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Abstract
This paper proposes a high-security chaotic encrypted power sparse coding division (CE-PSCD) scheme for 7-core fiber based on non-orthogonal multiple access (NOMA) technology. The method utilizes power multiplexing to realize parallel transmission of two signals. Joint encryption of the four-dimensional region is realized using constellation mapping encryption, carrier frequency encryption, symbol scrambling, and sparse code scrambling. What we believe to be a new dimension for encryption of autonomously designed sparse codes is proposed. Meanwhile, we hide the chaotic key in training sequence (TS) to realize the co-transmission of the key and the message. A 70 Gb/s CE-PSCD signal transmission over 2 km of 7-core fiber is demonstrated experimentally. At the limit of forward error correction (FEC) ∼3.8 × 10−3, the difference in the encrypted sensitivity among different users at the equal power level is 0.36 dB, which means that the fairness of users will not be destroyed. The key space can reach 10134, with a bit error rate (BER) of about 0.5 for brute-force cracking at illegal receivers. As long as the key bits in the hidden TS are wrong by one bit, the BER stays around 0.5. The results show no significant attenuation of the signal before and after encryption at either high or low power, verifying the high-security performance of our proposed scheme.
© 2024 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
5 G technology is booming, bringing new changes, new scenarios and new demands. A new era of innovations has unfolded for the researchers. Cloud computing, artificial intelligence, big data, and industrial internet are birthed, driving the global Internet data traffic to grow [1–3]. These groundbreaking technologies are propelling the data traffic to unprecedented growth. As a result, higher requirements are placed on optical access network capacity and speed. Compared with other bandwidth access technologies, passive optical network (PON) has become a much-anticipated research hotspot in today's society under the advantages of long transmission distance, lower cost, lower energy consumption, and comprehensive coverage [4]. To cope with the exponentially growing data capacity, PON systems have been continuously upgraded, starting with time-division multiplexing (TDM), evolving to wavelength-division multiplexing (WDM), and then upgrading to orthogonal frequency-division multiplexing (OFDM) [5,6]. OFDM is one of the most widely used multicarrier transmission systems in the future, requiring strict orthogonality between all subcarriers in the operating frequency band. In orthogonal multiple access (OMA) technology, each user is assigned a different block of orthogonal resources, and the number of users accessed is limited as a result.
In contrast, non-orthogonal multiple access (NOMA) technology in 5 G is the key to solving this problem [7,8]. In NOMA, there are two main approaches, one is based on the code domain where each user is assigned a non-orthogonal extension code, such as the sparse code multiple access (SCMA) technique, enables overloading [9]. The other most common NOMA technique is power domain-based multiplexing, which allows multiple terminals to share the same resource block simultaneously [10]. In a traditional PON architecture, the difference between the two optical network units (ONUs) closest and farthest from the optical line terminal (OLT) device is nearly 4 dB, assuming that the OLT device supports 20 km of standard single-mode fiber coverage, which has a loss of about 0.2 dB/km. Obviously, in this traditional PON architecture, the performance varies greatly between different ONUs. The farther away from the OLT, the higher the user loss, and it is impossible to ensure fairness among users on different paths. To ensure maximum fairness for users, the power domain is multiplexed using NOMA technology to optimize the power allocation to ONUs on different paths. As shown in Fig. 1, according to the losses on different paths, higher power is allocated to users far away from the OLT, thus improving the performance of the entire PON access network architecture. At the transmitter side, various signals are superimposed in the power domain to form a composite signal containing multi-user information for transmission. At the receiving end, the successive interference cancellation (SIC) module needs to be installed to distinguish the signals of different users, and ultimately to realize the multiplexing of limited spectral resources, which focuses on assigning different power values to users with varying qualities of link on the same channel [11,12]. However, when SIC is used to distinguish signals from other users, a high-power signal is first recovered, likely to leak privacy among users [13,14].
