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Abstract
In order to guarantee the information of the W-band wireless communication system from the physical layer, this paper proposes the sliced chaotic encrypted (SCE) transmission scheme based on key masked distribution (KMD). The scheme improves the security of free space communication in the W-band millimeter-wave wireless data transmission system. In this scheme, the key information is embedded into the random position of the ciphertext information, and then the ciphertext carrying the key information is encrypted by multi-dimensional chaos. Chaotic system 1 constructs a three-dimensional discrete chaotic map for implementing KMD. Chaotic system 2 constructs complex nonlinear dynamic behavior through the coupling of two neurons, and the masking factor generated is used to realize SCE. In this paper, the transmission of 16QAM signals in a 4.5 m W-band millimeter-wave wireless communication system with a rate of 40 Gb/s is proved by experiments, and the performance of the system is analyzed. When the input optical power is 5 dBm, the bit error rate (BER) of the legitimate encrypted receiver is 1.23 × 10−3. When the offset of chaotic sequence x and chaotic sequence y is 100, their BERs are more than 0.21. The key space of the chaotic system reaches 10192, which can effectively prevent illegal attacks and improve the security performance of the system. The experimental results show that the scheme can effectively distribute the keys and improve the security of the system. It has great application potential in the future of W-band millimeter-wave wireless secure communication.
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1. Introduction
With the development of information technology, the number of internet users and access devices is increasing, and more new information services will appear. The demand for traffic in communications networks has increased dramatically, which requires faster broadband speeds and greater information capacity [1,2]. Fiber communication system has the characteristics of ultra-wideband, but the high infrastructure cost and long deployment time of fiber transmission systems are not convenient in some cases [3]. Wireless transmission links do not need pipes and can be quickly deployed, which can make up for the shortcomings of fiber networks [4]. W-band (75-110 GHz) as a more high-frequency millimeter-wave, with its rich bandwidth resources, has the carrying capacity of ultra-high-speed signals, can meet the needs of large-capacity transmission of communication systems. The structure of the W-band signal generated by the photon-assisted beat frequency is simple and easy to realize. It can fit with the ultra-bandwidth characteristics of optical fiber communication, and it is easy to realize the seamless fusion of optical fiber-wireless-optical fiber, and further integrate the data migration of the communication network. This band has a great application prospect in the next generation of future wireless communication [5,5].
Due to its rich bandwidth resources, W-band is widely used in all aspects of military, commercial, healthcare, aerospace, Internet of things and other fields, which will inevitably cause problems such as network attack and information leakage [6,7]. Information leakage and malicious use may cause serious consequences to individuals, organizations and countries, so the security of information transmission has attracted more and more attention [8–10]. Chaotic system provides a feasible scheme for data encryption due to its sensitivity of initial value, irregular behavior, high randomness and convenience of hardware and software implementation [11–13]. At present, many scholars have studied chaotic neuron-coupled model, which can capture complex neuronal behavior using simple discrete mapping, and simulate the key features of biological neurons such as subthreshold oscillation and spike behavior [14]. Many scholars have done extensive research on the application of chaotic characteristics to encryption [15,16]. For fiber transmission system, three independent pseudorandom sequences generated by multi-vortex chaotic system are proposed for secure data transmission [17]. S. Chen, et al propose that the chaotic sequences generated by 7-dimensional cellular neural networks generate masking vectors to encrypt the phase, carrier frequency and time [18]. For W-band millimeter-wave fiber wireless communication system, a 7-D convolutional neural network chaotic system is proposed to implement information encryption [19]. In addition, novel multi scrolls chaotic encryption [20], phase ambiguity encryption [21], power division multiplexing [22] and manifold learning assisted generation of adversarial networks [23] are also proposed. However, most of the current encryption schemes pre-share the key by default, and the same key may be used repeatedly, which has the potential risk of information leakage. Therefore, key distribution technology is worth studying in the information security encryption scheme [24,25]. R. Wang, et al propose that phase-matching quantum key distribution with advantage distillation. The method can tolerate high system misalignment errors and improve the secret key rate and transmission distance significantly [26]. A new design of theoretically loophole-free plug-and-play QKD scheme with two-way protocol is proposed [27]. However, the implementation of quantum key distribution technology requires a high cost of system design and high complexity. Therefore, it is necessary to implement key masked distribution (KMD) and chaotic encryption based on chaotic neuron-coupled model.
