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Abstract
In this paper, a flexible physical security coding scheme integrating chaotic neural network (CNN) and non-linear encryption is proposed for orthogonal frequency division multiplexing wavelength division multiplexing passive optical network (OFDM-WDM-PON). The scheme improved the flexibility, adjustability and the key space of chaotic encryption system by introducing chaos into neural networks. The system will encrypt the bit series, probability shaping points, and subcarriers position of the OFDM signal through linear encryption and non-linear encryption concurrently. Results show that a key sensitivity of 10−15 and a key space of more than 10279 can be achieved. The encrypted system's Lyapunov is 5.2631, along with 12 parameters can be dynamically changed in the range of 0∼5. Furthermore, when the bit error rate (BER) is less than 3.8×10−3, probabilistic shaping (PS) technology decreases power loss by around 0.5 dB. A 20.454 Gb/s data transmission experiment was successfully verified for a span of 25 Km single-mode fiber. According to the experimental results, the proposed encryption scheme is likely to be used in future OFDM-WDM-PON transmission systems.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
In recently years, due to the continuous increase in communication demand, the capacity and optimization algorithms of optical communication have been extensively studied [1,2]. The author designs algorithms for both transparent and opaque virtual optical network embedding (VONE) over flexible-grid elastic optical networks in [3,4] investigates how to serve multicast requests over EONs with multicast-capable routing, modulation level, and spectrum assignment (RMSA). [5] introduces the spectrum fragmentation issue, which undermines the bandwidth efficiency in elastic optical networks.
Among these technologies, WDM-OFDM-PON has been widely used due to its excellent performance 6 –9]. OFDM can achieve high-speed serial-parallel transmission, and due to the orthogonality of its carriers can ensure that it has a better ability to resist multipath fading, its ultra-high frequency utilization rate can transmit a large amount of data under narrowband bandwidth. The passive optical network (PON) system don’t need expensive active devices, is one of promising access network system in the industry, consisting of an optical line terminal (OLT) linked to various optical network units (ONU) [10,11]. Among them, the security of the entire optical communication system has recently been extensively studied by researchers. However, the security research of communication systems is often concentrated in the upper structure of the OSI model, and various confidentiality protocols are used for encryption, but there is a lack of corresponding research on security transmission of the physical layer [12,13]. In OFDM-WDM-PON physical layer, every ONU node shares the same data frame. If a third-party listener maliciously intercepts the data packet and decodes it, it will cause information leakage, password loss or even a lot of money damage. As a result, one of the big research hotspots in the optics communication field is how to improve the information security of the physical layer. In [14], the strategy proposed three-dimensional Brownian motion and chaos in cell. In [15], an approach for peak-to-average-power ratio reduction and security improvement in OFDM-PON system is analyzed. [16] proposed a chaotic multilevel separated encryption scheme. The security of the physical layer is constantly being improved and developed.
The chaotic mechanism is similar to the principle of encryption because it has pseudo-randomness, sensitivity to initial values, and a large iteration space [17–20]. Many researchers have been involved in chaos communication in recent years. In [21], the logistic model is proposed to encrypt the physical layer, and [22] proposes the use of chaos to achieve DNA encryption. In terms of compressing data and enhancing transmission security, [23] propose chaotic compressive sensing (CS) encryption algorithms for OFDM-PON. In [24], A chaotic multilevel separated encryption (CMSE) scheme is proposed. [15] proposes the use of high-dimensional chaos to swap sub-carriers. [25] proposes a chaotic constellation transformation (CCT) technique for physical-layer security. In addition, due to the rise of PS, the encryption of constellation points after PS has also been studied by many scholars. In [26], the scheme proposed a novel physical layer encryption method based on digital and encrypt the PS signal. Nevertheless, these OFDM-PON encryption schemes are iterated by nonlinear equations. The number of their variable parameter values are generally less than 3, which leads to poor flexibility. The adjustable parameter value is range in 0 to 0.5, which has poor adjustability. The key space is less than 10100, so the encryption effect is still defective [27]. At the same time, in the past OFDM-PON encryption methods, the encryption schemes are linear encryption. After the encryption results and initial parameters, the newest neural network can be used to train the data and fit the encryption model, so there will be great security flaws [28].
