A Quantum-Inspired Approach for audio hiding in Images via Frequency Domain representation of image channel

A Quantum-Inspired Approach for audio hiding in Images via Frequency Domain representation of image channel | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Article A Quantum-Inspired Approach for audio hiding in Images via Frequency Domain representation of image channel Manar Hafez, Tasneem Hatem, Alia Youssif This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8495483/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract Steganography, throughout history, is the science of concealing secret information. This art ambuscade in hiding a message into a cover data. This data can be seen by unauthorized observers, and they cannot recognize that there is something strange. With no doubt, the data could be image, audio, or video. There is a shortage of research in the arena of quantum steganography, especially, audio in image steganography. Reading the upcoming era of quantum computing, doors are open for innovation. This paper doesn’t apply quantum libraries directly, but it simulates quantum concepts such as superposition, using Hadamard gate, and entanglement, using control phase gate. This is implemented using classical methods. That is, this paper introduces “quantum-inspired” approach for audio in image steganography. As secret information is subject to sever changes while embedding, like any steganography project, it is important to preserve the robustness of the cover image, and ensure high imperceptibility. This is achieved in this paper. This paper has chosen 60 high resolution images from Div2K dataset, and tested the proposed approach on them. Each image has its own evaluation metrics. Thirty four of them have PSNR greater than 40%, MSE near zero, and SSIM and VIF near one. One of the promising results from the thirty four images is PSNR, MSE, VIF, and SSIM are 61.52 dB, 0.0458, 0.997, and 0.9995, respectively for a specified image. Those results are impressive. Despite the successfulness of this “quantum-inspired” approach, it has constraints regarding the image. Physical sciences/Engineering Physical sciences/Mathematics and computing Physical sciences/Optics and photonics Physical sciences/Physics Entanglement Superposition Quantum Steganography Control phase gate Hadamard gate multi-channel quantum image representation Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 Figure 9 Figure 10 Figure 11 1. INTRODUCTION Steganography is not a newly introduced science to the humanity. It has fascinating records since ancient times, and has survived through our digital era. During ancient times, specifically 5th century BC, Greeks used to shave one of their slaves’ heads, then tattoos the secret message. After that they send the slaves to the 2nd party after their hair grows. In the early modern period, Johannes Trithemius in the 15th century, has explored methods of concealing secret messages using a cipher within a religious text. [1] Now, in the digital era tremendous techniques has been introduced. And efficiently used, by prestigious entities and Partys. This involves hiding messages within digital files like audio, images, and other digital file formats, with high evaluation metrices. For audio it is essential to generate the spectrograph of it to be embedded [2] The emergence of quantum computing has foreseen new horizons for steganography, that revolutionize processing power, and introduce an intriguing challenge, but opportunity for data security. This paper adapts the multi- channel quantum image representation using classical approach [3]. This representation is based upon applying Hadamard gate and controlled phase gate. Those gates give the opportunity to mimic superposition and entanglement. And in the quantum realm, the fundamental principles of superposition and entanglement allow novel ways to hide and extract data. The Hadamard gate puts the image pixel of the blue channel into superposition state, through applying fast Fourier transform (FFT). We can determine its value. Adding to that, the controlled-phase gate helps in embedding the pixels and putting it into entanglement. It takes two qubits. It takes the frequency transformed qubit of the blue-channel and phase map derived from resized audio spectrogram. After that, it applies phase shift to the frequency components of the image blue channel based on the values of the spectrogram. As of this, the amount of phase shift applied to image is controlled by the spectrogram (Audio). And that is how this paper has implemented the embedding of audio into image using quantum image inspired approach. The contribution of this paper resides in the following: Applying the multi-channel quantum image representation MCQI through Hadamard gate and control phase shift gate using classical programming methods. The embedding process of the audio is applied through a phase shift to the frequency component of the blue channel in the cover image by a value based on the corresponding audio spectrogram data (S_dB_resized). The evaluation matrixes used are PSNR, MSE, VIF, SIMM. The remainder of this article is structured as follows. Section 2 discusses the related work and classification of steganography. Then it discusses the research found in audio and image steganography techniques. After that it discuses quantum steganography. Section 3 provides a detailed explanation of the presented proposed quantum approach. Section 4 showcases the experimental and numerical outcomes of the proposed approach. In conclusion, Section 5 summarizes the main findings of this paper. 2. Background Audio in image steganography, is hiding secret information, that is audio message, inside a digital, cover image. [ 2 ] Digital image are digital files that can be processed in computers and can be divided into two categories, which are bitmap images and vector images. First, the bitmap images. Image of size MxN is composed of finite element of MxN columns each has definite position called pixels, and amplitude representing the color of this point/pixel. Second, is the vector images. Those kinds of images are not visible as they are mathematical formulas to draw lines and curves. For audios, they are sound waves, or signals. In audio steganography, audio is converted into spectrograph, a visual sound representation of the audio [ 2 ]. After loading the image, the audio enters some preprocessing steps. Using Librosa library. Thanks to the wide range of functions this library provides, loading and manipulating audio files like WAV and mp3. It can trim, resample and change the audio volume. Adding to that, for sure feature extraction like spectrograph. In the field of audio in image steganography, audio spectrograph is the embedding factor in the digital image. This Paper uses classical NumPy arrays to represent pixels and spectrograph, then performs mathematical operations that are congruent to quantum gates. The multi-channel quantum image representation for high resolution-colored images (MCQI) is applied using Hadamard gate, and controlled rotation/phase gate with complexity O(N) [ 3 ]. There are many research held in the field of audio steganography. There are two main techniques. Many methodologies are held in frequency-domain techniques, while others in spatial-domain techniques. For frequency domain techniques, analysis of image is interpreted through sin and cos waves, rather than over time or space. Through Fourier transform and other transform methods image can be transformed from the spatial, or time domain into frequency domain. This is to identify and manipulate periodic patterns, filter noise, or enhance certain features. On the contrary spatial domain techniques operate on image pixels to modify it. After image transformation, some of the researches are encrypting the secret message before it is embedded into the cover image. This is to make sure that the secret message is kept save and sound. This way requires encrypting keys, public and private keys [ 4 ]. On the other hand, some research required the second party to extract the embedded message, after it travels to the second party. Both ways depend on the fundamental idea of steganography, which is concealing secret message into a digital file. This is whether the secret information is encrypted, or not. The following paragraphs will give a brief note about steganography and its background. There are two types of steganography. One is the spatial domain that deals with pixels, while embedding the secret information. Algorithm like LSB follows this approach. For illustration, image pixels in RGB are interpreted into binary of 32-bit color. 