With the escalating flow of information and digital communication, information security has become an increasingly important issue. Traditional cryptographic methods are being threatened by advancing progress in computing, while physical encryption methods are favored as a viable and compelling avenue. Metasurfaces, which are known for their extraordinary ability to manipulate optical parameters at the nanoscale, exhibit significant potential for the revolution of optical devices, making them a highly promising candidate for optical encryption applications. Here, a single-sized metasurface with four independent channels is proposed for conducting steganography and multi-key information encryption. More specifically, plaintext is transformed into a ciphertext image, which is encoded into a metasurface, while the decryption key is discretely integrated into another channel within the same metasurface. Two different keys for steganographic image unveiling are also encoded into the metasurface and can be retrieved with different channels and spatial positions. This distributed multi-key encryption approach can enhance security, while strategically distributing images across distinct spatial zones serves as an additional measure to reduce the risk of information leakage. This minimalist designed metasurface, with its advantages of high information density and robust security, holds promise across applications including portable encryption, high-camouflaged image display, and high-density optical storage.
Congling Liang, Tian Huang, Qi Dai, Zile Li, Shaohua Yu.
A Single-Sized Metasurface for Image Steganography and Multi-Key Information Encryption.
Engineering, 2024, 41(10): 64-73 DOI:10.1016/j.eng.2024.04.015
In an era characterized by the constant flow of information and the widespread use of digital communication, ensuring the confidentiality and integrity of sensitive data has become imperative. While traditional digital cryptographic methods are robust, they cannot resist the emerging threats posed by increasing computational power [1]. Therefore, there is an ongoing pursuit of innovative and more secure encryption techniques, which remain a central focus of research and innovation. Among these emerging techniques, optical encryption has emerged as a promising frontier, where the convergence of optical sciences and information security holds significant potential [2], [3], [4], [5]. Optical encryption harnesses the intrinsic properties of light waves, such as wavelength, amplitude, polarization, and phase, to encode and safeguard information. This newly developing field not only provides a fresh perspective on encryption but also presents a range of advantages, including ultra-fast processing speeds, high information density, robustness against conventional decryption methods, and the promise of enhanced security at the physical layer.
Metasurfaces, which are known for their exceptional capability to manipulate light wave properties, including amplitude [6], [7], [8], [9], [10], [11], [12], phase [13], [14], [15], [16], [17], polarization [18], [19], [20], [21], [22], [23], [24], [25], and frequency [26], [27], [28], [29], have revolutionized the field of optics, being positioned as robust leaders for next-generation optical encryption technology. Metasurface-based encryption has attracted considerable attention among researchers due to its huge advantages in terms of flexibility and security. In recent years, numerous studies have focused on harnessing the potential of metasurfaces for information encryption, yielding a gamut of noteworthy technological advancements.
Traditional visual encryption algorithms were the first to enter the domain of metasurface encryption [30], [31], [32]. The requirement to superimpose multiple images in these algorithms adds an extra layer of complexity and introduces redundant information storage, decreasing the effective information storage density. On the other hand, the integration of metasurfaces with multiple information channels has facilitated the covert embedding of encrypted data within one or more of these channels [33], [34], [35], [36], [37], [38], [39], [40], [41], [42]. However, a primary concern with these methods lies in the storage of information in plaintext, which poses a substantial security risk due to the challenge of safeguarding stolen messages.
Another avenue explored in metasurface encryption entails the utilization of computational imaging algorithms, such as computational ghost imaging and single pixel imaging [43], [44], [45]. In this context, metasurfaces often serve as phase modulators or masks, primarily replacing traditional optical components in computational imaging setups. Therefore, this approach may not fully exploit the powerful control capabilities of metasurfaces across various light parameters.
An additional popular encryption method within metasurface technology centers on the distribution of the message across multiple metasurfaces [46], [47]. The retrieval of information hinges on the precise combination of the specific metasurfaces, which effectively serves as the decryption key. Inadequate or erroneous utilization of the metasurfaces can lead to an inability to decipher the encrypted images. Moreover, in scenarios employing intricate design patterns, the potential for crosstalk between images exists, probably diminishing the efficiency of the encryption process.