This paper proposes a flexible approach for the OFDM-WDM-PON physical security based on chaotic neural network and non-linear encryption. By introducing a multi-frequency cosine function, the ordinary neural network structure will have a wealth of chaotic phenomena, and a six-dimensional chaotic sequence can be generated at one time for encryption. This OFDM-WDM-PON encrypted system has a Lyapunov index of 5.2631, along with 13 parameters can be dynamically combined in the range of 0∼5, and its key space is 10279. The randomness, adjustability and key space are substantially higher than other current OFDM-WDM-PON encrypted systems. The encrypted scheme realizes non-linear encryption by using S-box. While sacrificing 1/3 of the encryption sequence, the key space is increased by about 264 times, and the non-linear encryption with irreversible restoration is realized, which improve the security of the physical layer further. Furthermore, when the bit error rate (BER) is less than 3.8×10−3, probabilistic shaping (PS) technology decreases power loss by around 0.5 dB. A 20.454 Gb/s data transmission experiment was successfully verified for a span of 25 Km single-mode fiber. Compared with tradition OFDM system, the encryption efficiency has been improved by cubed, without any negative impact on peak-to-average-power ratio (PAPR). According to the experimental results, the proposed encryption scheme is likely to be a feasible solution used in future OFDM-WDM-PON transmission systems.
2. Principles of secure OFDM-WDM-PON system
The proposed non-linear physical layer encryption based on a chaotic neural network is shown in Fig. 1. After serial-to-parallel (S/P) conversion, a pseudo-random binary sequence (PRBS) data stream is mapped onto a 16-quadrature-amplitude-modulation (QAM) mapper at the transmitter. Following that, the signals are encrypted using three separate methods: XOR transformation, probability shaping points replacement, and sub-carrier replacement. These three dimensions are the original information, time domain information and frequency domain information of the signal, which have vital effect on the whole system. At the receiving end, decryption goes through the same steps to decode the subcarriers, probability shaping points and bits respectively, and finally obtain the initial signal.
In our transmission scheme, the PS technology is used to reduce the overall optical power loss by increasing the probability of the four points in the inner circle and reducing the probability of the four points in the outer circle. The specific probability distribution uses the Maxwell-Boltzmann distribution:
In the entire encryption process, the CNN algorithm is crucial. Different from general neural network, the activation function is composed of the multi-frequency cosine signal (MFCS) and the piecewise linear function. Activation function of CNN is f(x)=h(x)+g(x). h(x) is the mathematical expression of MFCS, which expresses as:
As shown in Figs. 2(a) and 2(b), the role of the piecewise linear function is to make the whole monotonic function, but due to the non-monotonicity of MFCS, the activation function is locally non-monotonic. This feature can make the neuron more prone to chaotic dynamics.
The mathematical model of the neural network can be described as:
As Fig. 3, three encryption dimensions are respectively encrypted with S-box non-linear encryption and two linear encryption. The first sequence is used to generate the key for bit XOR transformation, and the second and the third sequences are used to generate keys for probability shaping points permutation and subcarriers permutation. Make the following transformation to the first set of chaotic sequences Tr1 :
Table 1. S-box
Origin data is 100110. Combine the highest and lowest digits is 10, which represents decimal 2, and the middle 4 bits (0011) represents decimal 3, which means the second row and the third column. The value of (2,3) is 0, so the key is turned into 0000. XOR the compressed key with the bitstream and we can get a non-linearly mapped encrypted OFDM signal. Through the S-box encryption method that maps 6 bits to 4 bits, and the encryption reliability is improved by 264 times with 1/3 of the encoding cost, which can enhance the security ability of the system.