8-bit for each channel (plane) [ 5 ]. The other domain is the frequency domain. This involves converting the original image from its spatial domain to frequency domain using discrete wavelet transform (DWT), discrete Fourier transforms (DFT), and discrete cosine transform (DCT). The following steps after transforming the image into the frequency domain, is the embedding step. The hidden message is embedded into the coefficient of its transform domain. The power of this approach relies on the difficulty of detection, as the embedding is in the frequency not in the visual domain. Accordingly, this approach promises high robustness. In some cases, there might be trade-off between the imperceptibility and robustness, comparing to spatial domain approaches. For the complexity, the frequency domain may have higher complexity than the spatial one [ 6 ]. Moreover, audio steganography is the art of concealing a secret message into cover audio file. The goal of audio steganography is to hear the soundtrack without recognizing any noise signals. Following the classification of steganography techniques, the embedding process can be in spatial, or frequency domains. What must be achieved in the steganography, whatever it was, are three impactful goals. First, high imperceptibility. That is the cover medium can travel safely in a channel without being recognized by a third party. Second, high capacity. That is the ability to embed as much of a secret message as we can. Third, is high robustness. That is related to the changes made to the cover medium after embedding, and how cover medium is still as if no changes made to it i.e. robust. Until this steganography is in the classical domain. Quantum image steganography has a goal to improve tasks achieved through classical steganography based on quantum-based techniques. The first step is to represent and store the image into quantum computers. Here comes the trick. Quantum image representations are the doors for this step. example such as multi-channel quantum image representation of quantum images (MCQI). Each representation is based on gates that aim to apply the means of quantum mechanics; researchers should put into consideration quantum mechanics principals. Those are superposition, and entanglement. Superposition is the ability of qubit to be presented as |0 > and |1 > at the same time of equal probability. This is clarified by the following equation:[ 7 ][ 8 ] H |0> =(1/sqt2) * (|0> + |1>) and H |1 > = 1/sqt2) * (|0> - |1>) Equation 1 while entanglement is the strong dependability of the target qubit upon the value of the control qubit. Target qubit is the qubit that is affected by a control qubit through quantum gate [ 5 ][ 6 ][ 7 ]. How can the qubit be represented? The qubit is represented on the bloch sphere as shown in fig [ 1 ]. First, North pole: Represents the |0⟩ state Second, South pole: Represents the |1⟩ state. Third Surface: Represents all possible pure states of the qubit. Fourth, Interior: Represents mixed states.[ 9 ] 3. Related Work The following sections discusses the work done in the arena of quantum image steganography. 3.1. Quantum Image Steganography It is essential to choose a suitable quantum image representation for images. Some papers depend on mimicking classical concepts, and depends on how they work. The most famous steganography techniques is Least significant bit (LSB). As a logic research point and mimicking least significant bit approach, scientists are inspired and came up with least significant qubit (LSBq) approach. Where the data hiding is done through replacing least qubit in an image by the qubit of the concealing data. This method shows enhancement and further research opportunities by applying additional protocols and algorithms. For example, in 2018, Sahin et al. [ 10 ] recorded high security and efficiency by implementing LSBq approach. The steganography’s security has been achieved by placing the embedded qubits into the corresponding channel by a specific modulo value. Not only that, through applying LSBq Sahin was able to reduce the complexity of the proposed algorithm. Sahin used quantum multi-wavelength images (QRMW) for steganography implementation. They added different wavelength for each modulo value. they implemented quantum multi-wavelength image representation (QRMW). This is the secret behind their high capacity results. This allowed them to hide higher scales of the embedded message into the cover image through varying the wavelength Another research based on LSBq is QISLSQb: A Quantum Image Steganography Scheme done by İhsan Yilmaz et at [ 11 ]. In this approach the embedding is done through LSBq, and the secret information is the quantum secret image scrambled utilizing Arnold cat map. Many research papers in the arena encrypts the data before embedding it, while others uses chaotic maps before embedding like this one. On the other hand, Tudorache eh al [ 12 ] focused on implementing a quantum steganography scheme using LSBq to hide secret info in grayscale image in a cover image’s qubit as well as the qubit’s position, and put it in novel enhanced quantum image representation (NEQR). Their results demonstrate an impressive indication for performance speed in comparison to found alternatives. On the other hand, Sahin et al. used LSBq approach. However, another approach that targeted higher embedding efficiency is the used of the controlled alternate quantum walks protocol (CAQWs). This procedure is inspired by random walks designed by Wenda et al [ 13 ]. This approach has the ability to outperform classical approaches in terms of exponential algorithmic speedup through implementing quantum state characteristics. To sum up, to work in the quantum steganography work, it is essential to determine which quantum image representation needed. Then try to modify its parameters to attain the three goals of any steganography project. High capacity, high robustness, and high imperceptibility 3.2 Audio steganography techniques There are many research done in the audio steganography arena those research can be divided into two. One discusses the classified methods of audio steganography, while the other focuses on certain type of techniques. For example, there are papers that depends upon the chaotic systems and message encryption before embedding [ 14 ]. It uses chaos Henon, Baker, and Arnold maps for image encryption with audio steganography to allow robust and secure audio steganography. There are three points that should be into consideration. The inaudibility of distortion. This is the measurement of the audio transparency. After embedding the message, the third party should hear the audio well. The robustness, and it is how the audio can withstand with the attacks and distortions. The capacity, and this measurement involves the amount of data concealed within the audio file. After encrypting the image using the chaotic system, Inverse Short-time Fourier transform is used for embedding it into the high frequencies of the audio [ 15 ]. Hence, the image quality can be preserved, and the robustness is improved. This makes the provided technique resistant to many types of attack while traveling through a channel. On the other hand, there is a technique in audio steganography called echo hiding. This technique depends on the fact that the human ear cannot detect the short-term echoes exists in the sound file. From this, the secret audio is converted into signal echoes and those echoes are embedded into the cover audio file. This is achieved through dividing the secret audio into echo file, then transformed into frames of equal size. This defines the number of bits that can be embedded [ 16 ]. Adding to that, there is a very famous algorithm called phase shifting algorithm. This algorithm depends on embedding the secret information into the audio signal by taking advantage of the human auditory system (HAS) response to phase information. Bend et al worked on providing a phase coding algorithm based on HAS. In their approach, they depend on slicing the cover audio sequence into a set of equal-length segments. For each sliced segment, the DFT is applied. Then the manipulation with the phase in each segment will be according to the value of the secret message. This is better than amplitude embedding, as the embedding in the amplitude may cause a noticeable change in the cover audio. This summarizes some of the work done in the arena of audio steganography. To sum up, to embed an audio it is essential to represent it into spectrogram (this is what would be embedded), determine it shape, sample rate, and data type. From the previous work some papers depend on the least significant qubit (LSBq) and Quantum Fourier Transform Wang et al. [ 17 ] The Proposed method had better visual quality. The research gap Quantum image visual quality was not 100% good. Another ones depends on Positive operator valued measure and projective measurement operator used for data embedding and extraction WeiZH et al. [ 18 ] the results were high secrecy, security and capacity. The research gap of a secret message was extracted with the probability of 2/3. That was the imperfection of this research. Adding to that Qu et al. [ 19 ] worked on QUALPI, Quantum water mark protocol and Least Significant Qubit. The results were High performance on transparency, robustness, and data capacity. The research gap is that it does not deal with complex attacks. Another research made by Liu et al. [ 20 ] depends on Quantum key agreement, Bell states, and Paulis operation. The results were better performance, in efficiency, privacy and correctness. The research gap is Cloud secure storage of private data becomes a big concern. Proposed quantum inspired approach The following fig [ 2 ] describes the work implemented in this paper. This work brings to the scientific arena a novel quantum-inspired approach for audio-in-image steganography. The work done relies on classical python libraries, and quantum simulation. As mentioned in the introduction, this work doesn’t apply real quantum libraries, like qiskit, however in classical world analogies to quantum can be as effective as applying real quantum libraries and gates. The work can be divided into two parts. One part is how to apply the quantum approach, while the other is how to embed the secret information in the quantum domain. The following figures show the whole process. An audio is loaded, get its spectrogram and normalize it. On the other hand, there is the cover image that the audio will be embedded into it. The blue channel is then transformed to superposition through fast Fourier transform. The embedding of the audio is in the blue channel. The control gate gets two inputs the target qubit that is the image pixel, and the control qubit that normalized spectrogram. And this is how embedding is done. The arrows show the direction of the process, start by having audio and cover image, then end by having embedded stego image. The data source for the images is the Div2K dataset, while the audio used is an 8 seconds audio file. The key trend is the usage of Hadamard gate, and control gate to achieve entanglement and superposition. The takeaway of This process is that it is possible to mimic this using classical approaches. 