At the same time, the downlinks of fiber optic transmission systems all use broadcasting, which is susceptible to external eavesdropping, and its security is worth considering. With the increasing capacity of fiber optic transmission, people begin to pay more and more attention to the security of fiber optic communication. Cryptanalysis and key management are non-negligible factors for secure optical access systems. A cracking method based on differential cryptanalysis was proposed, which achieved complete decipherment with low complexity by obtaining equivalent aligned keys through differential cryptanalysis [15]. A video encryption algorithm based on chaotic block substitution and dynamic sequence multiplexing was proposed, which generated multiple obfuscated attached sequences with high security through key management [16]. For the secure transmission of PON, digital chaos-based physical layer encryption has been widely used to ensure the secure transmission of the system due to its advantages such as solid confidentiality, good randomness, low cost and ample key space [17–20]. A series of encryption schemes based on digital chaos in the physical layer domain have been proposed to address the security risks associated with fiber optic transmission systems. A Brownian motion based on an encryption scheme was implemented to achieve physical layer encryption using chaos in cell to scramble OFDM symbols [21]. A deoxyribonucleic acid (DNA) encoding-based encryption scheme was proposed, utilizing two DNA addition operation rules for encryption and reducing the computational complexity [22]. In [23], a chaotic compressed sense (CS) encryption algorithm is used to compress the data for OFDM-PON encryption. In [24], a 7-dimensional cellular neural network (CNN) based encryption scheme was proposed to achieve 100% scrambling using joint encryption with carrier frequency, phase and time. A multilevel chaotic encryption scheme based on a novel three-dimensional selective probabilistic shaping (3D-SPS) was proposed, which enhanced the security of data transmission while obtaining 0.9 dB shaping gain [25]. A three-dimensional encryption scheme for orthogonal chirp division multiplexing passive optical networks (OCDM-PON) was achieved, which utilized cascaded fractional-order chaotic mapping (CFCM) to achieve highly secure encryption [19]. A scheme based on constellation shaping technique and digital chaos was proposed to complete the system's real-time encryption [26]. These encryption schemes have good advantages, such as easy implementation and compatibility with the system. However, all of these encryption schemes default to a known key on both the sending and receiving ends, so this paradigm does not work and there is a risk of key leakage. In order to improve security, the key must change dynamically during transmission, so we propose to transmit the key along with the message while encrypting. In addition, some previous encryption schemes introduced phase noise to the system. An encryption scheme based on improved Lorenz chaotic model was proposed, which rotationally encrypted the constellation map of an OFDM system so that the phase of its constellation points is changed [27]. In [28], a scheme to encrypt the constellation modulation of 16QAM mapping by rotating the constellation points and utilizing the constellation mask vector was proposed. A high security encryption scheme based on constellation shaping (CS) technique and digital chaos was proposed, which utilized a chaotic model to generate chaotic sequences to perturb the phase of 64-ary circular quadrature amplitude modulation (64CQAM) [26]. Compared to these, our scheme does not introduce additional phase noise to the system and the performance of the system is hardly affected.
This paper proposes a high-security, chaotic, encrypted, power sparse coding division (CE-PSCD) scheme based on NOMA technology. Taking two power levels as an example, constellation mapping encryption and carrier-symbol cooperative encryption are performed on the high-power signal, and then sparse coding scrambling and carrier-symbol cooperative encryption are performed on the low-power signal. The encrypted two signals are superimposed according to power multiplexing, and the superimposed encrypted signals are fed into a 7-core optical fiber transmission system through OFDM modulation. The proposed 4-dimensional hyperchaotic model is used to generate masking vectors for sparse coding, frequency, constellation mapping, and symbols, which are encrypted in four dimensions masking each other. Meanwhile the key is hidden in training sequence (TS) to realize the key and message co-transmission for better protection against illegal eavesdropping. The scheme demonstrates 70 Gb/s CE-PSCD signaling in a 2 km 7-core fiber optic experimental system.
2. Principles
The main design scheme of CE-PSCD is shown in Fig. 2. It consists of constellation mapping encryption, carrier frequency encryption, symbol scrambling, sparse coding scrambling, and a process where the key is hidden in TS.
