## Abstract

In this paper, we propose and experimentally demonstrate a novel multi scrolls chaotic encryption scheme for CO-OFDM-PON. We analyze the principle of 3-dimension encryption scheme and discuss its encryption complexity. Compared with the previous hyper Chen chaotic encryption scheme, the proposed encryption algorithm can realize dynamic constellation point mapping of QAM signal with lower encryption complexity. We also compare the transmission performances of the two chaotic encryption schemes. The results show that the proposed multi scrolls scheme has better BER performance because it can decrease the peak to average power ratio (PAPR) of OFDM. What is more, the proposed encryption scheme is very sensitive to the initial secure key and a tiny discrepancy as small as 10^{−17} would lead to a completely different sequence. The high sensibility to the initial value can effectively increase encryption level and the key space of the multi scrolls encryption scheme is 10^{6} times of that hyper Chen. Further, to verify the effectiveness of the proposed encryption algorithm, encrypted transmission of a digital picture in 80 km SSMF is carried out.

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

## 1. Introduction

For next generation passive optical network (PON) technologies supporting data rate of 40-Gb/s or above, coherent detection is proposed [1–3]. Coherent PONs can effectively improve channel data rate and receiver sensitivity. It can greatly extend transmission distance and increase splitting ratio to support more access users for ultra-dense wavelength-division-multiplexing (UDWDM) application [4–6]. On the other hand, due to its high flexibility, high spectrum efficiency and robustness against chromatic dispersion (CD) and polarization mode dispersion (PMD), optical orthogonal frequency division multiplexing (OFDM) has caused wide interest around the world [7–10]. Previously, coherent optical OFDM passive optical networks (CO-OFDM-PON) has been proposed for access application to increase available network capacity and access distance [11,12]. In the downstream transmission of OFDM-PON, the signal sent by the optical line terminal (OLT) is split to all optical network units (ONUs). Because of the broadcasting property, the downstream signal can be easily eavesdropped by illegal eavesdropper. Even though lots of advanced upper-layer security schemes have been proposed for PONs, the upper layer security scheme cannot provide adequate protection because the encryption control information is still exposed in the physical layer [13,14]. By brute force or chosen plaintext attack, the illegal eavesdroppers can easily monitor other ONUs information. So how to ensure the legal ONU receive information normally and simultaneously prevent the other illegal eavesdroppers may be a serious problem in OFDM-PON.

The physical layer can be thought a transparent pipe for data communication. Physical-layer security can provide transparent encryption for all of the transmission data, which is different with the upper-layer security. Many methods have been proposed for physical-layer encryption. Among these technologies, the chaotic encryption is one of the promising methods for secure transmission due to its pseudorandom, concealment and high sensibility to the initial value. In chaotic system, a large number of non-periodic, noise-like, yet deterministic and reproducible signals can be generated, it has natural concealment. Previously, the chaotic encryption schemes such as time and frequency permutation [15], Brownian motion encryption [16], Stokes vector chaotic scrambling [17], hyperchaotic encryption [18] and chaotic Walsh-Hadamard transform [19] have been proposed for physical layer security. However, these proposed encryption schemes are traditional fixed mapping in symbol and it is easy to be attacked by statistical analysis once plaintext or ciphertext is intercepted. In [20], hyper Chen chaotic encryption was proposed and realized dynamic mapping of QAM constellation. The noisy-like constellation diagram can effectively mask the transmitted information and thus enhance the security of PON systems. The disadvantage of this encryption scheme is that it has relatively high computational complexity because it involves many time-consuming mod and rounding operations.