In this work, we propose an innovative single-sized multi-channel metasurface to establish a multi-key encryption system within the spatial domain. Here, we use the term “single-sized” to refer to the fact that the metasurface is composed of identically sized nanobricks. As shown in Fig. 1, the metasurface has four information channels, each of which can encode an independent image. The plaintext image is converted into an ciphertext image through encryption transformation in advance, and the ciphertext image is then embedded within the metasurface. Simultaneously, the decryption key, which is vital for decoding the ciphertext, is covertly concealed within another channel of the same metasurface. To enable seamless information transfer, the keys to unveil the steganographic image—effectively serving as the decryption key—are also encoded within this metasurface.
The metasurface design incorporates minimalism, as it consists of nanobricks with identical dimensions but varied orientation angles. Each nanobrick within this metasurface functions as a nano-half-waveplate (NHWP), granting precise control over both the polarization and phase of incident light. By deflecting the polarization direction of linearly polarized (LP) light through the NHWP, special patterns can be achieved on the metasurface plane with the help of an bulky-optic analyzer. Phase manipulation empowers coherent light diffraction intensity distribution, thereby creating additional information channels. By strategically arranging the orientation angles of the nanobrick arrays, accurate intensity distributions can be generated across different polarization states and within various diffraction domains, resulting in four independent information channels. The design strategy maximizes the utilization of diffraction distance as a parameter at the output end, where images are distributed across a considerable spatial region extending from the metasurface plane to the Fresnel and Fraunhofer diffraction zones. By leveraging the variations in observation results caused by changes in diffraction distance across a wide range, we achieve high-fidelity multi-image multiplexing displays and facilitate multi-key encryption applications without necessitating alterations to the shape, size, or position of the nanostructures, or requiring the construction of supercells or stacked configurations.
The ciphertext image is encoded into one of the polarization-controlled nanoprinting channels of the metasurface, while the decryption key is integrated into a specific holographic channel of the same metasurface. The steganography keys are situated within another pair of information channels. As a result, the plaintext undergoes a dual transformation, first being converted into ciphertext and subsequently being concealed within the metasurface along with the decryption keys, in accordance with the established protocol. This approach not only enhances security through multi-key encryption techniques but also simplifies the concealment and transmission of keys through a unified medium. The images encoded in each information channel are spatially distributed at specified locations relative to the metasurface, and the designed spatial separation serves to further enhance the security and reduce the risk of information leakage. A comprehensive solution is thus proposed for information protection and secure communication at the physical level. Thanks to its minimalist design and robust security features, the proposed methodology holds immense promise across various applications, including information encryption, data storage, image display, and numerous other domains.
2. Materials and methods
2.1. Numerical simulations
The design mechanism of the metasurface is depicted in Fig. 2. The proposed metasurface is composed of a top layer of polycrystalline silicon (p-Si) nanobrick arrays sitting on a transparent fused quartz substrate, as depicted in Fig. 2(a). We adopted the commercial software CST Studio Suite (Dassault Systèmes, France) to optimize the geometric parameters of the nanobrick structure. The working wavelength was designed to be 633 nm. At this wavelength, the real and imaginary parts of the refractive index of p-Si utilized in the simulation were 4.219 and 0.085, respectively. In the electromagnetic simulation of the nanobrick, the boundaries in the x- and y-axis directions were set to be periodic, while that of the z-axis was set to be open. For the light source, we employed a plane wave with a circular polarization state. Throughout the design process, we effectively employed parametric sweeps to calculate the response characteristics of diverse nanostructures with varying geometric dimensions. These sweeps entailed incremental 5 nm adjustments to the length, width, and height parameters, while maintaining a constant cell period of 300 nm × 300 nm. Subsequently, we designed a comprehensive library of these nanostructures. The primary goal was to identify nanostructures that could effectively function as NHWPs. More specifically, we sought structures that could facilitate efficient cross-polarization conversion while simultaneously minimizing co-polarization efficiency. More details are provided in Appendix A Section S1. This optimization process yielded nanobricks with the following geometric dimensions: a height (H) of 380 nm, length (L) of 120 nm, width (W) of 90 nm, and cell period (C) of 300 nm, operating at a wavelength of 633 nm.