4. Methodology Audio preprocessing The processing of the audio secret message is initially processed to get its frequency content over time. Visually represented as a spectrogram. Using librosa library: Loading and conversion using python: the audio file is of type int16 data type, is of sample rate 24000, and is of data shape 213696 is converted to float32 for robust numerical operation. The following fig [ 3 ] is Wav form for the audio file Spectrograph Generation using python: the audio secret message is transformed into a decibel (dB) spectrogram. This spectrogram provides a visual representation of audio’s frequency spectrum as it changes over time. The following fig [ 4 ] shows the spectrograph of the audio file. Normalization using python: for effective embedding, normalization of spectrogram values is important. The results of the spectrograph values (S_dB) is rescaled linearly to fit within the interval [0,1]. The minimum (S_dB) value is mapped to 0, while the maximum (S_dB) value is mapped to 1. This step crucial as it ensures consistent control over the phase shifts in the embedding process. The embedding process is done through manipulating the frequency domain representation of the blue channel of the cover image, mimicking quantum superposition and entanglement. Image preparation: the high-resolution cover image is represented as NumPy array of numerical pixel values. The blue channel of the RGB image is chosen for the embedding channel. Hadamard- like Transform and Fast Fourier transform (FFT): FFT is applied to the blue channel of the image. This simulates the superposition state. FFT transforms the spatial domain pixel values into frequency domain. Each frequency component can be thought of as a superposition of different states. This is similar to how Hadamard gate puts qubit into superposition |0> and |1>. This transformation prepares the image data for frequency-domain phase manipulation. Controlled Phase Gate (embedding through entanglement): this step alters the phase of the frequency components of the blue channel based on the normalized values of the audio spectrograph. The Control Phase Gate takes two inputs. First, the frequency- transformed blue channel and the phase map derived from the resized audio spectrograph. Mimicking the concept of target qubit and control qubit. It only applies rotation by X, Y, Z to the target qubit by angle theta, only if control qubit is |1> The normalized spectrograph values directly control the amount of phase shift applied to corresponding frequency components of the blue channel. This creates the entanglement like effect, where the image’s frequency components become dependent on the audio spectrograph’s values, and thus the embedding is achieved. The following two graphs represents the Phase distribution before and after the control phase gate. The angle describes the complex numbers in the frequency domain representation of the image data after the "Hadamard-like" transform (FFT). The proposed model is implemented using Python 3.11.13. The libraries used are classical libraries, includes the following: Cv2, Numpy, Matplotlib.pyplot, Wave, Librosa, Librosa.display, Skimage.metrics, Structural_similarity, Skimage.restoration, Sewar.full_ref, and OS. Data used for audio is an audio length of 8 seconds. The audio sample rate is 24000. The audio data shape is 213696, while the audio data type is int16. The embedding of audio file is held upon 60 randomly chosen, high resolution images from Div2K dataset. This dataset was originally designed for challenges @NITRE (CVPR 2017 and CVPR 2018). 4. Results and discussion This paper shows a state-of-the-art result in the arena of quantum image representation. It uses multi-channel quantum image representation approach in putting the cover image into quantum image representation. This paper depends on applying this image representation through its basic gates Hadamard gate and cphase gate. The Hadamard gate puts the blue channel into quantum state. Fast Fourier Transform (FFT) is the means to mimic it using classical approach. The application of quantum embedding is implemented through controlled phase gate. The evaluation metrices are based upon four metrices. First, PSNR: Metric used to evaluate the quality of the quantum (reconstructed) image in comparison to the original image. Second, MSE: Metric used to Quantifies the difference between two images through averaging the square differences of their corresponding pixels. Third, VIF: Metric used to measure the quantify the improvement in visual quality. Fourth, SSIM: Metric used to measure the similarity between two images. The following graphs shows the values for each evaluation matrix across the 60 chosen images. The x-axis represents the expected range of each evaluation metrics, while the y-axis represents the image number in the arrangement. The accepted PSNR value is a value greater than 40 decible, while the accepted MSE value is a value near 0. On the other hand, the accepted SSIM and VIF value is a value near 1. The graphs are generated using python. Those metrics tells that the quantum-inspired method image preserves a high quality of image after embedding. The experimental results show the efficacy of the proposed quantum-inspired audio in image steganography method using frequency domain phase modulation. Which is noticed in the results is the variation of measurement matrices. This variation of measurement depends upon the alterations made to the cover image; however, no stego image shows distortion, nor changes seen by naked eye. Based on this the proposed method which is the quantum-inspired image steganography method using frequency domain phase modulation presents significant results. High PSNR, high SSIM, high VIF, and low to moderate MSE. This proves that the proposed methodology achieves embedding with high imperceptibility, high robustness, and low deformation of image quality. Figure 10 a and Fig. 11 a are two samples from the Div2K dataset. The cover image is the main image, while the stego image is the image that contains the secret audio. The evaluation metrics is calculated based on PSNR, MSE, SSIM, VIF. First, is the PSNR, used to evaluate the fidelity of a compression or reconstruction algorithm. where MAX is the maximum possible pixel value of the image and MSE is the mean squared error. MSE or mean squared error is defined by Equation where I(i, j) is the pixel value of the original image at position (i, j), K(i, j) is the pixel value of the modified image at position (i, j). and m and n are the dimensions of the images. On the other hand, it is critical to measure the quality of the stego image after embedding. This is through SSIM and VIF. For SSIM, the following equation describes it. 𝑥 and 𝑦 are the two images. The more the value is nearest to one, the highest quality the stego image is. The equation uses different variables to compare both the cover image with the stego image. 𝑙 stands for luminance, which measures the brightness of the images. 𝑐 is contrast, which helps to defines the brightest and darkest regions of the images. 𝑠 is structure. It compares the local luminance patterns of the images to determine their similarity or dissimilarity. Additionally, the equation includes three positive constants: 𝛼, 𝛽, and y. The SSIM is better than PSNR in measuring the perceived quality of the stego image, or the reconstructed image. That is because SSIM requires local statistics computations, and correlates better with human perception. Similarly, is the VIF. Both of the SSIM and VIF evaluate how well the embedding process keeps the visual content of the image. VIF i = 1 / (1 - R i ²) (24) For this paper, there are 60, randomly, chosen images from Div2K dataset. From the 60 images there are 34 images with flourished and promising evaluation metrices. The highest and lowest Performance from the 34 images are demonstrated as follows: The following pictures shows a sample from the 34 images, the highest and the lowest evaluation metrices. On the left-hand side (Fig. 10 a) and (Fig. 11 a), there is the original cover image, while the right-hand side (Fig. 10 b) (Fig. 11 b), there is the embedded stego image. As seen below, the quality of (Fig. 10 b) and (Fig. 11 b) did not change. As a human being, by naked eye, there is no observable changes in it. This proves the successfulness of the steganographic approach used in this paper. This implies that the stego image can travel safely through an external channel between two parties. On the other hand, the variation of measurement metrics across the 60 tested images brings an attention for a good aspect of discussion. The characteristics of cover image and its inherit complexity are variations that makes the measurements metrics depend upon. Factors like texture, color distribution, smooth and highly detailed regions affect how the audio spectrogram phase modulation can be applied in the frequency domain. For illustration, images with richer frequency component leads to higher