This paper proposes a sliced chaotic encrypted (SCE) transmission scheme based on KMD, which is applied to W-band millimeter-wave communication system. The masking factor generated by chaotic system 2 (CS-2) is used to disrupt the ciphertext bit stream, and then quadrature amplitude modulation (QAM) mapping is performed on the ciphertext bit stream, and the constellation points after sliced grouping are replaced and disrupted respectively to complete the information SCE. Firstly, the masking factor generated by CS-2 disrupts the bit stream, and then, after QAM mapping, the constellation points after sliced grouping are replaced and disrupted respectively to complete the information SCE. Then, chaotic system 1 (CS-1) selects the random position of the ciphertext, inserts the key information, and then encrypts it to complete the key masking and distribution. Finally, the information is sent to the W-band millimeter-wave communication system for transmission. The proposed scheme is experimentally verified in a 4.5 m W-band millimeter-wave wireless transmission system with a rate of 40Gb/s. When the offset of chaotic sequence x is 1, the bit error rate (BER) is 0.029. When the offset of chaotic sequence y is 1, the BER is 0.0282. When the offset of chaotic sequence x and chaotic sequence y is 100, their BERs are more than 0.21. The results show that the scheme can effectively implement the masked distribution of key and the secure transmission of ciphertext information. It has a good prospect in the future physical layer security optical network.
2. Principles
The schematic diagram of the SCE transmission scheme based on KMD in W-band millimeter-wave communication is shown in Fig. 1. The proposed W-band encryption scheme is implemented in off-line digital signal processing (DSP). The scheme has the function of original data encryption and key embedding masking distribution. There are two main parts. The first part is sliced bit encryption and constellation sliced group encryption based on CS-2. The second part is based on CS-1, key sliced embedding and chaotic sequence sliced mapping masking embedding. At the transmitter, the w1, w2 sequence generated by CS-2 performs the sliced XOR scramble on the original bit. The encrypted bit information is QAM mapped and then grouped according to sliced grouping rule. The constellation points are divided into three groups according to the rule. The three groups of constellation points are permutation encryption by p1, p2 and s sequences generated by CS-2. The encrypted constellation points need to be re-mapped to bit information in preparation for subsequent key embedding. At this point, all sequences of CS-2 complete the encryption task, that is, the implementation of SCE mechanism. The three sets of chaotic sequences generated by CS-1 are used to complete the key slicing embedding and the chaotic sequence slicing mapping masking embedding. The x sequence is used to select the location of the key embeddedness, which can be identified as random by the chaotic sequence mapping. The y sequence is used to select the location where the bit stream of the chaotic sequence mapping is embedded. The z sequence is mapped into bit stream and inserted according to the position selected by the y sequence. At this point, the embedding and masking of the key are completed. The adoption of two chaotic systems can further improve the security of the transmission system. The chaotic systems used for ciphertext and key are independent, and the encryption mechanism is also independent, thus increasing the difficulty of cracking. The masked bit information needs to be QAM mapped again before transmission. The information can be analyzed and recovered by the opposite operation at the receiver. It is worth noting that the proposed scheme has key distribution function, and the key transferred in this article are only related to CS-2. After removing the bits mapped by the chaotic sequence z, the information is divided into two ways, one is to delete the key to obtain the data, and the other way is to extract the key and transfer the obtained key to CS-2 for chaotic sequence generation, so as to decrypt the constellation points and baud of the original data. The proposed scheme is a coherent W-band transmission system based on photon-assisted beat frequency. Before decrypting the data, the receiver needs to perform down-conversion, IQ unbalanced recovery and orthogonal normalization, clock recovery, matching filtering, down sampling, frequency offset estimation, phase recovery and equalization.
Fig. 1. The schematic diagram of the SCE transmission scheme based on KMD in W-band millimeter-wave communication.
