c_x, fly/z+c_y)$. With $\alpha =fk$, $\beta =fl$, and $\alpha , \beta$ as the camera parameters, then the homogeneous coordinate is $P^{\prime }=(\alpha x/z+c_x, \beta y/z+c_y)$.

The pixel blocks in the real case are not square, but parallelograms. There will be angles $\theta$ between the pixels, and then the mapping relation from the spatial point P under the camera coordinate system to the image point P^′ in the pixel coordinate system will be:

$$P^{\prime }=\left[\begin{array}{l}{x}^{\prime }\\ y^{\prime }\\ z^{\prime }\end{array}\right]=\left[\begin{array}{cccc}\alpha & -\alpha \cot \theta & c_x& 0\\ 0& \beta /\sin \theta & c_y& 0\\ 0& 0& 1& 0\end{array}\right]\left[\begin{array}{l}x\\ y\\ z\\ 1\end{array}\right].$$

(1)

The encryption method is to regard (N, S, Q) as (x, y, z) in the real space, and subsequently, the encrypted (x^′, y^′, z^′), which is (N^′, S^′, Q^′), is obtained by processing the camera projection scrambler of Equation (1). The data scrambling encryption is realized by using the positional changes on the coordinates of the equation.

2.2. Key Generation and Processing

To defend against strong attacks by eavesdroppers, a 5D hyperchaotic system is introduced that allows the generation of unpredictable sequences, which is described as:

$$\left\{\begin{array}{l}{\dot{x}}_1=a(x_2-x_1)\\ {\dot{x}}_2=c{x}_1+d{x}_2-x_1{x}_3+x_5\\ {\dot{x}}_3=-b{x}_3+{x_1}^2\\ {\dot{x}}_4=e{x}_2+f{x}_4\\ {\dot{x}}_5=-r{x}_1-k{x}_5\end{array}\right.,$$

(2)

where $\{x_1-x_5\}$ are state variables, $a>0, b>0, c, d$ and f are constant parameters, e is a coupling parameter, and r and k are two control parameters, where $d>-c, er\ne 0$. Fix $a=10,$ $c=28,$ $e=10,$ $f=0,$ $r=10,$ $k=0,$ and $b\in [2,11]$. The system has two or three positive Lyapunov exponents of hyperchaotic attractors [25]. The resulting $\{x_1-x_5\}$ sequences are processed as Key1–Key5 by the following equation:

$$\left\{\begin{array}{l}Key1=\mathrm{mod}(ceil(abs(x_1)),10000)\\ Key2=\mathrm{mod}(ceil(abs(x_2)),10000)\\ Key3=\mathrm{mod}(ceil(abs(x_3)),10000)\\ Key4=\mathrm{mod}(ceil(abs(x_4)),10000)\\ Key5=\mathrm{mod}(ceil(abs(x_5)),10000)\end{array}\right.,$$

(3)

where Key1 and Key2 are the camera parameters $\alpha$ and $\beta$, respectively, Key3 is the skew angle $\theta$, and Key4 and Key5 are the coordinate offsets $c_x$ and $c_y$.

3. Simulation Experiments and Results

The computer simulation experiment for encrypted transmission of camera projections for 16QAM CO-OFDM is built according to Figure 2. A pseudo-random binary sequence (PRBS) is generated at the transmitter side as the raw data, which has a length of 204,800 bits. The original data are mapped into 16QAM symbols, and the signal is converted into a symbol matrix of the number of subcarriers × the number of OFDM symbols by S/P conversion, and the real and imaginary numbers are separated to obtain the three-dimensional coordinates (N, S, Q). Next, the camera projection encryption technique obtains the coordinates (N^′, S^′, Q^′) after the perturbation, and the original data are placed according to the coordinates to obtain the encrypted data. IFFT and added CP processing are performed to obtain encrypted OFDM symbols, where the CP length is 1/16 of the length of an OFDM symbol, a training sequence of 20 symbols, and 4 pilots. The encrypted OFDM symbols are processed through an arbitrary waveform generator (AWG) to obtain an electrical signal. An external cavity laser (ECL) with a center wavelength of 1550 nm is used as a light source for an optical IQ modulator so that an encrypted electrical signal is modulated into an encrypted optical signal by the IQ modulator. A 0 dBm optical signal is transmitted over 80 km SSMF with fiber dispersion of dispersion factor 17 × 10⁻²⁷ s²/m and Gaussian white noise. The total attenuation of the optical signal is 15 dB. Optical filtering and coherent receiver detection are performed to convert the signal into an electrical signal. Where the laser coherent detection power is a −6 dBm optical signal, the linewidth of the local laser is less than 100 kHz and the frequency offset is ~300 kHz. Perform digital storage oscilloscope (DSO) sampling. Compensate for IQ timing bias. Perform GSOP compensation for receiver IQ mismatch [26,27]. Perform electronic dispersion compensation (EDC) for distortion generated by dispersion. Carry out frequency bias estimation and phase noise [28]. Suppress narrow-band interference caused by clock leakage of the DAC in the 20 GHz band with an adaptive trap filter [29], and other treatments. After synchronization and S/P conversion to obtain the signal matrix, the signal is converted to the frequency domain by FFT and the data are decrypted by camera projection. The decrypted signal is channel estimated and balanced [30], and the remaining phase noise is estimated with the help of the pilots. The signal is de-mapped to obtain the bit data.