In Fig. 2, we take two input powers as an example. First, input power one is encrypted. When the binary data is modulated by quadrature phase shift keying (QPSK), the constellation is selectively mapped to complete the encryption of the constellation dimension. The carrier frequency and symbols are encrypted by perturbation, and finally the driving key for our chaotic system is hidden in TS. In this way, input power one is realized pre-encrypted. Then, the input power two is encrypted, the binary data is encrypted when sparsely encoded, the sparse matrix is encrypted, and the carrier frequency and symbols are encrypted with the same encryption operation as the input power 1. It is worth noting that the encryption operations of input power one and input power two are separated, and each is encrypted and then superimposed for transmission. The key-driven 4-dimensional hyperchaotic model generates four chaotic sequences for constellation mapping encryption, carrier frequency encryption, symbol scrambling and sparse coding scrambling. At the receiver, the key of the chaotic model needs to be solved first, and then demodulated by the SIC for high power one and low power two, respectively. The whole encryption process is reversible, and finally, the original data can be obtained by computing these two power signals by the reverse procedure for decryption.
2.1 4-dimensional hyperchaotic model
The proposed nonlinear 4-dimensional hyperchaotic dynamics model is represented as follows:
2.2 CE-PSCD four-dimensional encryption principle
In our proposed encryption scheme, which is based on two input powers, Fig. 4 shows the flowchart of its signal generation. It mainly includes high power constellation mapping encryption, low power sparse coding scrambling, key masking, joint encryption of minor and large-power subcarrier frequencies and symbols, Inverse Fast Fourier Transform (IFFT), addition of cyclic prefix (CP), and power allocation. S1(t) and S2(t) are denoted as the signal transmitted by channel one and the signal transmitted by channel two. The final transmit signal generated by the superposition of the two signals is denoted as:
where P1 and P2 are set to denote the assigned power one and power two, and the powers P1 and P2 in turn satisfy the following relationship: where P denotes the total power, and the ratio between power P1 and power P2 is designed as the power distribution ratio (PDR), which can be expressed as:It is worth noting that the high-power one uses the QPSK modulation format. The low-power two uses the designed I-8QAM, whose four different constellation points correspond to the four quadrants of the high-power QPSK modulation format, as shown in Fig. 5. By symmetrically flipping one of the constellation points along the x and y axes, the constellation points of the final 4 quadrants can be obtained, and then superimposed with the power of the high-power QPSK modulation format, a 32QAM constellation diagram can be obtained. Compared to conventional rectangular 8QAM, this I-8QAM constellation structure performs better regarding higher constellation figure of merit (CFM) and better noise immunity.
The chaotic sequence (x, y, z, w) is used to realize low-power sparse coding perturbation, high-power and low-power subcarrier frequency encryption, high-power constellation mapping encryption, and high-power and low-power symbol perturbation, respectively. First, the chaotic sequence z is utilized to perform high-power constellation mapping encryption. The encrypted vector M of the high-power constellation mapping can be obtained as follows:
In this case, multiplying the chaotic sequence z by 107 improves the randomness of the encrypted vector M. Here, multiplying the chaotic sequence z by any other number has a similar encryption effect. The reason for taking the remainder of 24 is that there are $A_4^4 = 24$ ways of high-power constellation mapping. In this way, all chaotic sequences z become integers in the interval [1,24], and then one of them is chosen as the final mapping of the high-power constellation, which can be obtained by the following process:
where, the number 2000 represents the mapping method of selecting the value of the 2000th column of the 1st row as the high power from M, and any value within the length range of M can be selected. Mapping0 represents all 24 mapping methods and Mapping represents the final mapping method selected.Secondly, the subcarrier frequencies and symbols of low and high power are encrypted by cooperative substitution using chaotic sequences y and w, as shown in Fig. 6.
The specific encryption rules are as follows:
Finally, the sparse coding for low power is perturbed using chaotic sequence x. Before perturbation, this scheme's design principle of sparse coding is introduced. Multi-user decoding of SCMA needs to rely on the Message Passing Algorithm (MPA). At the same time, the MPA algorithm has high complexity, and it is more difficult to decode the multi-user codebook. It is not easy for us to accurately differentiate the data of different users, and the whole decoding process is irreversible. Therefore, we propose a new sparse coding approach on the basis of a balanced incomplete block design (BIBD). The design has five parameters, which can be denoted as BIBD (b, ν, κ, r, λ), where b, ν, κ, r and λ indicate the number of these five parameters: block groups, levels, levels in each block group, block groups containing each level and block groups including each pair of levels. The association matrix of BIBD is a 0-1 matrix of order b ×ν, denoted as follows:
In our design scheme, b, ν, κ, r and λ indicate the number of these five parameters: resources, users, users in each resource, resources including each user and λ is set to 1. The designed BIBD correlation matrix needs to fulfill two conditions. Condition one is that the elements of the BIBD matrix have the same weights and the subset of the BIBD matrix is unique. Condition two is that, compared to the OMA technique, it allows a resource block to be assigned to multiple users in the same area at the same time, and by doing so, it realizes the reuse of ν resources by b users (b>ν).