PSNR values. On the contrary, images with flatter regions are sensitive to changes leading to slightly lower, but still very good, measurements metrics. Comparing with another paper that worked on the same point, embedding audio in image, the PSNR value 42.54 dB for stego-image and 45.02 dB for the reconstructed image. This offers high storage efficiency and infrastructure for additional security measures. This is done through analysis and resynthesis of sound spectrographs (ARSS) framework. This framework ensures efficient and secure data storage using a simplistic, multi-channel, and non-lossy approach to embed an audio spectrograph in a high-resolution image file. Table 1 results of the proposed quantum inspired PSNR MSE SSIM VIF Highest evaluation Figure 10 b 0.6152 0.0458 0.9995 0.997 Lowest evaluation Figure 11 b 0.4023 6.1687 0.9874 0.9277 5. Conclusion and future work In conclusion, to sum up, the proposed method successfully embeds audio secret message into cover image with high degree of imperceptibility, high degree of robustness, and low deformation of image quality. This presents a promising research point in the quantum-inspired principles for robust steganography in the era of quantum computing. Through altering the phase of the blue channel of each pixel, and controlling its value through the spectrogram of the embedded audio. this improves that the embedding process of secret message is successfully attained in the quantum domain. This work is not only combination research of audio and image steganography, but also dives into quantum image representation. It ensures that multidisciplinary approach in the research is critical to addresses new points that opens doors for innovative solutions. The proposed solution leverages quantum properties for enhanced security and efficiency in information hiding. By training deep learning models on diverse data sets, redefinition of embedding techniques in the field of quantum will be attained. This will lead to more sophisticated methods. This proposal is flexible to be scaled into higher benchmark. This can be done through encrypting the audio itself before embedding. Not only that, applying deep learning model, based on quantum approach, after training on various datasets, is possible. Exploration for applying this research for real-time application is also possible, investigating the impact of this results in secure communication. This opens the door for future improvements and further research This work has taken into account audio steganography, image steganography, and quantum image representation research. Declarations Funding: "The Authors received NO FUNDING for this work" Author Contribution Tasneem Hatem has wrote the manuscript as it is a master research paper. Manar Hafez and Alia Youssif have revised it. 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Available: https://doi.org/10.21014/actaimeko.v13i1.1679 Potters, C. & Definition, V. I. F. Investopedia, [Online]. (2024). Available: https://www.investopedia.com/terms/v/variance-inflation-factor.asp . [Accessed: 27-Jun-2024]. Additional Declarations No competing interests reported. Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-8495483","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":580837825,"identity":"98c92f5b-6b08-49dd-ad2f-a5ddda39b5aa","order_by":0,"name":"Manar 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[9]\u003c/p\u003e","description":"","filename":"1.jpg","url":"https://assets-eu.researchsquare.com/files/rs-8495483/v1/14531191f896e0a907bad041.jpg"},{"id":101274602,"identity":"efab5e64-0872-49d2-86ee-a08183409fd2","added_by":"auto","created_at":"2026-01-28 03:12:02","extension":"jpg","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":64353,"visible":true,"origin":"","legend":"\u003cp\u003eProposed quantum inspired approach.\u003c/p\u003e","description":"","filename":"2.jpg","url":"https://assets-eu.researchsquare.com/files/rs-8495483/v1/dac2552774df4edd6a1eecbe.jpg"},{"id":101298099,"identity":"d614fa2b-aca9-4cb4-bb6c-14bb001c74a4","added_by":"auto","created_at":"2026-01-28 09:30:20","extension":"jpg","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":58096,"visible":true,"origin":"","legend":"\u003cp\u003eWav form of the used audio file\u003c/p\u003e","description":"","filename":"3.jpg","url":"https://assets-eu.researchsquare.com/files/rs-8495483/v1/dbaf2ded45d6be4cfb1fdb8a.jpg"},{"id":101274603,"identity":"a968d2fd-189f-4651-b355-f044ab803772","added_by":"auto","created_at":"2026-01-28 03:12:02","extension":"jpg","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":108848,"visible":true,"origin":"","legend":"\u003cp\u003eSpectrogram for the used audio file\u003c/p\u003e","description":"","filename":"4.jpg","url":"https://assets-eu.researchsquare.com/files/rs-8495483/v1/c3c0d4ef7b70009ae584c561.jpg"},{"id":101298025,"identity":"8031d426-4200-4841-863f-5b7dfe2555d7","added_by":"auto","created_at":"2026-01-28 09:29:48","extension":"jpg","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":79558,"visible":true,"origin":"","legend":"\u003cp\u003ea. before cphase \u0026nbsp;\u0026nbsp;b. after cphase\u003c/p\u003e","description":"","filename":"5.jpg","url":"https://assets-eu.researchsquare.com/files/rs-8495483/v1/ef6c714dff82608962b404ce.jpg"},{"id":101297628,"identity":"af5ef943-68f5-4761-812d-a17375872424","added_by":"auto","created_at":"2026-01-28 09:28:21","extension":"jpg","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":96013,"visible":true,"origin":"","legend":"\u003cp\u003ePSNR of the 60 sample images\u003c/p\u003e","description":"","filename":"6.jpg","url":"https://assets-eu.researchsquare.com/files/rs-8495483/v1/018fbba6bd69014dc557202b.jpg"},{"id":101274607,"identity":"b3d8a483-a612-4a6d-8c7c-349f00029c7e","added_by":"auto","created_at":"2026-01-28 03:12:03","extension":"jpg","order_by":7,"title":"Figure 7","display":"","copyAsset":false,"role":"figure","size":95142,"visible":true,"origin":"","legend":"\u003cp\u003eMSE of the 60 sample images\u003c/p\u003e","description":"","filename":"7.jpg","url":"https://assets-eu.researchsquare.com/files/rs-8495483/v1/2deab40ed30fe99fc98f913f.jpg"},{"id":101274610,"identity":"2d8b7c78-606e-44ab-9470-e04dcca9e34b","added_by":"auto","created_at":"2026-01-28 03:12:04","extension":"jpg","order_by":8,"title":"Figure 8","display":"","copyAsset":false,"role":"figure","size":122022,"visible":true,"origin":"","legend":"\u003cp\u003eSSIM of the 60 sample images\u003c/p\u003e","description":"","filename":"8.jpg","url":"https://assets-eu.researchsquare.com/files/rs-8495483/v1/1f944af855b98a97b60ca75c.jpg"},{"id":101274611,"identity":"e51aa885-e14c-46a1-8791-5392376c4a89","added_by":"auto","created_at":"2026-01-28 03:12:04","extension":"jpg","order_by":9,"title":"Figure 9","display":"","copyAsset":false,"role":"figure","size":123732,"visible":true,"origin":"","legend":"\u003cp\u003eVIF of the 60 sample images\u003c/p\u003e","description":"","filename":"9.jpg","url":"https://assets-eu.researchsquare.com/files/rs-8495483/v1/653b474166229d844c408ac9.jpg"},{"id":101298092,"identity":"0e0b50d6-2213-486d-86f1-25007c0c56ec","added_by":"auto","created_at":"2026-01-28 09:30:17","extension":"jpg","order_by":10,"title":"Figure 10","display":"","copyAsset":false,"role":"figure","size":60741,"visible":true,"origin":"","legend":"\u003cp\u003ea. before embedding \u0026nbsp;\u0026nbsp;b. after embedding\u003c/p\u003e","description":"","filename":"10.jpg","url":"https://assets-eu.researchsquare.com/files/rs-8495483/v1/cee266563bfb4672a21af293.jpg"},{"id":101274608,"identity":"365d4ad9-fd8b-4778-9d02-8136a53b45ba","added_by":"auto","created_at":"2026-01-28 03:12:03","extension":"jpg","order_by":11,"title":"Figure 11","display":"","copyAsset":false,"role":"figure","size":98677,"visible":true,"origin":"","legend":"\u003cp\u003ea. before embedding. b. after embedding\u003c/p\u003e","description":"","filename":"11.jpg","url":"https://assets-eu.researchsquare.com/files/rs-8495483/v1/a9f200b2780a3373752eb2ea.jpg"},{"id":105177109,"identity":"04a71f89-eaa8-4bd9-9766-18b5ae7d7b3f","added_by":"auto","created_at":"2026-03-23 06:11:37","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1438586,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-8495483/v1/b69e5e75-7c24-4d94-af9d-bece9daf3f94.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"A Quantum-Inspired Approach for audio hiding in Images via Frequency Domain representation of image channel","fulltext":[{"header":"1.\tINTRODUCTION","content":"\u003cp\u003eSteganography is not a newly introduced science to the humanity. It has fascinating records since ancient times, and has survived through our digital era. During ancient times, specifically 5th century BC, Greeks used to shave one of their slaves’ heads, then tattoos the secret message. After that they send the slaves to the 2nd party after their hair grows. In the early modern period, Johannes Trithemius in the 15th century, has explored methods of concealing secret messages using a cipher within a religious text. [1] Now, in the digital era tremendous techniques has been introduced. And efficiently used, by prestigious entities and Partys. This involves hiding messages within digital files like audio, images, and other digital file formats, with high evaluation metrices. For audio it is essential to generate the spectrograph of it to be embedded [2]\u003c/p\u003e\n\u003cp\u003eThe emergence of quantum computing has foreseen new horizons for steganography, that revolutionize processing power, and introduce an intriguing challenge, but opportunity for data security. This paper adapts the multi- channel quantum image representation using classical approach [3]. This representation is based upon applying Hadamard gate and controlled phase gate. Those gates give the opportunity to mimic superposition and entanglement. And in the quantum realm, the fundamental principles of superposition and entanglement allow novel ways to hide and extract data. The Hadamard gate puts the image pixel of the blue channel into superposition state, through applying fast Fourier transform (FFT). We can determine its value. Adding to that, the controlled-phase gate helps in embedding the pixels and putting it into entanglement. It takes two qubits. It takes the frequency transformed qubit of the blue-channel and phase map derived from resized audio spectrogram. After that, it applies phase shift to the frequency components of the image blue channel based on the values of the spectrogram. As of this, the amount of phase shift applied to image is controlled by the spectrogram (Audio). And that is how this paper has implemented the embedding of audio into image using quantum image inspired approach.