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Abstract
The purpose of this study is to present a physical layer security scheme for key concealment and distribution based on carrier scrambling. The three-dimensional (3D) Lorenz system is used to generate independent chaotic sequences that encrypt the information with bit, constellation and subcarrier. In order to realize the flexible distribution of the key and ensure its security, the key information is loaded into a specific subcarrier. While key subcarrier and the ciphertext subcarrier are scrambled simultaneously. The encrypted key position information is processed and transmitted in conjunction with the training sequence (TS) to facilitate demodulation by the legitimate receiver. The processed TS can accommodate up to 10 key position information, thereby demonstrating the scheme's exceptional scalability. Experimental results show that the proposed scheme can safely transmit 131.80 Gb/s Orthogonal frequency division multiplexing (OFDM) signals across 2 km 7-core fiber. Meanwhile, the scheme enables simultaneous flexible distribution and concealment of the key, thereby offering a promising solution for physical layer security.
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1. Introduction
Due to the development of emerging services such as virtual reality (VR), artificial intelligence (AI) and big data, the demand for capacity in optical communication systems is surging. Space division multiplexing (SDM) technology is considered to be one of the solutions to solve the crisis [1–3]. SDM technology can improve the transmission rate by simultaneously transmitting multiple channels in one fiber [4], which mainly includes two forms: pattern reuse and fiber core reuse [5,6]. The principle of mode multiplexing is to exploit the orthogonality of different spatial modes in optical fibers for simultaneous transmission of multiple data modes within a single optical fiber, thereby enhancing the transmission capacity of optical communication systems [7,8,9]. While core multiplexing achieves capacity enhancement by incorporating multiple cores within a single optical fiber [10]. Intermode crosstalk occurs between different modes of light, resulting in a decline in data transmission quality. In contrast, weakly coupled multicore fibers (MCF) can maintain better transmission quality.
With the enhancement of communication system capacity and the growing interaction of information, ensuring data transmission security has become a primary research focus in the field of optical communication [11,12]. Research has been focused on encryption for fiber optic communications, and even optical wireless communications [13]. It is really a necessity to pay attention to the physical layer security [14]. The commonly used encryption methods encompass digital chaos encryption, optical chaos encryption, quantum key distribution (QKD), and upper-layer encryption. Upper-layer encryption primarily refers to the encryption of the network layer during data transmission. It offers the advantages of flexible encryption modes, low implementation complexity, and comprehensive data protection. However, it is important to note that upper-layer encryption technology can only encrypt data at its current layer and does not encompass header and control data. Consequently, there may be potential risks for transmitted data when it reaches subsequent layers [15]. QKD is based on the uncertainty principle of quantum mechanics [16], which generates quantum keys to encrypt transmitted data, making it difficult for eavesdroppers to intercept. However, the key generation rate of QKD is slow and susceptible to noise and channel attenuation, resulting in limited communication rates and transmission distances with poor communication capacity [17]. Optical chaos encryption [18–19] utilizes the chaos phenomenon in optical systems to implement encryption at the physical layer of communications. It constructs chaotic optical fields to encrypt information in an inherently parallel manner. Compared with digital chaos encryption, optical chaos encryption directly builds chaotic optical fields using nonlinear optics in illumination and transmission systems, such as interference, resonance and four-wave mixing effects. Digital chaos encryption mathematically models dynamical chaos using discrete or continuous nonlinear transformations in computer systems. Encryption is implemented through logical operations on digital representations. The digital chaotic encryption method compensates for the limitations of the previous two encryption methods. Based on the sensitivity to initial values, unpredictability, ease of operation and other characteristics. Chaos is perceived as an efficient and secure method for data transmission and encryption at the physical layer [20–21]. This technology utilizes chaos to encrypt data transmission. The encryption process is typically implemented through software or algorithms, without the need for additional hardware equipment, resulting in a relatively low implementation cost [22]. The unpredictable characteristics of chaos make it difficult for illegal users to steal and crack the transmitted data at the physical layer [23–26], making up for the defects of upper-layer encryption. Compared with QKD, its key generation rate is faster, transmission distance is longer, and communication capacity is stronger. Combination of chaotic disturbance in digital signal processing technology can effectively improve the security of optical communication system.