2.1 Chaotic sequence generation
In this scheme, the chaotic sequence generated by two chaotic systems is used to complete the system KMD and the physical layer encryption of the original data. CS-1 is mainly used for KMD. CS-1 inspired by the work [28], the novel 3D discrete chaotic map is constructed. Its expression is as follows:
Three parameters are extracted in the proposed memristive chaotic map: a is the bifurcation parameter and b and c are non-bifurcation parameters. Amplitude control in the chaotic system realizes the simple signal amplification and attenuation solution based on a single non-bifurcation parameter. This new class of chaotic map is heading amplitude control, which is realized by a single knob. Typical rescaling phase orbits are shown in Fig. 2, and the corresponding rescaled basins of attraction are plotted in Fig. 3. The Lyapunov exponents (LE) are exhibited in Fig. 4, and the stable feature indicates that the non-bifurcation amplitude controller just induces the signal rescaling without introducing any change in the dynamical evolution. Rescaled discrete sequences controlled by a partial amplitude knob are displayed in Fig. 5. The chaotic system generates three dimensional chaotic sequences for key distribution. At the same time, the chaotic system has the function of amplitude modulation and can also be used to generate dynamic masking factors.
Fig. 2. Amplitude control in the memristive chaotic formula (1). (a) total amplitude control with a = 1.99, c = 1 and (x0, y0) = (0.001, 0.001), where green: b = 1, red: b = 2, blue: b = 4, (b) partial amplitude control with a = 1.85, b = 1 and (x0, y0) = (0.001, 0.001), where green: c = -1, red: c = 1, pink: c = -2, cyan: c = 2.
Fig. 3. Rescaled basins of attraction for formula (1) with a = 1.99, c = 1 under (x0, y0) = (0.001, 0.001). (a) basin expansion when b = 1, (b) basin shrink when b = 2.
Fig. 4. Stable Lyapunov exponents feature of amplitude controller for formula (1) with a = 1.99 under (x0, y0) = (0.001, 0.001), and b, c varies in [1,9]. (a) LE1, (b) LE2.
Fig. 5. Rescaled discrete sequences in the formula (1) with a = 1.99, b = 1 under (x0, y0) = (0.001, 0.001). (a) rescaled discrete sequences x, (b) rescaled discrete sequences y.
CS-2 is used for sliced physical layer encryption of the bit stream and constellation points of raw data. Incorporating the nonlinear attributes and dynamic equation of a discrete memristor, a coupled neural network emerges as a consequence of connecting two Rulkov neurons [29–31], as depicted in Fig. 6. Represented by tanh (φn), the memductance of the memristor is intricately entwined with the positive constant k, signifying the coupling gain between neurons and triggered when two neurons manifest diverse firing modes and initial states, discrete memristor coupling comes into play. The orchestration of synchronous behavior among neurons is deftly executed by skillfully taming the coupling channel. Emphasizing phase synchronization is paramount, as neural information finds expression predominantly in the nuanced firing rhythm of neurons, sidelining considerations of amplitude. In the exchange of information between two coupled neurons, the synaptic current generated within the discrete memristor is defined as in. The corresponding model of the discrete memristor synapse can be articulated as follows:
Represented by wn and pn, the potential and recovery variables, respectively, delineate the discrete time evolution of the system with iteration steps denoted as n. The potential variable equation allows parameter I to function as either a constant or a time-dependent additive disturbance. In the recovery variable equation, a (where a < 1) signifies the recovery time constant, b (where b < 1) characterizes potential correlation recovery, and c stands for the offset, with all parameters (a, b, c) being positive. Notably, classical parameter sets are available: (a, b, c) = (0.89, 0.18, 0.28) for chaotic discharge The parameter I fall within the range of (0.025, 0.05) in both scenarios. And different currents I are given the coupling Chialvo neuron model. Different current stimuli are input to the coupling neurons, and typical firing oscillations with I1 = 0.03, I2 = 0, e = f = 1, and k = 0.05 are plotted in Fig. 7. Synchronization bahaviors with I1 = 0.03, e = 0.5, f = 0.1 are plotted in Fig. 8. Complete synchronization of neurons is characterized by their activities being precisely coordinated, with identical patterns and simultaneous firing observed. Compensatory synchronization, conversely, is marked by a dynamic wherein neuronal activities are adjusted to maintain a balanced interaction, compensating for any discrepancies in their individual dynamics. Sample entropy with I1 = 0.03, I2 = 0, e and f vary in the range of [0.1, 1] are displayed in Fig. 9, indicating that the feedback strength of the memristor exhibits robust chaotic output within this specific range. The above neuronal chaotic system can produce very complex nonlinear dynamic behavior, which provides a highly complex masking factor for the encryption scheme proposed in this paper.