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eThe contribution of this paper resides in the following:\u0026nbsp;\u003c/p\u003e\n\u003cul\u003e\n \u003cli\u003eApplying the multi-channel quantum image representation MCQI through Hadamard gate and control phase shift gate using classical programming methods.\u0026nbsp;\u003c/li\u003e\n \u003cli\u003eThe embedding process of the audio is applied through a phase shift to the frequency component of the blue channel in the cover image by a value based on the corresponding audio spectrogram data (S_dB_resized).\u003c/li\u003e\n \u003cli\u003eThe evaluation matrixes used are PSNR, MSE, VIF, SIMM.\u0026nbsp;\u003c/li\u003e\n\u003c/ul\u003e\n\u003cp\u003eThe remainder of this article is structured as follows. Section 2 discusses the related work and classification of steganography. Then it discusses the research found in audio and image steganography techniques. After that it discuses quantum steganography. \u0026nbsp; Section 3 provides a detailed explanation of the presented proposed quantum approach. Section 4 showcases the experimental and numerical outcomes of the proposed approach. In conclusion, Section 5 summarizes the main findings of this paper.\u0026nbsp;\u003c/p\u003e"},{"header":"2. Background","content":"\u003cp\u003eAudio in image steganography, is hiding secret information, that is audio message, inside a digital, cover image. [\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e] Digital image are digital files that can be processed in computers and can be divided into two categories, which are bitmap images and vector images.\u003c/p\u003e \u003cp\u003eFirst, the bitmap images. Image of size MxN is composed of finite element of MxN columns each has definite position called pixels, and amplitude representing the color of this point/pixel. Second, is the vector images. Those kinds of images are not visible as they are mathematical formulas to draw lines and curves.\u003c/p\u003e \u003cp\u003eFor audios, they are sound waves, or signals. In audio steganography, audio is converted into spectrograph, a visual sound representation of the audio [\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e]. After loading the image, the audio enters some preprocessing steps. Using Librosa library. Thanks to the wide range of functions this library provides, loading and manipulating audio files like WAV and mp3. It can trim, resample and change the audio volume. Adding to that, for sure feature extraction like spectrograph. In the field of audio in image steganography, audio spectrograph is the embedding factor in the digital image.\u003c/p\u003e \u003cp\u003eThis Paper uses classical NumPy arrays to represent pixels and spectrograph, then performs mathematical operations that are congruent to quantum gates. The multi-channel quantum image representation for high resolution-colored images (MCQI) is applied using Hadamard gate, and controlled rotation/phase gate with complexity O(N) [\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eThere are many research held in the field of audio steganography. There are two main techniques. Many methodologies are held in frequency-domain techniques, while others in spatial-domain techniques.\u003c/p\u003e \u003cp\u003eFor frequency domain techniques, analysis of image is interpreted through sin and cos waves, rather than over time or space. Through Fourier transform and other transform methods image can be transformed from the spatial, or time domain into frequency domain. This is to identify and manipulate periodic patterns, filter noise, or enhance certain features. On the contrary spatial domain techniques operate on image pixels to modify it.\u003c/p\u003e \u003cp\u003eAfter image transformation, some of the researches are encrypting the secret message before it is embedded into the cover image. This is to make sure that the secret message is kept save and sound. This way requires encrypting keys, public and private keys [\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e]. On the other hand, some research required the second party to extract the embedded message, after it travels to the second party. Both ways depend on the fundamental idea of steganography, which is concealing secret message into a digital file. This is whether the secret information is encrypted, or not.\u003c/p\u003e \u003cp\u003eThe following paragraphs will give a brief note about steganography and its background.\u003c/p\u003e \u003cp\u003eThere are two types of steganography. One is the spatial domain that deals with pixels, while embedding the secret information. Algorithm like LSB follows this approach. For illustration, image pixels in RGB are interpreted into binary of 32-bit color. 8-bit for each channel (plane) [\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e]. The other domain is the frequency domain. This involves converting the original image from its spatial domain to frequency domain using discrete wavelet transform (DWT), discrete Fourier transforms (DFT), and discrete cosine transform (DCT). The following steps after transforming the image into the frequency domain, is the embedding step. The hidden message is embedded into the coefficient of its transform domain. The power of this approach relies on the difficulty of detection, as the embedding is in the frequency not in the visual domain. Accordingly, this approach promises high robustness. In some cases, there might be trade-off between the imperceptibility and robustness, comparing to spatial domain approaches. For the complexity, the frequency domain may have higher complexity than the spatial one [\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eMoreover, audio steganography is the art of concealing a secret message into cover audio file. The goal of audio steganography is to hear the soundtrack without recognizing any noise signals. Following the classification of steganography techniques, the embedding process can be in spatial, or frequency domains. What must be achieved in the steganography, whatever it was, are three impactful goals. First, high imperceptibility. That is the cover medium can travel safely in a channel without being recognized by a third party. Second, high capacity. That is the ability to embed as much of a secret message as we can. Third, is high robustness. That is related to the changes made to the cover medium after embedding, and how cover medium is still as if no changes made to it i.e. robust. Until this steganography is in the classical domain. Quantum image steganography has a goal to improve tasks achieved through classical steganography based on quantum-based techniques. The first step is to represent and store the image into quantum computers. Here comes the trick. Quantum image representations are the doors for this step. example such as multi-channel quantum image representation of quantum images (MCQI). Each representation is based on gates that aim to apply the means of quantum mechanics; researchers should put into consideration quantum mechanics principals. Those are superposition, and entanglement. Superposition is the ability of qubit to be presented as |0\u0026thinsp;\u0026gt;\u0026thinsp;and |1\u0026thinsp;\u0026gt;\u0026thinsp;at the same time of equal probability. This is clarified by the following equation:[\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e][\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e]\u003c/p\u003e \u003cp\u003eH |0\u0026gt; =(1/sqt2) * (|0\u0026gt; + |1\u0026gt;) and H |1\u0026thinsp;\u0026gt;\u0026thinsp;=\u0026thinsp;1/sqt2) * (|0\u0026gt; - |1\u0026gt;)\u003c/p\u003e \u003cp\u003eEquation 1\u003c/p\u003e \u003cp\u003ewhile entanglement is the strong dependability of the target qubit upon the value of the control qubit. Target qubit is the qubit that is affected by a control qubit through quantum gate [\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e][\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e][\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e]. How can the qubit be represented? The qubit is represented on the bloch sphere as shown in fig [\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eFirst, North pole: Represents the |0⟩ state\u003c/p\u003e \u003cp\u003eSecond, South pole: Represents the |1⟩ state.\u003c/p\u003e \u003cp\u003eThird Surface: Represents all possible pure states of the qubit.\u003c/p\u003e \u003cp\u003eFourth, Interior: Represents mixed states.[\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e]\u003c/p\u003e \u003cp\u003e \u003c/p\u003e"},{"header":"3. Related Work","content":"\u003cp\u003eThe following sections discusses the work done in the arena of quantum image steganography.