## Abstract

In this article we have enhanced the security of an orthogonal frequency division multiplexed passive optical network (OFDM-PON) based on four dimensional (4D) encryption, including constellation, subcarrier, symbol and time, which is proposed for the first time in this paper. 4D-hyperchaotic mapping is used to generate four masking factors to achieve ultra-high security encryption in four different dimensions. During the encryption, dimension coordination optimization is adopted, which effectively reduces the time cost of the system and improves the encryption efficiency by 3 times. At the same time, probabilistic shaping (PS) technology is used to further optimize the system that has effectively improved the bit error performance by about 1 dB. The proposed encryption technique for OFDM-PON has been demonstrated successfully with the help of experiments. The generated OFDM signal is modulated by the quadrature amplitude modulation (QAM) technique, which transmitted 16 Gb/s data rate across a 25 km fiber span of standard single-mode fiber. The values of bit error rate (BER) and peak-to-average-power ratio (PAPR) are analyzed during the experiments, and the obtained results show that the proposed security-enhanced OFDM-PON has high sensitivity and security and can be well compatible with PS and OFDM technologies. The proposed scheme has very reliable security performance and also has excellent benefit improvement, which is very promising in the future PS-OFDM-PON.

© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

## 1. Introduction

In recent years, the orthogonal frequency division multiplexing (OFDM) technology has been receiving special attention in the field of optical communication due to its advantages of high spectral efficiency, reduced multipath interference and large capacity [1,2]. In the both of frequency and time domains, OFDM can provide finer granularity for the network, moreover, it can also provide huge capacity by using relatively cost-effective optical components [3]. Meanwhile, passive optical network (PON) has attracted a lot of attention in recent years due to its flexible bandwidth and large capacity. There has been a lot of research on OFDM-PON [4–6], but these studies are always focused on improving the capacity of OFDM network or digital signal processing, while ignoring the security problems of communication systems due to the rapid growth of optical network capacity and the opening of communication systems [7].

At present, the encryption of the communication system has always concentrated on the upper layer of the optical network, such as various security protocols. However, encryption at upper-layer cannot protect the control data or headers, so there are hidden security threats. And as the number of users increases, the keys that need to be managed will also increase, resulting in an inconvenient management [8,9]. However, the physical layer can provide transparent encryption for all types of data, which can make the system as a whole more secure, so the physical layer encryption is a promising method. Simultaneously, chaotic technology is also widely used in various encryption schemes due to its high initial condition sensitivity [10,11]. These encryption schemes are often based on optics or optical components, which are oftenly expensive with insufficient stability. In OFDM, the digital signal process (DSP) module can complete the process of signal generation and modulation, which provides the feasibility and convenience for using chaotic encryption technology to improve the security of the OFDM system in the DSP process. Earlier, Liu and Zhang et al. proposed to use chaos scrambling to implement encryption in the OFDM frequency domain [12–15]. Their research tends to focus on the level of encryption. However, it is difficult to crack the information under normal encryption conditions. Therefore, we need concentrate at some other domains instead of the level of encryption only, such as the complexity, calculation time and cost of the encrypting system. In order to improve the encryption efficiency, some new encryption methods have also been proposed, such as cell chaos and optimum block dividing [16–18]. Other chaotic encryption methods based on optics or optical devices such as phase modulator (PM) and optically pumped lasers have also been proposed [19,20]. However, these methods tend to deal with lower dimensions, which are generally limited to symbolic dimension or subcarrier dimension, and do not balance the time cost and bit error rate (BER). What is more, probabilistic shaping (PS) has received increasing attention due to its supportive nature in higher spectral efficiency (SE), higher capacity and longer transmission distance in optical fiber communication systems [21,22]. It has been proved that using PS can enhance the confidentiality of communication system and increase the security level [23–25]. Some encryption schemes are not suitable for probabilistic shaping techniques, such as constellation expansion, because they change the constellation distribution [26,27]. Therefore, on the basis of existing encryption research, we proposed an optimized encryption scheme based on four-dimensional chaos, which can guarantee the enough higher security level while minimizing the time cost and system complexity. Furthermore, it is interesting that our proposed encryption scheme is perfectly compatible with PS technology.