The previous physical layer security schemes based on digital chaotic encryption technology often relied on a fixed key shared between the transmitter and receiver by default. However, once the keys are compromised, it poses a significant challenge to the overall system security [27,28]. Key co-transmission effectively solves the problem by transmitting to the receiving end along with the data through a specific distribution method in each transmission. The existing simultaneous key transmission schemes primarily rely on power division multiplexing (PDM) [29] and training sequence (TS) hiding [30]. However, the scheme based on PDM exhibits excessive redundancy, while the one based on TS hiding lacks sufficient key protection. Therefore, it is imperative to explore key co-transmission schemes that ensure both security and efficiency.
In this paper, we propose a physical layer security scheme for key concealment and distribution based on carrier scrambling. The chaotic sequences generated by three-dimensional (3D) Lorenz map encrypt the information in bit, phase and subcarrier. The key information is loaded into the subcarriers along with the ciphertext for carrier scrambling, thereby achieving secure key distribution. Encrypted key position information is transmitted through the set rules combined with the TS. The scheme is validated through experiments conducted on an intensity modulation and direct detection (IM/DD) system utilizing the 2 km seven-core fiber. Experimental demonstrate that the proposed scheme can achieve secure and flexible key distribution without significantly compromising transmission performance. The scheme's high expansibility endows it with a wide range of potential applications.
2. Principles
The block diagram of key concealment and distribution based on carrier scrambling is shown in Fig. 1. The key-driven 3D chaotic mapping is utilized to generate perturbation vectors for encrypting Orthogonal frequency division multiplexing (OFDM) signals. Firstly, the first dimensional perturbation vector is used for XOR encryption of the original data bit sequence. After serial-parallel(S/P) conversion and constellation mapping, the second dimensional perturbation vector is used to realize the 16 Quadrature amplitude modulation (QAM) constellation scrambling encryption. The encrypted information after already two levels is mapped to the subcarrier, while the key information is mapped to the reserved empty carrier. The third level of encryption is performed using the subcarrier perturbation factor. The third level encryption arranges the key carrier and the information carrier randomly, which further enhances the information security performance and ensures the security of the key.
The position of the key carrier after encryption can be obtained from the subcarrier perturbation factor, and this information will be transmitted in combination with the training sequence (TS) for the receiver to extract the key. During the TS design process, 10 spaces are reserved for loading key position information, making the system being scalable. As each chaotic sequence is loaded onto a subcarrier, the system can expand up to 10 dimensions. After the designed data transformed by IFFT, cyclic prefix (CP) is added and the encrypted time domain multiplexed complex signal is converted to a single channel real signal by parallel to serial conversion (P/S). At the receiving end after the serial-to-parallel conversion, the key location information is first obtained through the training sequence, and after obtaining the correct key, the signal is correspondingly decrypted and demodulated, and the original transmitted data bit stream can be obtained.
2.1 3D encryption principle
In this manuscript, the 3D Lorenz chaotic model is used to encrypt the data from three dimensions: bits, constellation points, and subcarriers. The equations of the 3D Lorenz chaos model are as follows:
The parameter t denotes the time, and Eq. (1) is a system of partial differential equations derived from time t. The system is in a chaotic state when the system parameters are at σ = 10, ρ = 28, and β = 8/3. In this paper, the initial values are set within a specific interval x∈(-20, 20), y∈(-20, 20) and z∈(10, 40), and the key for each dynamic transmission is within this interval and dynamically changed. At this time, the phase diagram of the 3D Lorenz chaotic model is shown in Fig. 2.
Fig. 2. Phase diagram of Lorenz chaotic model (a) Phase diagram of 3D Lorenz chaotic model (b) Phase diagram of xy plane chaotic model (c) Phase diagram of xz plane chaotic model (d) Phase diagram of yz plane chaotic model.
It can be seen that the phase diagram of the 3D Lorenzian chaotic model shows complex chaotic trajectories and bifurcation dynamics. According to the sensitivity of the initial value of the chaotic model, when the initial value of the chaos is slightly changed, it will produce almost completely different complex chaotic trajectories, which ensures that the illegal receiver cannot steal the information without an accurate key. The chaotic sequences x, y, and z generated by the chaotic model need to be further processed into three-dimensional perturbation vectors for bit data, constellation points, and subcarrier frequency encryption.
Firstly, after processing the x sequence according to Eq. (2), the data sequence Q is obtained and used for XOR encryption of the original bit data.