Probability shaping points and sub-carriers are important components of OFDM signals. For probability shaping points and subcarriers encryption in OFDM signal, they are processed as follows:
Among them, M2&3 is the transformed key matrix, f2(x) is the mapping rule, and sort means sorting the data from small to large, ()−1 means the reciprocal of each element in the sequence. For example, given Tr=[0.11,0.88,−0.56,−0.23], we can get sort(Tr)−1=[−0.56,−0.23,0.11,0.88]−1. Using Eq. (6), we can get
In this example case of subcarriers is [f1, f2, f3, f4], and we have encrypted signal [f3, f4, f1, f2] after encryption. Faced with different dimensions, we only need to set the initial matrix size to the corresponding number of dimensions. After probability shaping points and subcarriers shifting, the inverse fast Fourier transform (IFFT) operation is performed and a cyclic prefix is appended to the OFDM signal for eliminating potential inter symbol interferences (ISI). After the above changes, the transformed OFDM signal becomes:
3. Experiment setup
As shown in Fig. 4, we performed legal ONU receiving ends and illegal ONU receiving end to check the efficacy of the system experimentally. The OLT is in charge of allocating the legal ONU's safe key. The encrypted OFDM signal is generated in the electrical domain at the OLT via offline DSP. A total of 128 subcarriers are used to carry the encrypted OFDM data, while another 128 subcarriers are used to carry the corresponding complex conjugates to fulfill hermitian symmetry. The size of IFFT is 512. The 1/4 of the OFDM symbol length is added as a cyclic prefix (CP) to reduce inter-symbol interference (ISI). The data rate of 20.454 Gb/s (subcarrier number× entropy × AWG sampling rate/(FFT + GI) ×Number of wavelengths) is produced by a 10 GSa/s arbitrary waveform generator (AWG, TekAWG70002A). After an electrical amplifier (EA), the electrical OFDM signal and optical signal are coupled through Mach-Zehnder modulator (MZM) for intensity modulation to generate a modulated optical signal for SSMF transmission. Three continuous-wave (CW) lasers with a wavelength of 1550 nm, 1549.4 nm and 1550.7 nm and optical power of 10 dBm functions as the light source. The wavelength division multiplexing (WDM) multiplexer (MUX) can multiplex multiple signals of different wavelengths into one signal for transmission. The WDM demultiplexer (DEMUX) can separate optical carriers of various wavelengths. The values of the CNN parameters are shown in Table 2.
Fig. 4. Experiment framework setup (AWG: arbitrary waveform generator; EA electrical amplifier; MZM: Mach-Zehnder modulator; SSMF: standard single-mode fiber; VOA: variable optical attenuator; PD: photodiode; MSO: mixed-signal oscilloscope; MUX: multiplexer; DEMUX: demultiplexer).
Table 2. Parameter value
At the ONU, we use a variable optical attenuator (VOA) to adjust the received optical power. A photodiode (PD) and a mixed-signal oscilloscope (MSO, TekMSO73304DX) are used to capture the optical OFDM signal. After time synchronization, OFDM demodulation, key decryption, and BER test, we can get the original signal. In DSP processing, a large number of chaotic sequences are generated through the chaotic neural network, it is worth mentioning that after each time series, it will dynamically change the initial value and generate a different key to encrypt the signal.
4. Results and discussions
For a better explanation of the proposed method, it is essential to analyze the security performance and transmission performance. The exponential function of chaos, key space, and sensitivity analyses are all included in the security performance. The BER test and the image transmission test are two ways to assess transmission efficiency.
4.1 Security performance
4.1.1 Exponential feature
The relationship between the power spectrum and the entropy rate is defined by Spectral entropy(SE). The higher the entropy value, the more unpredictable the chaotic system's potential outcomes. As shown in Fig. 5, the maximum SE value of the four chaotic systems is similar; however, the average SE value of CNN is far higher than the other three chaotic models. This reflects that CNN's average level of sequence uncertainty is much higher than that of other systems, and it can provide more confidential chaotic sequences. The chaotic phase diagram does not converge to a single attractor due to the nonlinearity of the activation function. Lyapunov represents the average exponential divergence of adjacent trajectories in phase space. Lyapunov values of CNN are 5.2631, −0.0005, −0.9956, −4.01, −7.5025 and −104.034. In Table 3, CNN shows the largest Lyapunov exponent, which means CNN has a more discrete chaotic sequence. After each iteration, the system is separated deeply from the equilibrium point. The locations are more unstable, and the keys generated by CNN are more difficult to crack. In our encryption scheme, the adjustable parameters of CNN are as many as 12, while the common encryption scheme has only 2∼3. Therefore, CNN can provide more flexible control schemes instead of completely fixed models. Besides, the adjustable parameter range has also become more flexible, which can provide key space by more than 5 times.
Table 3. Security performance of different encrypted systems
4.1.2 Key space and sensitivity analyses
Since the Lyapunov exponent of the chaotic system is greater than 0, there is an exponential separation phenomenon in adjacent orbits. As shown in Fig. 6(a), the two sets of data whose initial values differ by 10−10 are completely separated in the phase space after only 3 iterations, becoming two seemingly unrelated orbitals. For encryption system, it should have high sensitivity to the initial values. As shown in Fig. 6(b), the keys turn to two different sequences by using CNN. After calculations, the chaotic sensitivity of the CNN system can reach up to 10−15. That is, a slight change in the initial value will cause the entire chaotic system to change. Therefore, the sensitivity of the confidentiality system can be guaranteed.