In this paper, we propose for the first time a security-enhanced OFDM-PON based on the four different dimensions, the four-dimensional (4D) hyper-chaotic mapping is used to generate masking factors to achieve ultra-high security encryption of information. Beside, PS and dimension coordination optimization are used to improve the efficiency of the system. The transmission of a 16 Gb/s encrypted PS-16QAM OFDM signal is successfully demonstrated in our experiment. The experimental results show the effectiveness of the proposed scheme in optical OFDM systems. Compared with the traditional OFDM, the error performance of our scheme has been improved by 1dB and the encryption efficiency has been improved by 3 folds, without any negative impact on peak-to-average-power ratio (PAPR).

## 2. Principle

Figure 1 shows a model diagram of a four-dimensional chaotic encryption system, which includes a schematic diagram of the constellation masking effect and of subcarrier encryption in the OFDM frame. Firstly, the chaotic map is driven by the key to generate chaotic vectors for encrypting the OFDM signal. After the binary sequence is encoded by PS-16QAM mapping, the chaotic vector is used to randomly rotate the constellation to realize the masking of the constellation dimension. The points of different colors on the constellation diagram in Fig. 1 represent constellation points of different probabilities after being processed by PS technology. The data enters to OFDM module after the constellation masking. Before OFDM modulation, the OFDM frame can be divided into three dimensions of subcarriers, symbols and time, and the original information can be encrypted by scrambling the three dimensions. By introducing an optimization module, the dimensions are uniformly coordinated and optimized before encryption. Namely, the dimensions are combined and divided into units to reduce the number of objects that need to be processed in the encryption. In addition, as described in [12], the scrambling in the time-frequency dimension can be regarded as similar to bit interweaving, which can prevent the sudden noise in the communication process and thus improve the error performance of the system to some extent.

The permutation/de-permutation block of the proposed highly secured OFDM-PON scheme is illustrated in Fig. 2. After the serial to parallel conversion of data, PS-16QAM constellation mapping is implemented. According to the basic principle of PS, the constellation symbol point can be expressed as $X = \{{{x_1},{x_2}, \cdots {x_{16}}} \}$. In order to satisfy the Maxwell-Boltzmann distribution, the probability mass function (PMF) of each signal point can be expressed as:

Here 4D-hyperchaotic mapping is used to generate the corresponding masking factors to achieve the masking of constellation, subcarrier, symbol and time, respectively. 4D-hyperchaotic map can be expressed as:

*N*is the total number of constellation symbols after constellation mapping, the ${l^{th}}$ symbol on the ${k^{th}}$ carrier of OFDM is ${Q_{l,k}}$. $\log (k + 1)/\log N$ is a weighting coefficient, the purpose is to increase the masking accuracy as the number of symbols increases, where $\theta$ is any angle and can be set at will. That is, the symbol on the ${k^{th}}$ subcarrier rotates a random phase Angle under the action of masking factor, as shown in Fig. 3(b). It can be seen that the density of points in different circles is different, which is caused by PS. The non-uniform distribution of PS makes the number of constellations at different locations different.

The output after constellation masking can be regarded as an OFDM frame, where horizontal elements represent subcarrier and vertical elements represent symbols on subcarriers. Assuming that the total number of subcarriers in OFDM is *M*, and the time slot size is *T*, ${f_k}$ is the frequency of the ${k^{th}}$ subcarrier. Then the original OFDM signal masked by the constellation can be expressed as:

Then, the masking factor must be generated from the chaotic sequence $({y_n},{z_n},{w_n})$ to scramble and encrypt the subcarrier, symbol and time of the OFDM frame, as shown in the OFDM frame in Fig. 1. To reduce the processing time and improve the BER performance, before scrambling, we introduce an optimization algorithm to divide the subcarriers and symbols in the OFDM frame. The schematic diagram of unit division is shown in Fig. 4.

The combination of the subcarriers in the OFDM frame and the symbols on each subcarrier is regarded as a two-dimensional matrix, and then the matrix is divided into cells, this is done to reduce the number of scrambled objects. To facilitate scrambling, we set the size of each cell’s block to be the same. It is assumed that the number of subcarriers is $M$, and the number of symbols on each subcarrier is *L*, therefore the number of subcarriers in each unit after division is *m* and the number of symbols is *l*. The process can be expressed as under:

After the division, the number of subcarrier units is ${N_{car}} = M/m$, and the number of symbol units is ${N_{sym}} = L/l$. Then the chaotic sequence is used to generate masking factors to scramble the units. The chaotic sequence $({y_n},{z_n})$ is used to generate two sets of masking factors $({Y_n},{Z_n})$. In addition, in the time dimension, we process the chaotic sequence ${w_n}$ to generate the time replacement factor ${W_n}$. The process can be expressed as:

*M*is the total number of subcarriers, and

*T*is the size of the time slot. The encryption algorithm is reversible, so the receiver only needs to generate the corresponding decryption factor according to the key and carry out the reverse operation of the encryption process to realize the decryption of the information. The constellation received by the receiver is shown in Fig. 3(c), and the constellation recovered after the correct decryption is shown in Fig. 3(d).