Secondly, constellation mapping is performed after concatenating and transforming the bit scrambled data. The constellation rotation scrambling is realized using chaotic sequence y. The y- sequence is processed as a constellation point phase scrambling factor θ with values {0, π⁄2, π, (3π) ⁄2}, where S is the constellation point before encryption and S’ is the constellation point after encryption, and each constellation point is rotated by one of these four angles. The specific steps are as follows:
Finally, the signal subcarrier frequency is perturbed by random substitution using chaotic sequence z. Assume that the subcarrier group M consists of m subcarriers, and the chaotic sequence z is used to obtain m positive integers which are unequal and not larger than the number of subcarriers, and consists of a random disordered vector g. The original subcarriers M are rearranged according to the order of vector g, and then the encrypted subcarriers M’ are obtained to realize the order perturbation of the subcarriers, in which the carriers containing the key are encrypted at the same time to realize the key hiding. The effect diagram of subcarrier encryption is shown in Fig. 4.The specific rules are as follows:
After the above three steps, the original signal has been encrypted and scrambled in the three dimensions of bit symbol, constellation point and subcarrier frequency.
2.2 Key co-transmission and masking
In order to realize the flexible distribution of the key while improve the security of the system, we design a scheme to transmit the key and data simultaneously. Specifically, the key carrier and the information carrier are jointly encrypted, with the key’s location randomized. To facilitate receiver decryption, the information of the key carrier location is placed in the Key Location (KL) sequence and transmitted in combination with TS, which plays an important role in channel estimation and signal equalization at the receiving end to obtain accurate symbol synchronization. OFDM has a total of m subcarriers, in which three key subcarriers are set to accommodate sequences generated by the three-dimensional chaotic model respectively. The subcarrier containing the encrypted data information has been randomly disturbed according to the three-dimensional perturbation principle, thereby enabling covert cooperative transmission of the key.
Reserve (A, B, C, D, E, F, G, H, I, J, K) sequences in KL, where A represents the number of keys with two digits, and the following few have three digits representing the key position. As shown in Fig. 5. Since the position information of up to 10 key carriers can be transmitted in KL, our scheme can be extended to 10-dimensional chaotic systems for higher security. In a three-dimensional system, there is only corresponding position information at the BCD position, and the last seven digits can be set to 0. After converting it to binary, it becomes 128 bits, with each position repeating two bits and being loaded into KL. This KL scheme has 256 subcarriers and a corresponding TS of 1 * 256 matrix, allowing the 256-bit binary data containing key position information to be perfectly hidden in the TS.
The specific key hiding process is as follows:
In this way, the 256-bit binary key location data is hidden in $T{S_n}$ and the original data cannot be recovered if there is an error in one of the binary keys. At the receiver side, we can extract the key without redundancy according to the following rules:
3. Experimental setup and results
We experimentally validate the proposed scheme on IM/DD system, which has been shown in Fig. 6. At the transmitter, the initial signal is modulated and encrypted to generate the encrypted OFDM signal in the off-line digital signal processing. The modulation format of OFDM signal is the 16QAM and the number of subcarriers is set to 256. 253 subcarriers are allocated for information to be transmitted and 3 subcarriers are used for storing the key. The FFT size, CP length and training sequence length are set to 1024, 256, 256. The analog signal is generated by an arbitrary waveform generator (AWG, Tektronix, AWG 70002A) with a sampling rate of 24 GSa/s, which is amplified by the electrical amplifier (EA). The AWG supports transmission rates up to 25GSa/s. Then, the laser generates an optical carrier with a bandwidth of less than 100 kHz and a center wavelength of 1550 nm for injection into the MZM, and the radio frequency (RF) signal is injected into the MZM for intensity modulation. The transmitted signal is amplified using an EDFA, then passing through a 1:8 power splitter (PS), which splits the signal into seven equal parts and fans it into the corresponding cores of a 7-core fiber. The net rate of the system reaches 131.80 Gb/s. After 2 km of transmission, the 7-core signal is spatially demultiplexed into the single-mode fiber through the fan-out device. At the receiver, a variable optical attenuator (VOA) is used to adjust the received optical power in real time. A photodiode (PD) is used for the conversion of photoelectric signal conversion. Finally, we implement the analog-to-digital conversion (ADC) by a mixed signal oscilloscope (MSO, TekMSO73304DX) with sampling rate of 50 GSa/s and bandwidth up to 33 GHz to receive the waveform, and demodulate the data with an off-line DSP.
Figure 7 displays the BER curves of encrypted OFDM signals in 7-core fiber. We measure the performance of transmission in each fiber core at the BER of 3.8 × 10−3 with limit of the hard verdict threshold forward error correcting code (FEC). The BER curves show that the transmission quality of the seven fiber cores has little difference. When the FEC threshold is reached, the received optical powers of the seven cores are -9.0 dBm, -9.2 dBm, -9.2 dBm, -9.1 dBm, -9.1 dBm, -9.3 dBm and -9.3 dBm respectively. This experiment fully proves that the experimental system has good stability. Accordingly, all of the comparison group experiments were done in core 7.