2.2. Sample fabrication
The fabrication of the metasurface samples involved the utilization of polysilicon on a fused quartz substrate through a standard electron beam lithography (EBL) process. The fabrication sequence was initiated by uniformly coating a polymethyl methacrylate (PMMA) photoresist with a concentration ratio of 1:1 onto an unblemished substrate consisting of a fused quartz substrate and a polysilicon structural layer. To ensure an even coating, a spin coater operating at 4000 r·min−1 was employed for 1 min. Subsequently, the coated sample was placed on a hotplate and subjected to a 150 °C bake for 3 min. After cooling, a conductive adhesive was evenly applied to the sample via the same procedure, and the sample was then situated on a hotplate at 90 °C for 2 min. Then, the EBL system (eLINE Plus, Raith, Germany) was engaged for the exposure process. Following exposure, the photoresist was developed accordingly. Next, a thermal evaporation system (JSD-400, Anhui Jiashuo Vacuum Technology Co., Ltd., China) was utilized to deposit a chromium (Cr) layer with a thickness of 30 nm onto the sample, serving as a mask for the subsequent pattern-transfer process. Once the deposition was completed, a lift-off process was executed to remove any excess photoresist. Finally, the sample underwent etching by means of an inductively coupled plasma etcher (PlasmaPro 100Cobra 300, Oxford Instruments, UK). Upon the completion of the etching procedure, the sample was immersed in a Cr etchant solution for approximately 30 s. Consequently, the final metasurface sample was attained. Partial scanning electron microscope (SEM) images of the sample are provided in Appendix A Section S2.
3. Theory
3.1. Working principle of the multi-channel metasurface
As described above, our approach facilitates the integration of four independent images into a single-sized metasurface. More specifically, the metasurface is comprised of four distinct information channels: two polarization-controlled nanoprinting channels and two phase-assisted holography channels.
First, the intensity modulation in the polarization-controlled nanoprinting channels is considered. The flexibility to adjust each nanobrick’s orientation angle enables the precise control of the outgoing light polarization at a point-to-point level. Combined with an analyzer, the formation of specific images obeys Malus’s law. Denoting the orientation angle of the NHWP as θ and considering an incident LP light with a polarization direction angle of −π/4 and an intensity of I0, the output light passes through the analyzer with a transmission axis direction angle of π/4. The intensity of the outgoing light (I) can be calculated as follows:
In another scenario, when the polarization direction of the incident light and the transmission axis direction of the analyzer are adjusted to be −π/8 and 3π/8, respectively, the intensity of the outgoing light obeys the following equation:
According to Eq. (1), continuous intensity modulation can be achieved, allowing the encoding of a grayscale image. This information channel refers to channel 1 in the following, as illustrated in Fig. 2(b). It is also worth noting that four specific orientation angles exist, leading to equal output intensity except for two angles corresponding to the intensity values of 0 and 1, as shown in Fig. 2(f). This phenomenon directly arises from orientation degeneracy, as governed by Malus’s law [14], [48], [49], [50], [51]. Considering Eq. (2), these four orientation angles correspond to two distinct intensities, with their average being 0.5, as shown in Fig. 2(g). Therefore, even when the pixel value in channel 1 is constant, both bright (intensity > 0.5) and dark (intensity < 0.5) states can be attained in Eq. (2) by choosing from the available angles. Since each nanobrick can induce either bright or dark intensity modulation, a binary image can be visualized at the input and output polarization combination of −π/8 and 3π/8. This information channel refers to channel 2, as illustrated in Fig. 2(c).
Two specific examples are selected to further clarify the intensity modulation degeneracy. Considering a pixel in channel 1 with an intensity of 0.300, a set of orientation angles corresponding to this intensity is obtained: 0.497, 1.075, 2.066, and 2.646 radians (rad; purple triangle points shown in Fig. 2(f)). Channel 2 exhibits intensities of 0.958 (bright) for the angles of 0.497 and 2.066 rads, and 0.042 (dark) for the angles of 1.075 and 2.646 rads. In another case, if the intensity in channel 1 is 0.854, the corresponding orientation angles are 0.196, 1.374, 1.767, and 2.945 rads (green dots in Fig. 2(f)). Channel 2 offers the angle options of 0.196 and 1.767 rads for the bright state and 1.374 and 2.945 rads for the dark state. This degeneracy introduces an additional degree of freedom for phase modulation, potentially enabling new information channels.