## 3. Experimental setup and results

In order to verify the performance of the proposed scheme, experiments are conducted for encrypting the OFDM-PON signal system as shown in Fig. 5. The encrypted OFDM signal is generated at the optical line terminal (OLT) via offline DSP, and the receiver is divided into normal receiving optical network unit (ONU) and illegal receiving ONU. The normal ONU represents the ONU with the correct key, while the illegal ONU represents the receiving ONU of the eavesdropper. In conducting the experiments, we set the number of subcarriers is to 128, the number of symbols to 200, the time slot is 200, the FFT size is 256, and the length of the guard interval is 1/16. At normal ONU side, the same subcarriers are used, but the time slots are different, and one ONU is served for every 200 time slots. An arbitrary waveform generator (AWG, TekAWG70002A) with a sampling rate of 10 GSa/s is used for digital-to-analog conversion of the encrypted OFDM signal. The light source is a Continuous Wave (CW) laser, where the wavelengths and power of the source is set at 1550 nm and 10 dBm, respectively. The modulation of the analogue OFDM (encrypted analogue) signal and the carrier is performed across MZM. After modulation, transmission is carried out through 25km single-mode fiber span. We studied the performance of the OFDM-PON system using PS-16QAM constellation mapping. After probabilistic shaping, the information entropy is 3.4 bits/symbol, and the final data transmission rate is 16 Gb/s. At the ONU port, a variable optical attenuator (VOA) is used to adjust the received optical power. After converting the received optical signal into electrical signal through photodiode (PD), it is pass through a mixed signal oscilloscope (MSO, TekMSO73304DX) with a sampling rate of 50 GS/s. After analog-to-digital conversion, it is decrypted by an offline DSP to restore the original data.

In order to facilitate the transmission experiment, the number of subcarriers and symbols are set as 120 and 200 respectively. First, Subcarriers and symbols are divided into blocks. After calculation according to Eq. (5), there are 96 encryption schemes. Since the encryption scheme will not affect the BER of the normal ONU, the time required for each encryption scheme is calculated at illegal ONU along with the received BER.

As shown in Fig. 6, in order to eliminate the contingency and make the comparisons more obvious between different schemes, the total time for performing 100 times encryption is calculated for each scheme along with the average BER, after 100 tests, at illegal ONU. It can be seen that cell division has obvious optimization effect on the encryption time, and the optimized efficiency can reach to 3 times of the original scheme. However, from BER statistics, it can also be seen that the division in some cases will seriously affect the security of the system, which is caused by the unit blocks when the division is too large. A large unit block reduces the number of permutation units. When it is large enough, the permutation unit is 1. At this point, it is equivalent to no permutation operation. Therefore, we have combined the BER and encryption time of the illegal ONU to select an appropriate encryption scheme. Here the Symbol Division Scheme 6 and Subcarrier Division Scheme 5 are randomly selected as the encryption scheme for this experiment.

After determining the block scheme, the encryption of information is started. First, the OLT uses a random key to encrypt the information, and the key will be distributed to the normal ONUs authorized by the OLT. The chaotic sequence is driven by the key. Here, the key $(a,b,c,d,r,{x_0},{y_0},{z_0},{w_0})$ are set as $({35,3,12,7,0.5,3, - 1,4,2} )$, and the 4D-hyperchaotic mapping patterns are shown in Fig. 7. It can be seen that complex bifurcation and chaotic dynamics are displayed after the key is driven. As described in the principle, four groups of masking factors $({X_k},{Y_m},{Z_l},{W_t})$ are generated by using this mapping to encrypt the information.

As shown in Fig. 8, in order to verify the sensitivity of the key, it is slightly changed for decryption when the optical power is reached to -12 dBm, and the variations in BER are recorded for changing each parameter. The abscissa in the figure represents the fineness of changing the parameters. For example, E-17 depicts that the parameters have been changed by ${10^{ - 17}}$. The coordinate of curve x at E-18 represents the BER after decrypting the information in the ONU when the value 35 of the parameter x in the key is changed to $35 + {10^{ - 18}}$. It can be seen from Fig. 8 that when a parameter of the key is changed beyond E-14, the BER will rise sharply above the FEC threshold, which proves that the proposed scheme is highly sensitive toward a minute change in the key. In chaotic systems, there are often typical parameters that drive chaotic mapping. In the experiment, we first set the parameter values to typical parameters, they are all integers. And we only adjust the fractional part to obtain the key space. Then our key space can be conservatively estimated as ${({10^{14}})^9} = {10^{126}}$. The key space is large enough to resist the brute force attack.