Fig. 6. The verification of three-dimensional chaotic encryption with key co-transmission scheme in the IM/DD system (DSP: digital signal processing; AWG: arbitrary waveform generator; EA: electrical amplifier; MZM: Mach-Zehnder modulator; EDFA: erbium-doped fiber amplifier; MCF: multi-core fiber; PS: power splitter; VOA: variable optical attenuator; PD: photodiode; MSO: mixed signal oscilloscope)
Figure 8 shows the BER performance comparison of key co-transmission scheme signals, standard 16QAM signals, and illegally received signals. The standard 16QAM signals are the unencrypted 16QAM signals without key co-transmission, whose 256 subcarriers are totally used to transmit the communication information. To standardize the net rate, we have the AWG transmit rate set to 24 × 253/256 = 23.72GSa/s. The experimental results show that the transmission performance of encrypted key co-transmission scheme signals is comparable to unencrypted standard 16QAM signals. When the transmission BER of the two signals reaches the FEC threshold, there is almost no difference in the received optical power. Meanwhile, for the encrypted signals, when the receiver forcefully decrypts the signals without the correct key (what the illegal receiver curve displays), the BER is 0.5. Due to the nonlinearity and sensitivity to the initial value of the chaotic system, the chaotic encrypted signal introduces additional nonlinear distortions and accumulates errors due to noise during the demodulation process. This causes a slight increase in the BER. Nevertheless, it still confirms the security of the encryption scheme proposed in this paper, which is effective in resisting the illegal attacks.
Fig. 8. Comparison of key co-transmission scheme signals, standard 16QAM signals, and illegally received signals BER performance for these three kinds of transmission.
In addition, to verify the overall impact of key accuracy on system performance, we used the wrong x, y, z sequence and key location information for decryption. We choose the extreme case where each sequence is only one bit wrong, and the experimental results are shown in Fig. 9. The figure reflects the robustness of the key encryption effect. It can be seen that any tiny wrong acquisition of sequence information or key location will result in a BER of 0.5, which prevents the correct demodulation of the message content. This proves that our scheme guarantees excellent security while achieving key distribution.
Finally, we compute the key space of our scheme. The figure reflects the sensitivity of the key encryption effect. As shown in Fig. 10, when the parameter $\sigma \; $ and the initial value y0 are changed by 10−14, there is no significant change in the BER value. Once the change becomes 10−13, the BER changes drastically and is close to 0.5. When the parameter $\rho $, $\beta $, and the initial values x0, z0 are changed by 10−15, there is also no significant change of the value of the BER, and once the change becomes 10−14, the BER changes drastically and is close to 0.5. The final key space is calculated as (1013)2 × (1014)4 = 1082. Although this value is not very large, the proposed scheme can be extended to 10-dimensional chaotic systems, which can be flexibly expanded according to different security requirements.
4. Conclusion
In this paper, a physical layer security scheme for key concealment and distribution based on carrier scrambling has been proposed. Three-level encryption of bits, constellations and carriers is performed using sequences generated by 3D Lorenz chaos. By carrying the key along with the subcarrier at a specific position, the integrated transmission of key and communication information is fulfilled. Since the key is mapped into the subcarriers before the carrier scrambling, this encryption process can achieve key concealment. The encrypted key position information is combined with the training sequence for decryption by the legitimate receiver. The safely data transfer has been successfully achieved at a net rate of 131.80 Gb/s using 7-core fiber based on IM/DD system. Experimental result manifest that the transmission BER performance of the encrypted signal is highly consistent compared with the unencrypted signal. The illegally received signals cannot be demodulated by means of violent decryption. In the encryption security performance test, the slight error and numerical change of the chaotic sequence value will lead to the failure of information demodulation and the key space reaches 1082. In addition, due to the preset space in the training sequence, the scheme can support up to 10 dimensional chaotic encryption systems. This scheme has a good expansion space and can realize the flexible adaptation of security performance, which is a more promising security scheme.
Funding
National Key Research and Development Program of China (2021YFB2800904); National Natural Science Foundation of China (U2001601, 62275127, 62205151, 62171227, 62225503, U22B2009); 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; Postgraduate Research & Practice Innovation Program of Jiangsu Province (KYCX23_1353).
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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