Next, the phase manipulation mechanism is taken into consideration. The geometric phase, also referred to as the Pancharatnam–Berry phase [52], [53], can be mathematically expressed as twice the orientation angle of the nanobrick:where + and − represent the incidence of left-handed circularly polarized (LCP) and right-handed circularly polarized (RCP) light, respectively; and φ is the geometric phase. Within the range of orientation angles, the geometric phase exhibits a monotonically increasing or decreasing behavior. Consequently, various orientation angles, corresponding to the same intensity in the polarization-controlled nanoprinting channel, can result in different phase modulations. That is, for each pixel location with a specific intensity in channel 1, there are several possible phase values, as shown in Fig. 2(h).
Employing a multi-objective optimization method [54], [55], multiple target holographic images within different diffraction regions are considered. In the Fraunhofer diffraction zone, the complex amplitude of the diffracted light wave (E) can be expressed as the Fourier transform of the complex amplitude of the metasurface:where θM represents the orientation angle distribution of the metasurface, z stands for the diffraction distance, k is the wave number, and λ denotes the wavelength. i is the imaginary unit. x1 and y1 denote the coordinates on the metasurface plane. x and y represent the coordinates on the observation plane.
According to Eq. (4), the holographic image remains unchanged in the Fraunhofer diffraction zone but scales with the observation distance. Due to the wavelength independence of the geometric phase, the holographic image is observable across a broad wavelength spectrum, despite changes in holographic efficiency. Considering the influence of polarization, an arbitrary polarization state can be represented as a linear combination of LCP and RCP light. The transition of helicity results in the conjugation of the metasurface’s complex amplitude, which is represented by a change in sign in Eq. (4). Due to the inherent symmetry introduced by Fourier transformation upon conjugation, a centrally symmetrical pattern emerges when the helicity of the incident light is reversed. Therefore, for an arbitrary polarization state, the desired image remains, although there may be additional images at centrally symmetrical positions. As a result, this information channel proves to be a highly efficient means for storing data without the risk of it being stolen. This information channel refers to channel 3, as illustrated in Fig. 2(d).
In the Fresnel diffraction region, the complex amplitude of the diffraction light wave can be expressed as follows:
It is evident that alterations in the viewing distance and incident light wavelength lead to variations in the diffraction pattern. Furthermore, reversing the helicity of the incident circularly polarized (CP) light results in an inversion of the phase, rendering the target image unobservable. Thus, the Fresnel holographic image can be strategically engineered as a steganographic channel, allowing the steganographic image to become distinguishable under specific conditions. This information channel refers to channel 4, as illustrated in Fig. 2(e).
3.2. Design of metasurface steganography and multi-key encryption
Upon the establishment of multiple information channels, the design of the information steganography and encryption becomes crucial. In the realm of steganography, channel 1 serves as an excellent choice for encoding the cover image, while channel 4 is well-suited for concealing the steganographic image. The remaining information channels can be effectively utilized to store observation conditions for concealed information, thereby establishing a robust spatial-domain information steganography technique.
Nevertheless, there will be a significant risk of leakage if the information is stored in its original form, which is susceptible to acquisition. To further enhance information security, a multi-key encryption strategy is introduced. First, the plaintext image is transformed through a transformation matrix, resulting in a ciphertext image with ambiguous meaning. This ciphertext image is then encoded into channel 1. The transformation matrix, which functions as both the encryption key and the decryption key, is concealed within steganography channel 4, while the remaining channels are used to encode the steganography keys. In this way, the plaintext undergoes a dual transformation, first being converted into ciphertext and then being concealed within the metasurface along with the decryption keys, in accordance with the established protocol. Thus, through the preprocessing of the encoded information within each channel, multi-key encryption is implemented, significantly enhancing the security of the information.
The design process of the metasurface is illustrated in Fig. 3. First, images for each channel are created. Subsequently, the potential orientation angles for each pixel can be computed according to Eqs. (1), (2). A simulated annealing algorithm (SAA) for multi-objective optimization is then employed to optimize the distribution of these orientation angles. More details about the optimization algorithm are provided in Appendix A Section S3. Finally, the nanobricks, designed as NHWPs, are arranged to compose the metasurface according to the ultimately optimized orientation angles.