Fig. 8. Synchronization bahaviors with I1 = 0.03, e = 0.5, f = 0.1. (a)-(b) complete synchronization with k = 0.05, I2 = 0.03, (c)-(d) compensatory synchronization with k = 0.15, I2 = 0.
2.2 Sliced chaotic encryption and key slice embedded masked distribution principle
In order to ensure the security of the transmitted information, this scheme uses masking factors generated by two chaotic models to complete the physical layer encryption of the system. There are two main parts. In the first part, the chaotic sequence generated by CS-2 are used to encrypt the original bit by sliced bit stream and constellation point. In the second part, the key is sliced embedded and masked by the chaotic sequence generated by CS-1. The schematic diagram of SCE of original data is shown in Fig. 10(a). The total number of original bits is 2N. The chaotic sequence ${w_1}$ generated by CS-2 is used to sliced and select the initial position of the bits to be encrypted, and a total of k groups of bits to be encrypted are selected. Among them, there are q bits in each group to be encrypted, that is, a total of $k \times q$ original sequences are encrypted. ${w_1}$ is the chaotic sequence generated by CS-2, which cannot be directly sliced and selected, and needs to be processed as follows:
where unique (–) is for deleting duplicate elements. $del({w_1}^{{\prime\prime}} > {2^N})\textrm{ }$ is to delete the number in ${w_1}^{{\prime\prime}}$ more than 2N. $cho({w_1}^{{\prime\prime}^{\prime}},k)$ is to pick k elements from ${w_1}^{{\prime\prime}^{\prime}}$. The data to be encrypted is $ori\_data(w_1^{{\prime\prime}^{\prime\prime}}:w_1^{{\prime\prime}^{\prime\prime}} + q)$.Fig. 10. Chaotic encryption diagram of slice bit and constellation point. (a) bit-sliced scramble, (b) Constellation slice grouping scrambles.
The chaotic sequence ${w_2}$ is used to map 01 bits to the original sequence for XOR encryption. The number of ${w_2}$ sequences mapped to 01 bits is consistent with the number of original bits to be encrypted, and the specific process is as follows:
In the constellation point encryption scheme, this paper proposes the constellation point sliced permutated encryption. The constellation points were divided into three groups in sliced form, as shown in Fig. 10(b). Sliced with diagonal lines, two diagonal lines each form two groups, and the remaining eight constellation points form a third group. The three groups of constellation points are respectively encrypted using the ${p_1}$, ${p_2}$, $s$ sequences generated by CS-2. The process of encryption is mainly to generate permutation matrix through chaotic sequence. Constellation points after sliced grouping are permutated by permutation matrix. As shown in Fig. 10(b), constellation points only exchange positions between points, and their phase information and amplitude information are not distorted. Take chaotic sequence ${p_1}$ to disturb constellation points as an example, the specific processing process is as follows:
The key sliced embedded masked distribution diagram is shown in Fig. 11. The x sequence produced by CS-1 is used to select the initial position of the sliced embeddings. x chaotic sequence and selected sliced embedding position are shown in Fig. 11(a). The number of keys embedded is M times, and the number of keys in each group is b. It is worth noting that chaotic sequence x cannot be directly used to select the position where the key sliced is embedded, and it needs to be processed as follows:
Fig. 11. Key sliced embedded masked distribution diagram. (a) key masked embedding, (b) chaotic sequence masked embedding.
It is worth noting that the chaotic sequence z is processed into 01 bits and then inserted into the data stream. The specific processing process of chaotic sequence z is as follows:
After the z sequence is processed into 01 bits, v groups are selected, and the total number of bits in each group is h. The total length of the bit data stream after the key sliced embedding masking is ${2^N} + M\cdot b + v\cdot h$.