\u003c/p\u003e \u003cdiv id=\"Sec3\" class=\"Section2\"\u003e \u003ch2\u003e3.1. Quantum Image Steganography\u003c/h2\u003e \u003cp\u003eIt is essential to choose a suitable quantum image representation for images. Some papers depend on mimicking classical concepts, and depends on how they work. The most famous steganography techniques is Least significant bit (LSB). As a logic research point and mimicking least significant bit approach, scientists are inspired and came up with least significant qubit (LSBq) approach. Where the data hiding is done through replacing least qubit in an image by the qubit of the concealing data. This method shows enhancement and further research opportunities by applying additional protocols and algorithms. For example, in 2018, Sahin et al. [\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e] recorded high security and efficiency by implementing LSBq approach. The steganography\u0026rsquo;s security has been achieved by placing the embedded qubits into the corresponding channel by a specific modulo value. Not only that, through applying LSBq Sahin was able to reduce the complexity of the proposed algorithm. Sahin used quantum multi-wavelength images (QRMW) for steganography implementation. They added different wavelength for each modulo value. they implemented quantum multi-wavelength image representation (QRMW). This is the secret behind their high capacity results. This allowed them to hide higher scales of the embedded message into the cover image through varying the wavelength\u003c/p\u003e \u003cp\u003eAnother research based on LSBq is QISLSQb: A Quantum Image Steganography Scheme done by İhsan Yilmaz et at [\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e]. In this approach the embedding is done through LSBq, and the secret information is the quantum secret image scrambled utilizing Arnold cat map. Many research papers in the arena encrypts the data before embedding it, while others uses chaotic maps before embedding like this one. On the other hand, Tudorache eh al [\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e] focused on implementing a quantum steganography scheme using LSBq to hide secret info in grayscale image in a cover image\u0026rsquo;s qubit as well as the qubit\u0026rsquo;s position, and put it in novel enhanced quantum image representation (NEQR). Their results demonstrate an impressive indication for performance speed in comparison to found alternatives. On the other hand, Sahin et al. used LSBq approach. However, another approach that targeted higher embedding efficiency is the used of the controlled alternate quantum walks protocol (CAQWs). This procedure is inspired by random walks designed by Wenda et al [\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e]. This approach has the ability to outperform classical approaches in terms of exponential algorithmic speedup through implementing quantum state characteristics.\u003c/p\u003e \u003cp\u003eTo sum up, to work in the quantum steganography work, it is essential to determine which quantum image representation needed. Then try to modify its parameters to attain the three goals of any steganography project. High capacity, high robustness, and high imperceptibility\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec4\" class=\"Section2\"\u003e \u003ch2\u003e3.2 Audio steganography techniques\u003c/h2\u003e \u003cp\u003eThere are many research done in the audio steganography arena those research can be divided into two. One discusses the classified methods of audio steganography, while the other focuses on certain type of techniques. For example, there are papers that depends upon the chaotic systems and message encryption before embedding [\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e]. It uses chaos Henon, Baker, and Arnold maps for image encryption with audio steganography to allow robust and secure audio steganography. There are three points that should be into consideration. The inaudibility of distortion. This is the measurement of the audio transparency. After embedding the message, the third party should hear the audio well. The robustness, and it is how the audio can withstand with the attacks and distortions. The capacity, and this measurement involves the amount of data concealed within the audio file. After encrypting the image using the chaotic system, Inverse Short-time Fourier transform is used for embedding it into the high frequencies of the audio [\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e]. Hence, the image quality can be preserved, and the robustness is improved. This makes the provided technique resistant to many types of attack while traveling through a channel. On the other hand, there is a technique in audio steganography called echo hiding. This technique depends on the fact that the human ear cannot detect the short-term echoes exists in the sound file. From this, the secret audio is converted into signal echoes and those echoes are embedded into the cover audio file. This is achieved through dividing the secret audio into echo file, then transformed into frames of equal size. This defines the number of bits that can be embedded [\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e]. Adding to that, there is a very famous algorithm called phase shifting algorithm. This algorithm depends on embedding the secret information into the audio signal by taking advantage of the human auditory system (HAS) response to phase information. Bend et al worked on providing a phase coding algorithm based on HAS. In their approach, they depend on slicing the cover audio sequence into a set of equal-length segments. For each sliced segment, the DFT is applied. Then the manipulation with the phase in each segment will be according to the value of the secret message. This is better than amplitude embedding, as the embedding in the amplitude may cause a noticeable change in the cover audio.\u003c/p\u003e \u003cp\u003eThis summarizes some of the work done in the arena of audio steganography.\u003c/p\u003e \u003cp\u003eTo sum up, to embed an audio it is essential to represent it into spectrogram (this is what would be embedded), determine it shape, sample rate, and data type. From the previous work some papers depend on the least significant qubit (LSBq) and Quantum Fourier Transform Wang et al. [\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e] The Proposed method had better visual quality. The research gap Quantum image visual quality was not 100% good. Another ones depends on Positive operator valued measure and projective measurement operator used for data embedding and extraction WeiZH et al. [\u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e] the results were high secrecy, security and capacity. The research gap of a secret message was extracted with the probability of 2/3. That was the imperfection of this research. Adding to that Qu et al. [\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e] worked on QUALPI, Quantum water mark protocol\u003c/p\u003e \u003cp\u003eand Least Significant Qubit. The results were High performance on transparency, robustness, and data capacity. The research gap is that it does not deal with complex attacks. Another research made by Liu et al. [\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e] depends on Quantum key agreement, Bell states, and Paulis operation. The results were better performance, in efficiency, privacy and correctness. The research gap is Cloud secure storage of private data becomes a big concern.\u003c/p\u003e \u003cp\u003eProposed quantum inspired approach\u003c/p\u003e \u003cp\u003eThe following fig [\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e] describes the work implemented in this paper.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eThis work brings to the scientific arena a novel quantum-inspired approach for audio-in-image steganography. The work done relies on classical python libraries, and quantum simulation. As mentioned in the introduction, this work doesn\u0026rsquo;t apply real quantum libraries, like qiskit, however in classical world analogies to quantum can be as effective as applying real quantum libraries and gates. The work can be divided into two parts. One part is how to apply the quantum approach, while the other is how to embed the secret information in the quantum domain.\u003c/p\u003e \u003cp\u003eThe following figures show the whole process. An audio is loaded, get its spectrogram and normalize it. On the other hand, there is the cover image that the audio will be embedded into it. The blue channel is then transformed to superposition through fast Fourier transform. The embedding of the audio is in the blue channel. The control gate gets two inputs the target qubit that is the image pixel, and the control qubit that normalized spectrogram. And this is how embedding is done. The arrows show the direction of the process, start by having audio and cover image, then end by having embedded stego image. The data source for the images is the Div2K dataset, while the audio used is an 8 seconds audio file. The key trend is the usage of Hadamard gate, and control gate to achieve entanglement and superposition. The takeaway of This process is that it is possible to mimic this using classical approaches.