Based on this, we design a novel encoding matrix. The non-zero elements in the association matrix are labeled, assuming that the subscripts of κ non-zero items in i resources are:
when aij = 1, χi(j)=j, all the zero elements in BIBD matrix are unlabeled, while the non-zero elements are labeled, and the labeled non-zero elements are what we need to transmit. In Eq. (9), depends only on the association matrix Ab × ν in Eq. (8). We assume that the data information matrix of ν users is:After our sparse coding, the sparse matrix becomes the following form:
${s_1}{s_2} \cdots \textrm{ }{s_b}$ represents the new QAM symbol formed after sparse coding. Here, we set the values of b and v to 4 and 6, i.e., our number of resources, users, users in each resource, resources per user are 4, 6, 3, 2. Since the 8QAM mapping carries 3 binary bits, which matches perfectly with our design of the I-8QAM mapping rule, this non-orthogonal sparse coding design can also achieve 150% overload.
Thus, the correlation matrix Ab × ν in Eq. (8) can be expressed as follows:
Each user contains two valuable bits of information, if the bit information of six users is “00 01 10 11 10 01”, the data matrix information after sparse coding is expressed as follows:
Based on this, we propose a new dimensional encryption. The sparse coded correlation matrix of Eq. (12) is perturbatively encrypted using the chaotic sequence x. The perturbation rule is as follows:
The transpose matrix X (masking factor) is generated by Eq. (14), and the transpose matrix X is realized by multiplying the correlation matrix of Eq. (12) by the transpose matrix X to perturb the correlation matrix by substitution. If the perturbed correlation matrix is changed to the following form:
The corresponding Eq. (13) is changed and the new constellation after perturbation is represented as follows:
This disrupts the original correlation matrix and realizes the perturbation encryption for sparse coding. Our encryption scheme is not only highly flexible, but also reversible. We only need to utilize the opposite algorithm at the receiving end to restore the original signal on the transmitter side.
The signal recovery principle is shown in Fig. 7. The received signal is first equalized and then decrypted using a key. SIC is used to demodulate NOMA power domain multiplexing, the basic principle of which is gradually subtracting the interference caused by the maximum signal power user. In this scheme, taking two power signals as an example, the low power signal two is considered as noise at the beginning of demodulation since signal two is low power, and the signal one in high-power QPSK modulation format is directly decoded. The channel response H1 is obtained by estimating the channel, and equalization is performed on the signals to get the encrypted high-power signal Data1, and the encrypted high-power signal one is remodulated and multiplied by H1, which is used for the recovery of signal two afterward, and then the high-power signal one is decrypted and demodulated so that the remodulation is achieved by Data1. Finally, the low-power signal two is recovered. It is worth noting that, since the encryption of small and large power is separated before the signal superposition, the encrypted signal one, which is remodulated and multiplied by H1, is subtracted from the receiver's signal, so that the encrypted low-power signal Data2 can be obtained. Then, the low-power signal Data2 is recovered. After the channel estimation, equalization, and decrypted signal demodulation, the original signal Data2 can be recovered. Then, the original signal Data2 can be recovered. Our encryption scheme is highly compatible with the modulation technique in the present NOMA technology, which is significant for the research of high-security encrypted communication.