Figure 9 depicts the BER curve and constellation diagram for normal, illegal, and brute force cases. For the entire system, we studied the communication situation with and without PS. Under normal reception conditions, ONUs decrypt the original information correctly using the same key. When the received optical power is greater than -16 dBm, the PS-OFDM BER is lower than ${10^{ - 3}}$, while Uniform-OFDM requires that the received optical power should be greater than -15 dBm. It can be seen that the communication system with PS scheme has a gain of about 1 dB compared with the system without PS scheme. This is because PS optimizes the mapping probability distribution of constellation points at different positions, reducing the overall transmission power. That is, under the same total transmission power, the PS scheme has better BER performance than the traditional scheme. Being able to be perfectly compatible with PS technology is also one of the prominent advantages of this encryption scheme. In the case of illegal reception, the BER of the two schemes is greater than 0.4, and the constellation diagram is in ring-shaped as shown in the Fig. 9. Among them, the BER of the uniform distribution scheme is stable at about 0.5, and the BER of the PS scheme is about 0.4, which is slightly lower than the uniform distribution scheme and that is caused by the inward aggregation of the constellation points due to the PS. By changing the PS coefficient the transmission performance of the system can be increased, but at the same time, it will also slightly reduce the BER of the illegally accepted segment, but it will not affect the security performance of the system within a reasonable range. Explicitly, in the enhanced security communication system, the positive impact of introducing PS technology is far greater than the negative effect.

As it is mentioned that the key space of the proposed scheme is huge enough∼${10^{126}}$ to defeat even the brute force cracking, but still the impact of brute force attack is studied here. It is assumed that the eavesdropper perceives the encryption operation in the transmission due to the abnormality of the constellation diagram. Therefore, the attacker uses all possible ways to crack the information, and finally restores the correct constellation diagram. In this case the BER curve is obtained by the illegal receiving end, as shown by the curve ‘Brute Force’ in Fig. 8, it can be seen that the BER is still very high. This is because that the system has still the encryption operations in the subcarrier, symbol and time dimensions, and therefore these encryptions are not easy to be detected, so the system still guarantees the security.

Furthermore, in the OFDM system, the PAPR is a non-negligible part, so after security enhancement of the OFDM signal, we tested the complementary cumulative distribution function (CCDF) of PAPR. As shown in Fig. 10, the OFDM signal after security enhancement has no deterioration in PAPR compared to the original signal. Therefore, our scheme will not negatively affect the performance of the OFDM system.

## 4. Conclusion

In this paper a new encryption model is proposed that has increased the encryption speed of OFDM-PON by 3 folds. Such a model is proposed for the first time which is based on four domains including, constellation, subcarrier, symbol and time, which has increased the security. 4D-hyperchaotic mapping is used to generate four masking factors to achieve ultra-high security encryption in four dimensions, he key space reaches ${10^{126}}$,even a brute force attack cannot be used to compromise the security of information. Further, it has been proved the PS technology can also be incorporated along the encryption technique, while ensuring information security, effectively improving the bit error performance by about 1 dB. The proposed high security OFDM-PON has been demonstrated by experiments. 16 Gb/s transmission was achieved in 25 km of SMF. We analyzed the BER and PAPR obtained in the experiment, and the experimental results show that the proposed security-enhanced OFDM-PON has high sensitivity and security. The proposed scheme has very reliable security performance, and at the same time, it also has excellent benefit improvement, which is very promising in the future PS-OFDM-PON.

## Funding

National Key Research and Development Program of China (2018YFB1801302); National Natural Science Foundation of China (61475024, 61522501, 61675004, 61705107, 61720106015, 61727817, 61775098, 61822507, 61835005, 61875248); Beijing Young Talent (2016000026833ZK15); BUPT Excellent Ph.D. Students Foundation (CX2020301); Open Fund of IPOC (BUPT); Jiangsu Talent of Innovation and Entrepreneurship; Jiangsu Team of Innovation and Entrepreneurship.

## Disclosures

The authors declare no conflicts of interest.

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