4. Results
4.1. Demonstration of multi-channel metasurface steganography
To demonstrate multi-channel metasurface steganography, two distinct samples—namely, sample 1 and sample 2—were designed. The metasurface comprises 1000 × 1000 pixels and has the dimensions 300 μm × 300 μm. Flower images were chosen as the cover image and were encoded into channel 1 for both samples. In channel 4, the steganographic text was concealed, while channel 2 stored essential information regarding the required wavelength and polarization state for observing the steganographic text. In addition, details regarding the designed diffraction distance were encoded in channel 3. For sample 1, the steganographic text was “WHU,” the observation wavelength was 633 nm, the observation distance was 800 μm, and the incident light polarization state was LCP. For sample 2, the steganographic text was “META,” the observation wavelength was 633 nm, the observation distance was 600 μm, and the incident light polarization state was RCP. All target images for both samples are shown in the first and fourth rows of Fig. 4, with each of the four columns from left to right representing the images encoded in channels 1 to 4. The theoretically calculated light intensity distributions for each channel of the two samples are showcased in the second and fifth rows of Fig. 4, respectively. The simulation results are consistent with the design images, confirming that the single-sized metasurface is capable of presenting different information under diverse observation conditions, effectively demonstrating the concept of multiplex channels.
Next, experiments were designed and conducted to verify the functionality of the metasurfaces. To observe images in the polarization-controlled nanoprinting channels, we employed an optical microscope (BA310Met, Motic China Group Co., Ltd., China) equipped with a complementary metal-oxide semiconductor (CMOS) camera (STC-MCS312POE, Changsha Lubon Photoelectric Technology Co., Ltd., China). A detailed schematic diagram of the light path is provided in Appendix A Section S4. In the experimental setup, the broadband light source of the microscope was utilized for observations without prior knowledge of specific wavelengths. Leveraging the broadband characteristic of intensity modulation exhibited by the metasurface in the orthogonal-polarization light path (also see Appendix A Section S5), the designed image was effectively observed on the metasurface plane when the transmission axes of the polarizer and analyzer were adjusted to the designed angles.
The experimentally captured images from the polarization-controlled nanoprinting channels are presented in Figs. 4(i), (j), (u), and (v). More details on the interaction between channels 1 and 2 are provided in Appendix A Section S6. It is evident from Figs. 4(j) and (v) that the observation wavelength for the steganographic information in both samples is 633 nm, with sample 1 being LCP and sample 2 being RCP. Following the wavelength information provided in channel 2, we employed a super-continuum laser source (SC-pro, Wuhan Yangtze Soton Laser Co., Ltd., China) to observe the images encoded in holographic channel 3. The resulting holographic images of sample 1 and sample 2 are depicted in Figs. 4(k) and (w). Consequently, we determined that the observing distances for sample 1 and sample 2 were 800 and 600 μm, respectively. Thus, we acquired essential information regarding polarization, wavelength, and the requisite observation distance for the steganographic image. More details on the Fresnel holographic image are provided in Appendix A Section S7. Subsequently, we employed a microscope light path to obtain the information encoded in channel 4, and steganographic information was obtained for the two samples, with sample 1 revealing “WHU” and sample 2 disclosing “META.” The illustrations of the holographic light paths are also provided in Section S4.
4.2. Demonstration of metasurface multi-key encryption
To further enhance information security, a multi-key encryption strategy is introduced and demonstrated. A dedicated metasurface, denoted as sample 3, was designed to showcase the multi-key encryption approach. The geometric dimensions of the nanobricks remain consistent with previous specifications, and the pixel count is maintained at 1000 × 1000.
In contrast to previous steganography methods, our multi-key encryption approach involves the initial transformation of the plaintext image into a ciphertext image through encryption, accompanied by the concealment of the decryption key. This ciphertext image is subsequently encoded into one of the information channels of the metasurface, with the decryption key also being stored within the same metasurface. To demonstrate this transformation, we utilize a 20 × 20 reversible transformation matrix, denoted as “P,” where each element is randomly assigned a value of either 0 or 1. The specific transformation matrix “P” utilized in this article is depicted in Fig. 5(a), and the original plaintext image is shown in Fig. 5(b). During the encryption process, the transformation matrix “P” is expanded to dimensions of 1000 × 1000 through the Kronecker product with a 50 × 50 all-one matrix. Subsequently, matrix multiplication is performed between the transformation matrix “P” and the plaintext image, resulting in a ciphertext image resembling a random pattern, as displayed in Fig. 5(c). The ciphertext image is then encoded into channel 1 of the metasurface, while the transformation matrix “P” is encoded into channel 4 as concealed information. Three white anchor points, outside of the matrix’s pixels, are designed at the upper left, upper right, and lower left corners of the image to identify the image’s orientation; these can correct any matrix rotation. The steganographic image, with these anchor points incorporated, is presented in Fig. 5(d). The steganographic image is designed for observation at a wavelength of 633 nm, an observation distance of 500 μm, and RCP light.