\u003c/p\u003e \u003c/div\u003e"},{"header":"4. Methodology","content":"\u003cp\u003eAudio preprocessing\u003c/p\u003e \u003cp\u003eThe processing of the audio secret message is initially processed to get its frequency content over time. Visually represented as a spectrogram. Using librosa library:\u003c/p\u003e \u003cp\u003e \u003col\u003e \u003cspan\u003e \u003cli\u003e \u003cp\u003eLoading and conversion using python: the audio file is of type int16 data type, is of sample rate 24000, and is of data shape 213696 is converted to float32 for robust numerical operation.\u003c/p\u003e\u003cp\u003eThe following fig [\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e] is Wav form for the audio file\u003c/p\u003e \u003c/li\u003e \u003c/span\u003e \u003cspan\u003e \u003cli\u003e \u003cp\u003eSpectrograph Generation using python: the audio secret message is transformed into a decibel (dB) spectrogram. This spectrogram provides a visual representation of audio\u0026rsquo;s frequency spectrum as it changes over time. The following fig [\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e] shows the spectrograph of the audio file.\u003c/p\u003e \u003c/li\u003e \u003c/span\u003e \u003c/ol\u003e \u003c/p\u003e\u003cp\u003eNormalization using python: for effective embedding, normalization of spectrogram values is important. The results of the spectrograph values (S_dB) is rescaled linearly to fit within the interval [0,1]. The minimum (S_dB) value is mapped to 0, while the maximum (S_dB) value is mapped to 1. This step crucial as it ensures consistent control over the phase shifts in the embedding process.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eThe embedding process is done through manipulating the frequency domain representation of the blue channel of the cover image, mimicking quantum superposition and entanglement.\u0026nbsp;\u003c/p\u003e\n\u003cul\u003e\n \u003cli\u003eImage preparation: the high-resolution cover image is represented as NumPy array of numerical pixel values. The blue channel of the RGB image is chosen for the embedding channel.\u003c/li\u003e\n \u003cli\u003eHadamard- like Transform and Fast Fourier transform (FFT): FFT is applied to the blue channel of the image. This simulates the superposition state. FFT transforms the spatial domain pixel values into frequency domain. Each frequency component can be thought of as a superposition of different states. This is similar to how Hadamard gate puts qubit into superposition |0\u0026gt; and |1\u0026gt;. This transformation prepares the image data for frequency-domain phase manipulation.\u0026nbsp;\u003c/li\u003e\n \u003cli\u003eControlled Phase Gate (embedding through entanglement): this step alters the phase of the frequency components of the blue channel based on the normalized values of the audio spectrograph.\u0026nbsp;\u003c/li\u003e\n\u003c/ul\u003e\n\u003cp\u003eThe Control Phase Gate takes two inputs. First, the frequency- transformed blue channel and the phase map derived from the resized audio spectrograph. \u0026nbsp;Mimicking the concept of target qubit and control qubit. It only applies rotation by X, Y, Z to the target qubit by angle theta, only if control qubit is |1\u0026gt;\u003c/p\u003e\n\u003cp\u003eThe normalized spectrograph values directly control the amount of phase shift applied to corresponding frequency components of the blue channel. This creates the entanglement like effect, where the image\u0026rsquo;s frequency components become dependent on the audio spectrograph\u0026rsquo;s values, and thus the embedding is achieved. The following two graphs represents the Phase distribution before and after the control phase gate. The angle describes the complex numbers in the frequency domain representation of the image data after the \u0026quot;Hadamard-like\u0026quot; transform (FFT).\u003c/p\u003e\n\u003cp\u003eThe proposed model is implemented using Python 3.11.13. The libraries used are classical libraries, includes the following: Cv2, Numpy, Matplotlib.pyplot, Wave, Librosa, Librosa.display, Skimage.metrics, Structural_similarity, Skimage.restoration, Sewar.full_ref, and OS.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eData used for audio is an audio length of 8 seconds. The audio sample rate is 24000. The audio data shape is 213696, while the audio data type is int16. \u0026nbsp;The embedding of audio file is held upon 60 randomly chosen, high resolution images from Div2K dataset. This dataset was originally designed for challenges @NITRE (CVPR 2017 and CVPR 2018).\u003c/p\u003e"},{"header":"4. Results and discussion","content":"\u003cp\u003eThis paper shows a state-of-the-art result in the arena of quantum image representation. It uses multi-channel quantum image representation approach in putting the cover image into quantum image representation. This paper depends on applying this image representation through its basic gates Hadamard gate and cphase gate. The Hadamard gate puts the blue channel into quantum state. Fast Fourier Transform (FFT) is the means to mimic it using classical approach. The application of quantum embedding is implemented through controlled phase gate.\u003c/p\u003e \u003cp\u003eThe evaluation metrices are based upon four metrices. First, PSNR: Metric used to evaluate the quality of the quantum (reconstructed) image in comparison to the original image. Second, MSE: Metric used to Quantifies the difference between two images through averaging the square differences of their corresponding pixels. Third, VIF: Metric used to measure the quantify the improvement in visual quality. Fourth, SSIM: Metric used to measure the similarity between two images.\u003c/p\u003e \u003cp\u003eThe following graphs shows the values for each evaluation matrix across the 60 chosen images.\u003c/p\u003e \u003cp\u003eThe x-axis represents the expected range of each evaluation metrics, while the y-axis represents the image number in the arrangement. The accepted PSNR value is a value greater than 40 decible, while the accepted MSE value is a value near 0. On the other hand, the accepted SSIM and VIF value is a value near 1. The graphs are generated using python.\u003c/p\u003e \u003cp\u003eThose metrics tells that the quantum-inspired method image preserves a high quality of image after embedding.\u003c/p\u003e \u003cp\u003eThe experimental results show the efficacy of the proposed quantum-inspired audio in image steganography method using frequency domain phase modulation. Which is noticed in the results is the variation of measurement matrices. This variation of measurement depends upon the alterations made to the cover image; however, no stego image shows distortion, nor changes seen by naked eye. Based on this the proposed method which is the quantum-inspired image steganography method using frequency domain phase modulation presents significant results. High PSNR, high SSIM, high VIF, and low to moderate MSE. This proves that the proposed methodology achieves embedding with high imperceptibility, high robustness, and low deformation of image quality.\u003c/p\u003e \u003cp\u003eFigure\u0026nbsp;\u003cspan refid=\"Fig9\" class=\"InternalRef\"\u003e10\u003c/span\u003ea and Fig.\u0026nbsp;\u003cspan refid=\"Fig10\" class=\"InternalRef\"\u003e11\u003c/span\u003ea are two samples from the Div2K dataset. The cover image is the main image, while the stego image is the image that contains the secret audio. The evaluation metrics is calculated based on PSNR, MSE, SSIM, VIF. First, is the PSNR, used to evaluate the fidelity of a compression or reconstruction algorithm.\u003c/p\u003e \u003cp\u003e\u003cimg 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\" style=\"width: 391px; height: 91.6774px;\" width=\"391\" height=\"91.6774\"\u003e\u003c/p\u003e\u003cp\u003ewhere MAX is the maximum possible pixel value of the image and MSE is the mean squared error.\u003c/p\u003e \u003cp\u003eMSE or mean squared error is defined by Equation\u003c/p\u003e \u003cp\u003e\u003cimg 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\" style=\"width: 329px; height: 77.9041px;\" width=\"329\" height=\"77.9041\"\u003e\u003c/p\u003e\u003cp\u003ewhere I(i, j) is the pixel value of the original image at position (i, j), K(i, j) is the pixel value of the modified image at position (i, j). and m and n are the dimensions of the images.\u003c/p\u003e \u003cp\u003eOn the other hand, it is critical to measure the quality of the stego image after embedding. This is through SSIM and VIF. For SSIM, the following equation describes it.\u003c/p\u003e \u003cp\u003e\u003cimg 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\" style=\"width: 439px; height: 57.7632px;\" width=\"439\" height=\"57.7632\"\u003e\u003c/p\u003e \u003cp\u003e\u0026#119909; and \u0026#119910; are the two images. The more the value is nearest to one, the highest quality the stego image is. The equation uses different variables to compare both the cover image with the stego image. \u0026#119897; stands for luminance, which measures the brightness of the images. \u0026#119888; is contrast, which helps to defines the brightest and darkest regions of the images. \u0026#119904; is structure. It compares the local luminance patterns of the images to determine their similarity or dissimilarity. Additionally, the equation includes three positive constants: \u0026#120572;, \u0026#120573;, and y.\u003c/p\u003e \u003cp\u003eThe SSIM is better than PSNR in measuring the perceived quality of the stego image, or the reconstructed image. That is because SSIM requires local statistics computations, and correlates better with human perception. Similarly, is the VIF. Both of the SSIM and VIF evaluate how well the embedding process keeps the visual content of the image.