3. Experiment setup and results
In order to verify the safety and reliability of the proposed scheme, the experimental platform as shown in Fig. 12 was built in this paper for verification. The system transmission distance is 4.5 m, as shown in Fig. 13(b). The DSP data processed offline is imported to the arbitrary waveform generator (AWG) for sending. The AWG sends data at a rate of 20Gsa/s. The baud rate set in DSP is 10GBand, and the multiple of up sampling is 2 times. The spectrum diagram of the originating data is shown in Fig. 13. The radio frequency (RF) signal output by the AWG is fed into the IQ modulator after electrical amplifier (EA). The optical signal input to the IQ modulator is generated by the free-running tunable external cavity laser 1 (ECL 1) with the wavelength set at 193.4046 THz and the power of 14.5 dBm. The IQ-modulated signal is amplified by erbium-doped fiber amplifier (EDFA) and coupled with the optical signal generated by free-running tunable external cavity laser 2 (ECL 2). The optical signal produced by ECL 2 has the wavelength of 193.3146 THz and the power of 8.5 dBm. The frequency difference between the two optical signals is 90 GHz, which is coupled together by optical coupler (OC). The spectra of the unmodulated ECL 1 optical signal and the ECL 2 optical signal are shown in Fig. 13(c). The spectrum diagram of the optical signal generated by ECL1 after photoelectric modulation and the optical signal generated by ECL 2 is shown in Fig. 13(d). The variable optical attenuator (VOA) after the OC is designed to adjust the power of the optical signal entering the coupler. The photonics aided method is used to produce the W-band signal with the frequency of 90 GHz by uni-traveling-carrier photodiode (UTC-PD). The W-band signal is sent to free space by the antenna after the amplifier. The gain of the amplifier is 25 dB. In the free space, the W-band signal is transmitted for 4.5 m and then received by the receiver. The W-band signal is received through the conical horn antenna (CA) at the receiver. It is worth noting that during the experiment, the CA should be strictly aligned, otherwise the reception quality of the signal will be affected. In the experiment, the height of the CA was set to 57 cm. The signal received by the CA is amplified with low noise and transmitted to the mixer. The bandwidth of the oscilloscope is only 33 GHz, and the W-band signal can not be extracted directly from the oscilloscope, so the mixer is used to mix the W-band. The W-band 90 GHz signal goes into the mixer and is mixed with the 75 GHz signal generated by the local frequency after the 6 multiplier to obtain the corresponding intermediate frequency (IF) signal. The IF signal is 15 GHz and the bandwidth is 10 GHz, and its spectrum diagram is shown in Fig. 13(f). At this time, the IF signal can be received by the oscilloscope, and the oscilloscope sampling rate is 50GSa/s. The data collected by oscilloscope is processed by DSP after down-conversion, and the signal spectrum after down-conversion is shown in Fig. 13(g).
Fig. 12. Experimental setup (AWG: arbitrary waveform generator, EA: electrical amplifier, EDFA: erbium-doped fiber amplifier, CA: conical horn antenna, VOA: variable optical attenuator, OC: optical coupler, PC: polarization controller, ECL: external cavity laser, LO: local oscillator, LNA: low noise amplifier, UTC-PD: uni-traveling-carrier photodiode).
Fig. 13. (a) Experimental installation, (b) 4.5 m transmission distance, (c) Spectrogram of unmodulated optical signals (d) Spectrogram of modulated optical signals (e) Spectrum diagram of the transmitter signal, (f) Spectrum diagram of IF signal received by oscilloscope, (g) Signal spectrum diagram after down-conversion.
The paper analyzes the BER of the system under different input power. Figure 14 shows BER curves of the normal receiver and the illegal receiver after 4.5 m wireless transmission. The normal receiver includes 4.5 m W-band millimeter-wave transmission system in encrypted case and 4.5 m W-band millimeter-wave transmission system in unencrypted case. As can be seen from the figure, the BER of the illegal receiver does not change with the change of the input optical power, and is stable at about 0.4. When the input optical power is less than 5 dBm, the BER of the normal receiver decreases with the increase of the input optical power. When the input optical power is more than 5 dBm, the BER increases with the increase of the input optical power. Therefore, the optimal input power of this scheme is 5 dBm. When the input optical power is 5 dBm, the BER of the legitimate encrypted receiver is 1.23 × 10−3, and the constellation diagram is clear. When the input optical power is −1 dBm, the constellation diagram appears as a cluster, which is very unclear and the BER increases. This is because the normal receiver receives the key distributed by the transmitter and can correctly decrypt the encrypted information. The illegal receiver without the correct key is unable to recover the signal after interference. Compared with the unencrypted case, the system performance in the encrypted case is slightly reduced. However, the scheme adopted in this paper makes the transmitted data effectively protected. Therefore, the performance loss caused by the encryption scheme introduced in this paper is acceptable.