In our previous work, multi scrolls chaotic encryption is demonstrated by numerical simulation [21]. In this paper, we propose a three-dimension (3-D) multi scrolls chaotic encryption scheme for physical layer security of polarization division multiplexing (PDM) CO-OFDM-PON. We discuss the principle of the 3-D multi scrolls chaotic encryption in detail and verify it in 80-km standard single mode fiber (SSMF) transmission system. In our proposed multi scrolls chaotic encryption scheme, the three dimensions are respectively used for XOR operation of bit stream and offset mapping of in-phase and orthogonal components of constellation points. We analyze the computing complexity of chaotic sequence generation and encryption process. Compared with the hyper Chen chaotic encryption scheme, the proposed encryption algorithm can realize dynamic constellation point mapping of QAM signal with lower encryption and decryption complexity, which is useful for cost-sensitive ONUs in PON. Meanwhile, the multi scrolls chaotic encryption algorithm can improve the transmission performance because it can decrease the peak to average power ratio (PAPR) of OFDM. Compared with the original signal transmission without encryption, a receiver sensitivity improvement about 2 dB is achieved. We also investigate the secrecy and find it is very sensitive to the initial secure key. Only the tiny discrepancy of initial value is less than 10^{−18}, the signal can be decrypted correctly. The key space of the multi scrolls encryption scheme is ∼10^{338} and it is 10^{6} times of that hyper Chen. Finally, encrypted transmission of a digital picture is performed to verify the effectiveness of the proposed scheme.

## 2. Operation principle

Chaotic constellation mapping is one-to-many mapping utilizing chaotic system, which means it is almost impossible to use statistical attacks to find the mapping relationship between plaintext and ciphertext. Figure 1(a) shows the original 16-QAM constellation diagram with conventional mapping. After masked by random phase scrambling, the constellation diagram is shown in Fig. 1(b). To further improve the encryption level, both amplitude and phase information can be scrambled by chaotic system. Dynamic mapping by chaotic parameters can be expressed as the following equation:

where*P*is the original complex value of 16-QAM constellation points and

*C*is the encrypted constellation points after mapping by chaotic parameters.

*I*and

*Q*are two independent chaotic sequences generated by chaotic system for the in-phase and quadrature. After scrambling by chaotic sequences, the constellation diagram is shown in Fig. 1(c). We can see the original information is effectively hidden in the noisy-like chaotic constellation diagram. Hyper Chen chaos is a way to get chaotic sequences. However, the chaotic parameters (

*y*and

*z*) in hyper Chen chaos range from 0 to 30, which cannot be directly used for encrypting calculation. So in hyper Chen chaotic system, after generating chaotic parameters

*y*and

*z*, $I = \bmod ({y,floor({y - 1} )} )$ and $Q = \bmod ({z,floor({z - 1} )} )$ are carried out. Additional mod and floor calculating operations are needed at transmitter. Correspondingly, additional mod and floor operations are needed at the receiver. Compared with simple addition, subtraction and sign operations, the mod and floor operations require more computational resources. It is not suitable for high speed access networks, especially in cost-effective ONUs that require real-time operation.

In this paper, we propose multi scrolls chaotic encryption for high speed CO-OFDM-PON. The multi scrolls chaos system can be expressed as:

*k*is a real constant to adjust the range of

*x*and

*y*.

The phase diagrams of multi scrolls jerk chaos system are shown in Fig. 2. We can see the generated chaotic sequences *x* and *y* range about from -1 to 1 and *z* ranges from -0.5 to 0.5. Due to the amplitude-limited characteristic of multi scrolls, the chaotic parameters can be directly used for encrypting calculation and no additional calculating operations are needed. So in Eq. (1), the *I* is equal to *x* and the *Q* is equal to *y*. The omitted calculating operations can effectively decrease the computational complexity at transmitter and receiver. What is more, the multi scrolls chaos system is extremely sensitive to the initial secure key and a tiny change would lead to a completely different one-to-many mapping. So compared with the others encryption scheme, the multi scrolls chaos has larger key space and higher encryption level.

Figure 3 shows the schematic of multi scrolls chaotic encryption for CO-OFDM-PON. An initial key is used to generate the multi scrolls chaotic sequences according to Eq. (2). The original transmitted PRBS sequence is firstly performing chaotic XOR operation. After serial to parallel (S/P) conversion, the data is mapped to QAM constellation, such as 16-QAM or 64-QAM. Then multifold in-phase and quadrature shifting encryption according to Eq. (1) is carried out. After multi scrolls chaotic encryption, the encrypted data is transformed to complex time domain by inverse fast Fourier transform (IFFT). Cyclic prefix (CP) is added before the signal is transmitted.