The corresponding encoded images in the four channels are presented in Figs. 5(e)-(h), and the simulation results for the channels of sample 3 are presented in Figs. 5(i)-(l), while the experimental results for sample 3 are depicted in Figs. 5(m)-(p) More details about the Fresnel holographic images at different distances are provided in Appendix A Section S8. The experimental optical setup and equipment used were the same as in the previous experiments.
The ciphertext image is first extracted, as shown in Fig. 5(m). Then, the image from Fig. 5(p) is used to generate the decryption key with sequential processing steps, including grayscale conversion, binarization, area segmentation, summation, and discrimination. More detail is provided in Appendix A Section S9. This series of steps ultimately yields the transformation matrix “P,” as shown in Fig. 5(r). After obtaining the transformation matrix “P,” the inverse of this matrix, “P-1,” is computed and expanded to a larger matrix of 1000 × 1000, as shown in Fig. 5(s). By multiplying the matrix “P-1” and the ciphertext image, the plaintext information is decrypted to “WHU,” as shown in Fig. 5(t). More details about the correlation of images across different channels are provided in Appendix A Section S10.
5. Discussion
The proposed multi-channel metasurface, which is characterized by its single-sized nanostructure design, provides a new methodology for optical information encoding and encryption. This approach offers several noteworthy advantages, foremost of which is the minimalist configuration of the metasurface. In our study, we exploit the potential of polarization modulation and phase modulation. The strategic utilization of these well-established principles enables the creation of multiple information channels without the necessity for complex design alterations or additional processing steps. The metasurface is composed of single-sized unit cells and boasts a compact structure, relatively robust processing, and highly scalable functionality.
The integration of multi-key encryption into a single metasurface is another significant advantage of our research, as leveraging the capability for multi-key encryption greatly enhances the information security. The process starts with the transformation of plaintext data into ciphertext. Next, the ciphertext is encoded into one of the metasurface’s information channels, while the decryption key is also concealed within the same metasurface. This enhances the efficiency of information transmission, ensures key and ciphertext integration, and streamlines the encryption and decryption procedures. Moreover, this method operates at a physical level, minimizing the risk of information leakage. Compared with traditional data-transmission methods, which rely on separate channels or networks for the transmission of ciphertext and decryption keys, our approach combines these elements within a single metasurface, simplifying the process and reducing the potential attacks.
Furthermore, the images encoded in each information channel are spatially distributed at specific locations relative to the metasurface. More specifically, the image is distributed over a considerable spatial region from the metasurface plane to the Fresnel and Fraunhofer diffraction zone. The designed spatial separation serves to mitigate crosstalk between distinct channels, enhance security, and minimize the risk of information leakage. By incorporating principles that introduce new degrees of freedom at both the input and device ends, such as altering the polarization state [19], [23], [25] or topological charge [7], [36] of the light wave, or utilizing stacked metasurfaces [11] or supercells [41], it is possible to achieve additional information channels and further enhance the design flexibility.
6. Conclusions
In summary, we proposed a multi-channel metasurface that presents an efficient solution to the challenges of optical information encoding and security. Its minimalist design harnesses the power of polarization and phase modulation, offering an elegant and efficient means of data multiplexing. In addition, the integration of multi-key encryption and steganography into the metasurface’s capabilities represents a significant advancement in data security. This approach mitigates contemporary concerns surrounding data protection by providing a robust defense against unauthorized access and information leakage. The metasurface’s potential applications include secure data encryption, storage, transmission, and display, making the proposed metasurface a significant prospect for application in various fields.
Acknowledgments
This work was supported by the National Natural Science Foundation of China (12204359 and 12174292), the China Postdoctoral Science Foundation (2022TQ0243 and 2022M722448), the Natural Science Foundation of Hubei Province (2022CFB641), and the Natural Science Foundation of Jiangsu Province (BK20231210).
Compliance with ethics guidelines
Congling Liang, Tian Huang, Qi Dai, Zile Li, and Shaohua Yu declare that they have no conflict of interest or financial conflicts to disclose.
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