2.3 Key “hide and seek”
To further enhance our encryption system's security, we propose a method to realize the co-transmission of keys and messages. We set the initial value of the key (x0, y0, z0, w0) of the chaotic model in this scheme cleverly at random as 5.121467238914136, 1.111255863541261, 1.132567112563262, 1.151564886625412. Each key has a total of 16 decimal digits; we convert each decimal number in these four keys to a 4-bit sequence, then each key will have a length of 64-bit binary string that corresponds uniquely to it, and these four keys have a total of 256 binary numbers. TS plays an essential role in channel estimation and equalizing signals at the receiver to get accurate symbol synchronization. Here, we transform the key of the chaotic system into a string of binary numbers embedded in the TS to realize the masking and simultaneous transmission of the chaotic key. The number of subcarriers in this scheme is 256, the corresponding TS is a 1 × 256 matrix. The 256-bit binary key can be perfectly hidden in the TS, making full use of every fragment of the TS. The specific key-hiding process is as follows:
At the receiving end, we can extract the key without the help of additional optics according to the following rules:
3. Experimental setup and results
An experiment has been carried out to verify the feasibility of our CE-PSCD scheme, the experimental setup is shown in Fig. 9. At the optical line terminal (OLT), the original data is mapped on 256 subcarriers, 1024 IFFF points, and the CP is set to 1/4. The information entropy carried by each constellation of points in Data1 is 2 bits/symbol, and that carried by each constellation of points in Data2 is 3 bits/symbol. Thus, the information entropy of each constellation point after superposition is 5 bits/symbol. The encrypted data output from the DSP is imported into an arbitrary waveform generator (AWG, TekAWG70002A) with a 50 GSa/s sampling rate. After digital-to-analog conversion, it is converted into an analog radio-frequency (RF) signal with a speed of 10 GSa/s and amplified by an electrical amplifier (EA) to achieve intensity modulation, and then goes through the Mach-Zehnder modulator (MZM) with a bandwidth of 40 GHz to carry out the electro-optical modulation. Then the actual signal transmission rate is: 10GSa/s × 5 bits/symbol × 256 ÷ 1024 × 1 ÷ (1 + 1/4) × 7 = 70Gb/s. The tunable laser wavelength used in the experiment is 1550 nm with a power of 12 dBm. The modulated signal is optically amplified by an erbium-doped fiber amplifier (EDFA). The amplified signal passes through a power splitter (PS) to generate seven parts, passes through different lengths of delay lines (DL), and then passes through a fan-in device, which injects the signal into 2 km of 7-core weakly coupled fiber. After being transmitted by 7-core fiber, it is decoupled into single-mode fiber through a fan-out device, and the decoupled optical signals are injected into different optical network units (ONUs). In each ONU, a variable optical attenuator (VOA) is used to regulate the received optical power, and a photodiode (PD) with a bandwidth of 40 GHz enables the conversion of photoelectric signals. A mixed-signal oscilloscope (MSO, TekMSO73304DX) finally captures the received electrical signals with a sampling rate of 50 GSa/s to achieve analog-to-digital conversion. Finally, the correct key is obtained, and offline DSP processing can recover the original data.
Fig. 9. Experimental setup (OLT: optical line terminal; ONU: optical network unit; DSP: digital signal process; AWG: arbitrary waveform generator; EA: electrical amplifier; MZM: Mach-Zehnder modulator; EDFA: erbium doped fiber amplifier; PS: power splitter; DL: delay line; OC: optical coupler; VOA: variable optical attenuator; PD: photodiode; MSO: mixed-signal oscilloscope).
The power distribution ratio (PDR) at the system's optimal performance can be found by traversal. When the optical power at the receiving end is -16 dBm, the BER curves of the system with and without encryption are shown in Fig. 10. It can be found that the trends of Fig. 10(a) and Fig. 10(b) curves are the same. As PDR increases, more and more power will be injected into the high-power QPSK signal, and its BER decreases all the time with it. As for the low-power I-8QAM signal, its BER curve shows a decreasing and then increasing trend as the PDR increases. The reason is that when demodulation is done, the whole signal is given to the high-power QPSK signal. When the PDR is small at the beginning, the high-power QPSK signal is poor, and the SIC algorithm demodulates the low power I-8QAM, the BER of the low-power I-8QAM signal will be higher. As the PDR increases, the high-power QPSK signal works better and the SIC error propagation is smaller, so the BER of the low-power I-8QAM will be reduced. However, too high a PDR results in too little power being allocated to the I-8QAM and its BER increases, with the inflection point appearing as a PDR value of 9 in Fig. 10. Therefore, the PDR at the lowest BER of the low-power I-8QAM signal is the optimal PDR for the system.
Fig. 10. (a) BER curves for different PDRs without encryption; (b) BER curves for different PDRs with encryption.