## 3. Experimental setup and results

To verify the feasibility of the proposed encryption scheme, a proof of concept experiment is demonstrated in CO-OFDM-PON, as shown in Fig. 4. At the optical line terminal (OLT), one laser with center wavelength of 1550.488 nm is used as optical carrier. In our demonstration, no optical amplifier is used at the transmitter so we increase the optical power of the laser to 15 dBm. An initial secret key is used to generate the chaotic sequences and then encryption operation is performed. The MZM IQ modulator is driven by a Tektronix arbitrary waveform generator (AWG) operating at 10-GS/s to produce encrypted 16QAM-OFDM signal. PDM is emulated by a PDM emulator. At the output of the PDM, 16QAM-OFDM signal with data rate of 80-Gb/s is generated. The insertion loss of the MZM modulator and PDM emulator is 5 dB and 3 dB, respectively. After 80-km standard single mode fiber (SSMF) transmission, the encrypted OFDM signal is split to two optical network units (ONUs). The total link loss from the output of the laser to the input of the receiver is about 27 dB. An optical amplifier can be added at the output of the transmitter to compensate the link loss. The optical amplifier can also reduce the power requirement of the laser. At each ONU, the signal is sent into an integrated coherent optical receiver (U2 T CPRV1220A) and then interfere with a local oscillator (LO). After balance detection, the electrical signals are sampled by a real-time digital storage oscilloscope (Tektronix DPO72004B) operating at 50 GSa/s. Then offline OFDM decoder and decryption are performed. Correct and wrong secret key are used for signal decryption at the ONUs.

The detailed encryption and decryption process for PDM-OFDM are shown in Figs. 5(a) and 5(b), respectively. We adopt the similar scheme in our previous work [22] to generate the baseband PDM-OFDM signal. In multi scrolls chaotic encryption, a secret key is firstly used to generate the chaotic sequences and then XOR operation of bit stream is performed. After S/P conversion, the data is mapped to 16-QAM constellation. Then multifold in-phase and quadrature shifting encryption is carried out in frequency domain. The encrypted 16-QAM signal are grouped into blocks with 200 OFDM symbols. In each OFDM symbol, the number of subcarriers used for data transmission and guard band are 240 and 10, respectively. Then a 256-point inverse DFT (IDFT) is performed and transforms the subcarriers to a complex time domain signal. Cyclic prefix (CP) and cyclic suffix (CS) with a length of 10 subcarriers are inserted into the time domain signal. For simplicity, *x* polarization and *y* polarization signal are generated using the same secret key. Before the signal is transmitted, a preamble includes 2 Chu-sequences for synchronization and 4 Chu-sequences for channel estimation are added to the block. At the ONU, the signals are transformed to frequency domain for channel equalization. The offline DSP includes symbol synchronization based on CHU sequence, frequency synchronization, channel estimation based on intra-symbol frequency-domain averaging (ISFA) algorithm and pilot-based phase recovery. Then corresponding decryption and de-mapping are performed.

For convenient comparison, traditional hyper Chen chaotic encryption scheme is also implemented. We firstly compare the computational complexity of the proposed multi scrolls and hyper Chen chaotic encryption. The chaotic sequence generation and mapping operation are both calculated, as shown in Table 1. From the results, we can see the multi scrolls has fewer add and multiply operation. More importantly, there is no complex round and mod operation in multi scrolls. Therefore, in terms of calculations, the multi scrolls chaotic encryption is more suitable for high-speed real-time access system.

Figure 6(a) shows the optical spectra of the original OFDM signal after fiber transmission. Figures 6(b) and 6(c) show the OFDM signal encrypted by hyper Chen and multi scrolls, respectively. We can see the optical spectra was little affected by the encryption algorithm and no visible difference is observed.

Figure 7(a) shows the BER versus the received power at the ONUs after 80 km SSMF transmission. Optical back to back (BTB) transmission is also measured as reference. From the results, we can see compared with hyper Chen encryption, the proposed multi scrolls encryption has better performance both in BTB case and 80 km SSMF transmission. Compared with BTB transmission, less than 2-dB power penalty is observed for multi scrolls encryption at the BER of 10^{−3}. After 80 km SSMF transmission, the received optical power of the original OFDM signal without encryption is about -15 dBm at the BER of 10^{−3} while -17 dBm for the multi scrolls encrypted signal. The multi scrolls encryption operation brings about 2 dB receive sensitivity improvement. Because of the different system parameters, the receiver sensitivity in the experimental demonstration is different with that of the simulation results in [21]. Figure 7(b) shows the complementary cumulative distribution function (CCDF) curves of PAPR with hyper Chen and multi scrolls encryption. We can see the multi scrolls encryption can reduce the PAPR of OFDM and thus improve the BER performance.