Fig. 6. (a) Exponential separation spectrum (b) The influence of the initial value on the sequence value
In CNN system, the key secret of initial values of x, y, z, u, w, v are (−1.9,−1.4),(−2,−1),(0,3),(−1.8,1.3),(−31,−27),(−80,0). Si,j is the parameter that controls the change of chaotic frequency, range in (0,5). Besides, this encryption design combines a non-linear encryption scheme. Through the S-box encryption method that maps 6 bits to 4 bits, and the encryption reliability is improved by 264 times with 1/3 of the encoding cost. Only take Si,j, initial values and S-box into consideration, the key space of the CNN is beyond 10279((1015)18×232). The high key space also means that it is more difficult to decipher the ciphertext using the exhaustive method.
4.2 Transmission performance
Figure 7(a) shows the value of BER of the legal ONUs under 3 different situations. They are B2B transmission, 25 Km probabilistic shaping technology transmission, and 25 km without probabilistic shaping technology transmission. In the experiment, we reduced the sampling rate to achieve the same baud rate as PS and without PS. Experiments can verify that the chaotic neural network OFDM transmission system is feasible. And through the introduction of probability shaping technology, the BER is lower than 3.8×10−3, a gain of about 0.5 dB can be obtained. Figure 7(b) shows the difference between the legal receiving end and the illegal receiving end. At the illegal receiving end, the bit error rate is as high as 50%. This experiment also included three separate illegal receiving end experiments, in which no parameters were defined, the initial value differed by 10−10, and the iteration order differed by one. The results show that in all three situations, the error rate is as high as 50%, and the decryption fails.
Fig. 7. (a) BER curves of the encrypted 16-QAM-OFDM with PS, 16-QAM-OFDM without PS, B2B 16-QAM-OFDM. (b) BER curves of legal ONUs and illegal ONUs.
When transmitting images, Fig. 8 depicts the condition of the legal receiving end and the illegal receiving end. We can see from the image that the unauthorized receiving end cannot see any detail from the original image. However, at the legal receiving end, the original picture may be correctly decrypted. And using the CNN encryption scheme, a one-time encryption scheme can be realized which only need to add the initial parameters in the frame header position. This further proves the viability of our encryption scheme. Through Runge-Kutta methods of partial differential equations, a total of 51 additions and 20 multiplications are obtained. Since one iteration can generate 6 chaotic values, each chaotic value requires 8.5 adder operations and 3.3 multiplier operations on average. Compared with the current DNA encryption and multi-dimensional chaotic encryption, the cost is the same. Commonly used DSP processors, such as MFLOPS, can perform millions of floating-point operations per second, which is far greater than our calculation requirements.
Fig. 8. (a) Origin image (b) Illegal receiver (c) Legal receiver in B2B (d) Legal receiver in 25 Km SSMF
5. Conclusion
We have proposed and experimentally demonstrated a novel secure strategy for the OFDM-WDM-PON system at the physical layer. The MFCS activation function is used to improve the nonlinear effect of the chaotic neural network. The Lyapunov values of the chaotic sequence are as high as 5.2631. Combining the S-box and permutation matrix, the OFDM bit information, probability shaping points, and subcarrier are respectively encrypted to ensure one encryption at a time. While using probability shaping technology to reduce the transmission power of 0.5 dB when the BER is lower than 3.8×10−3. In this way, the 20.454 Gbps encrypted OFDM-WDM-PON scheme is successfully transmitted over 25 km SSMF. Compared with the conventional encrypted signal, the transmission performance is improved by 0.5 dBm. The encrypted system's Lyapunov is 5.2631, along with 12 parameters can be dynamically changed in the range of 0∼5. The results also show that the proposed scheme is sensitive to the chaotic sequences on each dimension by 10−15, along with a key space of more than 10279. The proposed system has potential applications in future secure communications at the physical layer.
Funding
State Key Laboratory of Information Photonics and Optical Communications; Beijing University of Posts and Telecommunications; Jiangsu talent of innovation and entrepreneurship; National Natural Science Foundation of China (61720106015, 61727817, 61775098, 61822507, 61835005, 61875248, 61935005, 61935011, 61975084); National Key Research and Development Program of China (2018YFB1801703).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in the paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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