After determining the system’s PDR, we compared the transmission performance of the CE-PSCD encrypted signal over the seven fiber cores, as shown in Fig. 11. It can be found that both high-power QPSK signal and low-power I-8QAM signal show a decreasing trend in BER with increasing optical power, and the BER curves of all cores are close to each other. At the limit of FEC∼3.8 × 10−3, the difference in sensitivity between the best-performing core 4 and the worse-performing core 2 of the high-power QPSK signal is only 0.33 dB; the difference in sensitivity between the best-performing core 4 and the worse-performing core 2 for low-power I-8QAM signal is only 0.25 dB, which proves the 7-core fiber we use has excellent stability and uniformity.
We choose core 4, which shows better performance, to further test the system's performance. The BER curves of the system before and after encryption at different received optical power are shown in Fig. 12. It is obvious from the figure that the BER of the QPSK signal is always lower than the I-8QAM signal. The difference between unencrypted and encrypted BER is minor for high-power QPSK and low-power I-8QAM signals. At the FEC∼3.8 × 10−3 limit, the experimentally obtained received optical power for unencrypted QPSK signal, encrypted QPSK signal, unencrypted I-8QAM signal, and encrypted I-8QAM signal are -15.2dBm, -15.1dBm, -13.4dBm, -13.2dBm, respectively. The high-power QPSK signal with encryption has a sensitivity gain of 0.1 dB, and the low-power I-8QAM signal with encryption has a sensitivity gain of 0.2 dB. This proves that the system's performance is hardly affected because our encryption scheme does not change the position of the constellation points and has not introduced additional noise to the system. Our encryption scheme only changes the mapping rules of the constellation points, and the encryption is only scrambling at the bit level, which does not involve changing the phase of the constellation points, and does not introduce phase noise.
In addition, we study the BER curves for lawful reception and illegal reception under different transmission systems, as shown in Fig. 13. It can be found that the BER curves of the BTB and core 4 transmission systems are almost the same, which indicates that our 7-core fiber does not change the system's transmission performance. The legal reception ONU can extract our key to decrypt the encrypted signals, and the illegal reception can only be done using brute force decryption. When illegal receivers try to break it violently, the BER obtained is always close to 0.49, which proves that our encryption scheme has high-security performance.
Fig. 13. (a) BER curves of encrypted, unencrypted, and illegally received high-power QPSK signal transmitted in core 4 with a BTB system; (b) BER curves of encrypted, unencrypted, and illegally received low-power I-8QAM signal transmitted in core 4 with a BTB system.
To verify the fairness of our CE-PSCD scheme for users with the same power, we measure the BER of different users in the encrypted low-power ONU2, as shown in Fig. 14. From the figure, it is evident that the BERs of different users are very close to each other. At the limit of FEC∼3.8 × 10−3, the sensitivity difference between different users is merely 0.36 dB, meaning that our encryption scheme does not destroy the fairness between users. This is due to our sparse-coded encryption, which treats the users of the entire sparse-coded correlation matrix, instead of encrypting the users’ signals individually and contains the data of multiple users at each constellation point. Each constellation point is symmetric, so such a whole encryption does not affect the fairness among users. Meanwhile, our sparse coded encryption scheme does not affect the performance of the system while not affecting the fairness among system users. This is because our encryption scheme does not introduce phase noise and the difference in encryption sensitivity does not degrade the transmission performance of the system. We inserted the constellation diagram at an optical power of -12dBm with a 9QAM distribution of constellation points. The reason is that our encryption scheme does not change the location of the constellation points, when demodulating the low power with the SIC algorithm. The constellations obtained include the 4 cases of I-8QAM; these 4 cases of constellation points are demodulated simultaneously, and the total number of constellation points including these 4 cases is 9. Hence, the constellation diagram of the encrypted low-power signal obtained at the receiving end is 9QAM.
Figure 15 shows the BER for a 4-dimensional hyperchaotic model with a slight change in the initial value. For chaotic sequences, when their initial values change by 10−16, the BER of the system is the same as that of the correct key, while when their initial values change by 10−15 and above, the BER of the system increases significantly, approaching 0.49. At this point it is no longer possible to decrypt them. For parameters a and b, when their initial values are varied by 10−16, the BER remains the same as the correct key; while when their initial values are varied by 10−15 and above, the BER increases significantly. The BER increases significantly for parameters c and d when their initial values change by 10−14 and above. For parameter e, the BER increases rapidly when the initial value varies by 10−16 and above variations. This means that our chaotic model is susceptible to the initial value, and the key space can be as high as [(1015)6 × (1014)2 × (1016)1] = 10134, which is enough to defend against violent theft by unlawful receivers.
