Abstract
Keywords
1. Introduction
Recently, due to the rapid development of information technologies such as 4K video, cloud computing, and virtual reality (VR) and due to the merging of optical and wireless communications, bandwidth demand by the end users is continuously increasing[
However, these chaotic encryption methods for the PON at the physical layer are based on the quadrature amplitude modulation (QAM) constellation to perform random position change, phase compensation, position exchange between different constellation points, and rotation of the constellation points for encryption. In fact, the high-dimensional constellation can further expand the Euclidean distance between the constellation points, which makes the position of the constellation points more flexible and the encryption method more diverse. It can also improve the system’s bit error rate (BER) performance.
Compared to QAM, carrier-less amplitude and phase modulation (CAP) uses two fixed filters whose impulse responses are Hilbert transform pairs[
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In this paper, to the best of our knowledge, we propose for the first time a physical layer data encryption scheme using two-level constellation masking in 3D-CAP-PON. Chua’s circuit model is used to generate three sets of chaotic sequences, which are then applied to generate displacement and rotation vectors, respectively. The original constellation points are encrypted by these vectors. Through two-level encryption, the constellation points are distributed into a noise-like spherical structure, which effectively improves the security performance of 3D-CAP-PON. To further test the system performance, 25 km standard single-mode fiber (SSMF) data transmission employing the proposed encrypted 3D-CAP-8 signal is successfully demonstrated in the experiment.
2. Principle
The principle diagram of the proposed physical layer data encryption using two-level constellation masking in 3D-CAP-PON is shown in Fig. 1. The original data is transformed into three-way signals through serial-parallel (S/P) conversion, which are then mapped onto a 3D constellation diagram. The initial key is subjected to Chua’s chaotic mapping to generate chaotic sequences. According to these chaotic sequences, the constellation displacement and rotation masking vectors are generated, respectively. After two-level encryptions, the positions of the constellation have all been disrupted. 3D-CAP processes the three signals and merges them into a symbol for transmission. At the receiver, after 3D-CAP demodulation, the original key is employed to rotate and restore the position of the constellation point. Lastly, the original data is obtained by demapping and parallel-serial (P/S) conversion. The 3D constellation diagram we use is shown in Fig. 2(a). This diagram of the constellation is a structure of two concentric tetrahedrons. The inner four constellation points are distributed on a regular tetrahedron, and the other four constellation points are distributed on the outer regular tetrahedron. The minimum Euclidean distance between adjacent constellation points is two.
Figure 1.Schematic diagram of physical layer data encryption using two-level constellation masking in 3D-CAP-PON.
Figure 2.Constellation diagram (a) before masking, (b) after constellation displacement masking, (c) after two-level constellation masking, and (d) with all of the correct keys.
Specifically, we utilize Chua’s circuit model to encrypt constellation points, which can be expressed as[
Among them, , , a, b are constants, whose values are 8.8, 15, , . , are the variables. The initial value of () is set to (0.2, , 0.25). The ranges of the generated chaotic sequences are , respectively. The phase diagram and bifurcation diagram of Chua’s circuit model are shown in Fig. 3. It can be found from Fig. 3(a) that Chua’s circuit model has a double scroll attractor and has complex chaotic characteristics. Figure 3(b) is a bifurcation diagram of Chua’s circuit model. As can be seen from the figure, the distribution of the value varies greatly with different . The generated sequence is very sensitive to the initial value, which is precisely required for secure communication. In our scheme, in order to further improve the randomness of chaotic sequences, we introduce a sampling factor L = 5, which means that the generated sequence would be sampled with a sampling factor of 5. The masking vector of displacement change can be expressed as
Figure 3.(a) Phase diagram and (b) bifurcation diagram of the Chua’s chaotic model.
Here, is the new sequence after sampling. Assuming that the coordinates of the original 3D constellation point are (), then the coordinates of the constellation point after the displacement vector encryption can be expressed as
As can be seen from Fig. 2(b), the distribution of the constellation points after the displacement transformation is regular, and it is easy to be eavesdropped on by the illegal receiver. It is necessary to perform secondary encryption on the constellation points. Therefore, we utilize the transformation relationship between the Euler angle and quaternion to realize the rotation encryption of constellation points. In 3D graphics, the most commonly used rotation representation methods are quaternion and Euler angle, which has the advantages of saving storage space and easy interpolation compared to the matrix. Chua’s circuit model is also used to generate chaotic sequences in the rotation masking and deal with the produced chaotic sequence. Assuming that the original chaotic sequence is () in order to rotate the Euler angle of 0–360 deg, the chaotic sequence is amplified in equal proportions, and the remainder is generated to produce a rotation angle of 0–360:
Equation (5) turns the 3D Euler angle into a quaternion, and Eq. (6) rotates the constellation point after the displacement masking, where () is the coordinates of the constellation point after the masking of displacement, and () is the coordinates of the constellation point after two-level encryptions. The encrypted constellation is shown in Fig. 2(c). After two-level encryptions, the 3D constellation has been completely disrupted, and its distribution is similar to noise so that illegal receivers cannot correctly eavesdrop and steal the transmitted information, which greatly improves the security of the system and transmission performance of the system. If you have all of the keys, you can accurately restore the constellation diagram, as shown in Fig. 2(d).