We then investigate the secrecy of the proposed encryption scheme, as shown in Fig. 8(a). The received optical power input to the ONU is adjusted from -20 dBm to -14dBm. We can see even if two of the three initial key values (*x _{0}, y_{0}, z_{0}*) are revealed, the illegal eavesdropper cannot decrypt the OFDM signal at various received optical power level and the BER equals to 0.5. To measure the sensibility to the initial key of the proposed scheme, we slightly change the initial value of the chaotic sequence at the OLT while maintaining the original initial key at the ONU. We fix the received optical power at -16 dBm. When the ONU has the completely accurate key, the encrypted OFDM signal can be decrypted normally, as shown in Fig. 8(b). But once one of the initial values has a tiny offset, the encrypted OFDM signal cannot be decrypted normally and we get noise-like constellation points distribution. In hyper Chen encryption scheme, only when the tiny discrepancy of initial key is less than 10

^{−16}, the illegal eavesdropper can recover the original signal. While our proposed multi scrolls based encrypted scheme requires a more rigorous tiny discrepancy. Only the tiny discrepancy of initial value is less than 10

^{−18}, the signal can be decrypted correctly. Take into consideration of the 3-D characteristic, the key space of the multi scrolls encryption scheme is 10

^{6}times of that hyper Chen.

Figure 9 shows the sequences generation with different initial value x_{0} while y_{0} and z_{0} are the same. The blue line x_{0} = 0.0005438432 and the red line x_{0} = 0.0005438432 + 10^{−17}. We can see the scheme is very sensitive to the initial secure key and after several iterations the two initial secure keys will generate different encryption sequences. The sensitivity of the chaotic system is not related to the initial key. Therefore, if the eavesdroppers don’t know the accurate initial secure key, the signal cannot be decrypted correctly.

We then analyze the key space of the encryption scheme. In our experimental setup, each OFDM symbol has 256 subcarriers and each subcarrier contains 4 bits. So each OFDM symbol contains 1024 bits. In the XOR operation, the key space is 2^{1024}. In our scheme, if the discrepancy of initial value is larger than 10^{−18}, it will lead to decryption failure. Here we choose 10^{−10} for key space evaluation because it is much larger than 10^{−18} and meanwhile there is enough redundancy. Then the key space of shifting encryption operation is (10^{10})^{3}=10^{30}. The total key space of the proposed encryption scheme is 2^{1024}*10^{30}=∼10^{338}. Brute force attack will not work in the multi scrolls chaotic encryption. When for practical application, independent initial key can be allocated to each ONU and there are enough secret keys for allocation. The proposed scheme has good scalability. Adopting higher order modulation format (such as 64-QAM, 128-QAM) and long FFT can further increase the key space.

Finally, encrypted transmission of a digital picture is demonstrated to verify the effectiveness of the proposed encryption algorithm. We take a picture of our experimental platform and convert it to black & white picture. Figure 10(a) shows the original picture and its histogram. Figures 10(b) and 10(c) show the pictures received at an illegal ONU and a legal ONU, respectively. When we use the wrong key to decrypt the signal, the decoded image will be a confusing black-white-gray dot. The histogram of the picture is almost flat and barely get any statistical information used for brute force attack. Only we get the quite correct key, we can successfully restore the original image. The transmission results qualitatively verify the effectiveness of the proposed encryption algorithm.

## 4. Conclusions

A novel multi scrolls chaotic encryption scheme is proposed and experimentally demonstrated for physical layer encryption in CO-OFDM-PON. Compared with hyper Chen encryption scheme, the proposed scheme has lower encryption complexity and larger key space. The key space of the multi scrolls encrypted OFDM-PON system reaches the order of 10^{338}. Encrypted transmission of a digital picture is also demonstrated. Experimental results show that the proposed scheme is a promising physical layer encryption method for CO-OFDM-PON.

## Funding

National Key Research and Development Program of China (2018YFB2200903); National Natural Science Foundation of China (61821001, 61875239); State Key Laboratory of Advanced Optical Communication Systems and Networks; Beijing Excellent Ph.D. Thesis Guidance Foundation (CX2019124).

## Disclosures

The authors declare no conflicts of interest.

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