The chaotic sequence x is used to randomly select the key embedding position. Chaotic sequence y is used to randomly select the location of embedded key masking information. In order to verify the accuracy of the decryption key information at the receiver, the BER curves under different offsets are analyzed. It is important to note that this test is tested under ideal circumstances. The BER curves with offset ranging from 0-5000 are shown in Fig. 15(a). As can be seen from the figure, the BER increases with the increase of offset. Especially, the BER curves increase rapidly when the value of offset is in the earlier period. Therefore, the BER of offset in the range of 0-40 is analyzed in detail. It can be seen from the figure that when the offset of chaotic sequence x is 1, the BER is 0.029. when the offset of chaotic sequence y is 1, the BER is 0.0282. When the offset of chaotic sequence x and chaotic sequence y is 10, their BERs are more than 0.1. When the offset of chaotic sequence x and chaotic sequence y is 100, their BERs are more than 0.21. The illegal attacker cannot determine the location of the chaotic sequences x and y, and thus cannot decrypt the correct information. To sum up, the KMD method adopted in this scheme not only realizes the key distribution, but also guarantees the security of the system.
Fig. 15. BER curves under different offset conditions. (a) BER curves of offset in the range of 0-5000, (b) BER curves of offset in the range of 0-40.
In addition, we also analyze the effect of masking operation after key embedding on system performance. Figure 16 shows the comparison of BER curves of whether chaotic sequence z masking is performed during key distribution. As can be seen from the figure, the BER of the system decreases with the increase of the input optical power in the general trend. When the input optical power is 5 dBm, the BER of the system reaches the lowest. There is little difference in BER between the two cases. Therefore, the key distribution masking method adopted in this paper can guarantee the security of key distribution without affecting the performance of the system.
In this paper, we verify the encryption sensitivity of CS-2. As shown in Fig. 17, the change of BER corresponding to different parameters is very small when the initial value of the system changes. k, I1, I2 sequences have the highest sensitivity, reaching E-17. For k, I1, I2 sequences, when some parameter of the key changes to E-18 or more, the BER increases sharply, and the information cannot be decrypted. The key space can be represented as (a, b, c, e, f, k, I1, I2, s, p1, p2, w1, w2), which can realize the key space of $[{({10^{17}})^3} \times {({10^{15}})^3} \times {({10^{14}})^5} \times {({10^{13}})^2}] = {10^{192}}$. Therefore, CS-2 has high sensitivity. It is difficult for the thief to push the raw data from the system, which has high security.
4. Conclusion
In this paper, the SCE scheme based on KMD is proposed for W-band millimeter-wave wireless communication systems. The scheme adopts sliced bit encryption and constellation sliced group encryption based on CS-2 and key sliced embedding and chaotic sequence sliced mapping masking embedding based on CS-1, which effectively realizes the distribution of key masking and guarantees the security of information transmission. The wireless transmission experiment of 4.5 m W-band signal is carried out in this scheme. When the input optical power is 5 dBm, the BER of the legitimate encrypted receiver is 1.23 × 10−3. The proposed chaotic system has high sensitivity and the key space reaches 10192, which can effectively resist illegal attacks. The experimental results show that the KMD method and SCE scheme can guarantee the transmission performance and security of the system without increasing the complexity of the system. It has a broad prospect in the field of high-speed wireless networks and big data applications in the future.
Funding
National Key Research and Development Program of China (2023YFB2804805); National Natural Science Foundation of China (62171227, 62205151, 62225503, U2001601, U22B2009); Jiangsu Provincial Key Research and Development Program (BE2022055-2, BE2022079); 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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