We further test the computational complexity of the proposed scheme. The main computational complexity of this scheme comes from the system level encryption. To solve the differential equations of the chaotic model, we use the 4th Runge-Kutta method iteration. The main computational complexity of the system comes from its solution of the chaotic model. We have compared the model used in this paper with other models used and the comparison results are shown in Table 1. From the results, it can be seen that the computational complexity of the scheme is higher than that of the low-dimensional chaotic model. However, the low dimensional chaotic model has a small key space, which is not enough to resist brute force cracking. The chaos model we use has higher dimensions and larger key space, which effectively improves the security performance of the system. We also compare with the 4-chaos model in the same dimension and find that our computational complexity is relatively low and the key space is larger. Compared with the 7-D chaos model, the computational complexity is low and there is enough key space to resist intrusion. In conclusion, our encryption scheme has good security performance.
Table 1. Comparisons of the proposed scheme with other encryption schemes
According to the Fig. 8, we hide the key in binary form in TS. To verify the superiority of this scheme, we test the BER curves when the hidden keys {x, y, z, w} are each only one binary digit wrong. Taking the high-power QPSK signal as an example, the measured BER curves are shown in Fig. 16. It can be found that no matter which kind of key, as long as the bits are wrong by one, the received BER stays around 0.5, close to brute-force cracking at illegal receivers. Legal receivers need to accurately obtain all the binary digits of the key that we have hidden to ensure that the information received is error-free. Illegal receivers can only get the hidden key by brute-force decryption, and as long as one binary digit is wrong, the BER stays around 0.5, which means that all the signal can't be demodulated correctly. This shows that the high stability and low fault tolerance of our hidden keys, combined with our encryption algorithm greatly improves the system’s security.
Fig. 16. BER curves for illegal reception with one wrong binary number for each of the different keys.
4. Conclusion
This paper proposes a four-dimensional joint encryption scheme based on NOMA technology. Meanwhile, the chaotic key is hidden in the TS to realize the key and message co-transmission and experimental verification are performed. The four-dimensional hyperchaotic system generates four chaotic sequences, which generate sparse coding, frequency, constellation mapping, and masking vectors for symbols, respectively, to realize four-dimensional joint encryption. The proposed sparse coding achieves a 150% overload rate and increases the number of accessed users, while a new dimension of sparse coding encryption for autonomous design is proposed to integrate user information for sparse coding perturbation encryption. In addition, combined with our experimental 2 km weakly coupled 7-core fiber, the system transmission capacity is again enhanced. The transmission of 70Gb/s CE-PSCD signals over 2 km of 7-core fiber is experimentally demonstrated. The results prove that our scheme has high sensitivity with good encryption performance. At the equal power level, the sensitivity difference between different users after encryption is 0.36 dB, which does not affect the excellent fairness among users. At the FEC∼3.8 × 10−3 limit, the received optical power of the encrypted QPSK signal and the encrypted I-8QAM signal have a sensitivity gain of 0.1 dB and 0.2 dB, respectively. Our CE-PSCD scheme has a key space of 10134, which provides reasonable protection against brute force decryption by illegal receivers. In addition, the superiority of our hidden key strategy is verified. As long as the binary bits of our secret key are one bit wrong, the BER will remain around 0.5, which can further guarantee the safety of system. In conclusion, our proposed scheme can improve the system's transmission capacity and has high-security performance and good application prospects in the future of large-capacity and high-security optical communication.
Funding
National Key Research and Development Program of China (2021YFB2800904); National Natural Science Foundation of China (62225503, 61835005, 62205151, 62275127, 61935005, U2001601); Jiangsu Provincial Key Research and Development Program (BE2022079, BE2022055-2); The Natural Science Foundation of the Jiangsu Higher Education Institutions of China (22KJB510031); The Startup Foundation for Introducing Talent of NUIST.
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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