\u003c/p\u003e \u003cp\u003eVIF\u003csub\u003ei\u003c/sub\u003e = 1 / (1 - R\u003csub\u003ei\u003c/sub\u003e\u0026sup2;) (24)\u003c/p\u003e \u003cp\u003eFor this paper, there are 60, randomly, chosen images from Div2K dataset. From the 60 images there are 34 images with flourished and promising evaluation metrices. The highest and lowest Performance from the 34 images are demonstrated as follows:\u003c/p\u003e \u003cp\u003eThe following pictures shows a sample from the 34 images, the highest and the lowest evaluation metrices. On the left-hand side (Fig.\u0026nbsp;\u003cspan refid=\"Fig9\" class=\"InternalRef\"\u003e10\u003c/span\u003ea) and (Fig.\u0026nbsp;\u003cspan refid=\"Fig10\" class=\"InternalRef\"\u003e11\u003c/span\u003ea), there is the original cover image, while the right-hand side (Fig.\u0026nbsp;\u003cspan refid=\"Fig9\" class=\"InternalRef\"\u003e10\u003c/span\u003eb) (Fig.\u0026nbsp;\u003cspan refid=\"Fig10\" class=\"InternalRef\"\u003e11\u003c/span\u003eb), there is the embedded stego image. As seen below, the quality of (Fig.\u0026nbsp;\u003cspan refid=\"Fig9\" class=\"InternalRef\"\u003e10\u003c/span\u003eb) and (Fig.\u0026nbsp;\u003cspan refid=\"Fig10\" class=\"InternalRef\"\u003e11\u003c/span\u003eb) did not change. As a human being, by naked eye, there is no observable changes in it. This proves the successfulness of the steganographic approach used in this paper. This implies that the stego image can travel safely through an external channel between two parties.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eOn the other hand, the variation of measurement metrics across the 60 tested images brings an attention for a good aspect of discussion. The characteristics of cover image and its inherit complexity are variations that makes the measurements metrics depend upon. Factors like texture, color distribution, smooth and highly detailed regions affect how the audio spectrogram phase modulation can be applied in the frequency domain. For illustration, images with richer frequency component leads to higher PSNR values. On the contrary, images with flatter regions are sensitive to changes leading to slightly lower, but still very good, measurements metrics.\u003c/p\u003e \u003cp\u003eComparing with another paper that worked on the same point, embedding audio in image, the PSNR value 42.54 dB for stego-image and 45.02 dB for the reconstructed image. This offers high storage efficiency and infrastructure for additional security measures. This is done through analysis and resynthesis of sound spectrographs (ARSS) framework. This framework ensures efficient and secure data storage using a simplistic, multi-channel, and non-lossy approach to embed an audio spectrograph in a high-resolution image file.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab1\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eresults of the proposed quantum inspired\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"5\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003ePSNR\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eMSE\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eSSIM\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eVIF\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eHighest evaluation\u003c/p\u003e \u003cp\u003eFigure\u0026nbsp;\u003cspan refid=\"Fig9\" class=\"InternalRef\"\u003e10\u003c/span\u003eb\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.6152\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.0458\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.9995\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.997\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eLowest evaluation\u003c/p\u003e \u003cp\u003eFigure\u0026nbsp;\u003cspan refid=\"Fig10\" class=\"InternalRef\"\u003e11\u003c/span\u003eb\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.4023\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e6.1687\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.9874\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.9277\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e"},{"header":"5. Conclusion and future work","content":"\u003cp\u003eIn conclusion, to sum up, the proposed method successfully embeds audio secret message into cover image with high degree of imperceptibility, high degree of robustness, and low deformation of image quality. This presents a promising research point in the quantum-inspired principles for robust steganography in the era of quantum computing. Through altering the phase of the blue channel of each pixel, and controlling its value through the spectrogram of the embedded audio. this improves that the embedding process of secret message is successfully attained in the quantum domain.\u003c/p\u003e \u003cp\u003eThis work is not only combination research of audio and image steganography, but also dives into quantum image representation. It ensures that multidisciplinary approach in the research is critical to addresses new points that opens doors for innovative solutions. The proposed solution leverages quantum properties for enhanced security and efficiency in information hiding. By training deep learning models on diverse data sets, redefinition of embedding techniques in the field of quantum will be attained. This will lead to more sophisticated methods.\u003c/p\u003e \u003cp\u003eThis proposal is flexible to be scaled into higher benchmark. This can be done through encrypting the audio itself before embedding. Not only that, applying deep learning model, based on quantum approach, after training on various datasets, is possible. Exploration for applying this research for real-time application is also possible, investigating the impact of this results in secure communication. This opens the door for future improvements and further research This work has taken into account audio steganography, image steganography, and quantum image representation research.\u003c/p\u003e"},{"header":"Declarations","content":"\u003ch2\u003eFunding:\u003c/h2\u003e \u003cp\u003e\"The Authors received \u003cb\u003eNO FUNDING\u003c/b\u003e for this work\"\u003c/p\u003e\u003ch2\u003eAuthor Contribution\u003c/h2\u003e\u003cp\u003eTasneem Hatem has wrote the manuscript as it is a master research paper. Manar Hafez and Alia Youssif have revised it.\u003c/p\u003e\u003ch2\u003eData Availability\u003c/h2\u003e\u003cp\u003e\u0026bull; The datasets used and/or analyzed during the current study available from the corresponding author on reasonable request.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\u003cli\u003e\u003cspan\u003eNagaraj, K. Understanding the Trithemius Cipher: A Comprehensive Guide, Medium, [Online]. (2023). 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[Accessed: 27-Jun-2024].\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"Entanglement, Superposition, Quantum Steganography, Control phase gate, Hadamard gate, multi-channel quantum image representation","lastPublishedDoi":"10.21203/rs.3.rs-8495483/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-8495483/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eSteganography, throughout history, is the science of concealing secret information. This art ambuscade in hiding a message into a cover data. This data can be seen by unauthorized observers, and they cannot recognize that there is something strange. With no doubt, the data could be image, audio, or video. There is a shortage of research in the arena of quantum steganography, especially, audio in image steganography. Reading the upcoming era of quantum computing, doors are open for innovation. This paper doesn\u0026rsquo;t apply quantum libraries directly, but it simulates quantum concepts such as superposition, using Hadamard gate, and entanglement, using control phase gate. This is implemented using classical methods. That is, this paper introduces \u0026ldquo;quantum-inspired\u0026rdquo; approach for audio in image steganography. As secret information is subject to sever changes while embedding, like any steganography project, it is important to preserve the robustness of the cover image, and ensure high imperceptibility. This is achieved in this paper. This paper has chosen 60 high resolution images from Div2K dataset, and tested the proposed approach on them. Each image has its own evaluation metrics. Thirty four of them have PSNR greater than 40%, MSE near zero, and SSIM and VIF near one. One of the promising results from the thirty four images is PSNR, MSE, VIF, and SSIM are 61.52 dB, 0.0458, 0.997, and 0.9995, respectively for a specified image. Those results are impressive. Despite the successfulness of this \u0026ldquo;quantum-inspired\u0026rdquo; approach, it has constraints regarding the image.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e","manuscriptTitle":"A Quantum-Inspired Approach for audio hiding in Images via Frequency Domain representation of image channel","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2026-01-28 03:11:57","doi":"10.21203/rs.3.rs-8495483/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"f880ce76-4c2f-45c3-a959-ac598f7eb822","owner":[],"postedDate":"January 28th, 2026","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[{"id":61788761,"name":"Physical sciences/Engineering"},{"id":61788762,"name":"Physical sciences/Mathematics and computing"},{"id":61788763,"name":"Physical sciences/Optics and photonics"},{"id":61788764,"name":"Physical sciences/Physics"}],"tags":[],"updatedAt":"2026-03-23T06:11:07+00:00","versionOfRecord":[],"versionCreatedAt":"2026-01-28 03:11:57","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-8495483","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-8495483","identity":"rs-8495483","version":["v1"]},"buildId":"XKTyCvWXoU3ODBz1xrDgd","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}