The original and encrypted signals go through a transmission system of CO-OFDM with BTB and 80 km SSMF, and the relationship between the optical signal noise ratio (OSNR) and BER is observed in Figure 3. When data are passed through the camera projection encryption system, the BER of the data stolen by illegal users is about 0.5, which is equivalent to invalid data. When the OSNR is greater than 21.5 dB, after the authorized users use the key to decrypt the encrypted data transmitted over the BTB and 80 km SSMF, the data have a BER lower than the forward error correction (FEC), which is equivalent to valid data. The curves of the original and encrypted signals are very close to each other, which intuitively reflects that the encryption system has a negligible effect on the BER.

The OFDM signals generated by the superposition of multiple subcarriers will have the same phase signal modulation when the subcarriers are in the same phase, resulting in the generation of a large PAPR. However, OFDM signals with large PAPR easily cause nonlinear distortion, which makes the system performance degraded [1]. Figure 4 depicts the complementary cumulative distribution function (CCDF) of the PAPR of the original and encrypted signals in the CO-OFDM system. It is demonstrated that the encryption scheme can optimize the PAPR performance of the CO-OFDM system by about 0.8 dB, which in turn reduces the signal impairment.

Figure 5a shows a comparison of the sequence $x_1(400:600)$ after 1000 iterations of varying the initial value of $x_1$ by a gap of 10⁻¹⁵ in the chaotic system, and Figure 5b shows a comparison of the sequence $x_1(400:600)$ after 1000 iterations of varying the variable parameter b by a gap of 10⁻¹⁵ in the chaotic system. These two plots adequately illustrate the sensitivity of the 5D hyperchaotic system to initial values and variable parameter b. Slight variations in the initial values and the parameters of the system make the resulting sequences different, reflecting the unpredictability of the sequences generated by the system. The key space size of the camera projection encryption scheme is determined by the initial values and parameters of the 5D hyperchaotic system, so the key space size provided by the five initial values and variable parameters b is about (10¹⁵)⁵ × (11 − 2) × 10¹⁵ = 9 × 10⁹⁰, which can effectively resist brute force attacks.

Table 1. Scheme key space comparison.

Schemes	Key Space
DNA encoding [14]	2.25 × 1089
Digital optical polarization scrambling [17]	1060
Key concealment and distribution based on carrier scrambling [18]	1082
Chaos key enhanced based on the convolutional long short-term memory neural network [19]	10241
The proposed scheme	9 × 1090

shows the comparison of this paper with some representative schemes in terms of key space. By comparison, it is concluded that this scheme has superior key space size and low computational complexity compared to most of the security schemes [14,17,18], some of which have large key space, but require high computational complexity to achieve this effect [19].

Figure 6 is obtained by adding the analysis of the ability to resist statistical attacks, where the horizontal coordinate is the constellation points of 16QAM and the vertical coordinate is the percentage of constellation points to the total data. This figure shows that the distribution of the ciphertext data is uniform and the attacker cannot obtain the information by statistical attack.

4. Conclusions

In this paper, we propose an approach that utilizes the idea of camera projection to enhance the physical layer security and transmission performance of CO-OFDM systems. The randomized keys obtained through the 5D hyperchaotic system control the camera projection matrix and thus perturb the data. In the simulation experiments of the encryption scheme for a 16QAM CO-OFDM system over 80 km SSMF, the results show the feasibility and security of the scheme, which provides a key space of about 9 × 10⁹⁰. The eavesdropper cannot obtain the valid data—only the authorized users can. Also, the PAPR is reduced by about 0.8 dB.