3. Experimental Setup and Results
The experimental setup of the proposed physical layer data encryption using two-level constellation masking 3D-CAP-8 is demonstrated in Fig. 4. At the transmitter side, the original data is mapped onto 3D constellation points. Then, the Chua’s model is utilized to generate masking vectors to change the position and rotation of constellation points. The masked symbol will be up-sampled with a factor of 7. Three orthogonal filters of CAP process the corresponding parts of the signal, respectively, and add the output of three orthogonal filters as a 3D-CAP-8 signal. The encrypted signals are loaded to an arbitrary waveform generator (AWG, TekAWG70002A) to produce the corresponding electrical waveform, which is amplified by an electric amplifier (EA). Onward, a Mach–Zehnder modulator (MZM) is utilized for riding over the encrypted information signal over the carrier, where a continuous wave (CW) laser source emits a light beam with a wavelength of 1550 nm. The modulated 3D-CAP-8 signal is transmitted with a 25 km SSMF. At the receiver side, a variable optical attenuator (VOA) is used for testing the BER behavior at different optical receiving powers. The signal is then detected by a photodetector (PD), and a mixed signal oscilloscope (MSO, TekMSO73304DX) is applied to record the data. The digital signal processing (DSP) unit at the receiver side performs the reverse process done at the transmitter side, including matched filters, down-sampling, constellation demasking, demapping, and, lastly, to restore the original data.
Figure 4.Experimental setup (CW, continuous wave laser; MZM, Mach–Zehnder modulator; EA, electric amplifier; AWG, arbitrary waveform generator; SSMF, standard single-mode fiber; VOA, variable optical attenuator; PD, photodetector; MSO, mixed signal oscilloscope).
Figure 5 depicts the BER curve of the legal ONU and illegal reception before and after the transmission of 25 km. The legal ONU has the correct key including the control parameters, initial values, and step size of the chaotic model, while the illegal ONU does not know the key. For the encrypted 3D-CAP-8 signal, compared to back-to-back (b2b) configuration, the power penalty after 25 km SSMF transmission is about 0.45 dB at a BER of . At the same time, as the received optical power increases, the BER of the legal ONU gradually decreases, and the BER of the illegal ONU has been maintained at about 0.5. Obviously, the illegal ONU cannot obtain any information like the legal ONU without having the information about the correct key. Figure 5 also inserts the reception constellation diagrams of the legal ONU and the illegal ONU when the received optical power is −11 dBm. The legal ONU obtains a clear 3D constellation diagram, and the constellation diagram obtained by the illegal ONU is meaningless, dense, and disorderly in a spherical shape.
Figure 5.BER curves of illegal receiver, 3D-CAP-8 for back-to-back (b2b) and 25 km transmission.
In order to further explore the encryption security level of the proposed scheme, we have explored the sensitivity of the initial value. The experiment tests the BER curve when the received optical power is set to after a small initial value change, after 25 km SSMF transmission. The initial values () of Chua’s circuit model are set to (0.2, , 0.25), respectively. For the three initial values, we test their impact on the BER curve under different small changes. It can be seen from Fig. 6 that when the initial value changes to , there is no obvious change in the BER compared to the original correct parameter value. However, once the initial value changes to , the BER of the system has been dramatically increased, and the value of the BER is close to 0.48. When the change of the initial value is or larger, the system’s BER has no significant change. This shows that our encryption method is very sensitive to the initial value. Therefore, for our system, a total of seven key parameters () can at least achieve a key space of , which can effectively resist illegal attacks.
Figure 6.BER measurements with a tiny change in initial value.
To investigate the performance of an illegal receiver with different keys, we did further experiments without key of displacement and without key of rotation. The measured BER curves are illustrated in Fig. 7. When all of the security keys are wrong, the BER of the illegal receiver is around 0.5. The received constellation is shown in Fig. 7, which is completely non-understandable. When the keys of displacement are obtained, the BER would be around 0.46. The constellation diagram is similar to the illegal receiver, which is also like the spherical structure.
Figure 7.Measured BER curves at the illegal receiver with different keys.
However, compared with the illegal receiver, this constellation has a larger range of constellation distribution due to the displacement masking. When keys of rotation are known by the illegal receiver, the BER would be about 0.31. The constellation diagram is also shown in Fig. 7. Because of the rotating masking key, the entire constellation diagram is equivalent to only the displacement masking, and the constellation diagram is consistent with Fig. 2(b). With only the displacement masking, the constellation distribution is regular, and its BER is relatively low, which is the reason for second-level encryption. After two-level encryption, the constellation has a spherical distribution similar to noise whose key space reaches , which can ensure high security in short-distance communication.
4. Conclusion
We have proposed a physical layer data encryption using two-level constellation masking in 3D-CAP-PON. Chua’s model is applied to generate chaotic sequences to produce the masking vector of two-level encryption. The use of 3D constellation points for encryption can increase the minimum Euclidean distance, thereby obtaining a larger constellation space and a more flexible and variable encryption scheme. With two encryption methods to encrypt the constellation twice, the 3D constellation points turn into a noise-like spherical structure, which can effectively improve the security of the system. The encryption scheme we propose has a key space of , which can effectively resist attacks from illegal receiving ends. An experimental demonstration of encrypted 3D-CAP-8 signal transmission over 25 km SSMF is successfully conducted. The experimental results show that the proposed encryption system has very strong anti-attack performance and has good application prospects in future 3D-CAP-PON.
References
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