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Image encryption is a critical process aimed at securing digital images, safeguarding them from unauthorized access, tampering, or viewing to ensure the confidentiality and integrity of sensitive visual information. In this research, we integrate polynomial Chebyshev, fractal Tromino, and substitution S-box methods into a comprehensive image encryption approach. Our evaluation focuses on standardized 256·256-pixel images of Lena, Peppers, and Baboon, assessing key performance metrics like mean squared error (MSE), peak signal-to-noise ratio (PSNR), unified average changing intensity (UACI), number of pixel changes rate (NPCR), and entropy. The results reveal varying encryption quality across images, with Lena exhibiting the highest MSE (4702) and the lowest PSNR (12.89 dB). However, UACI, NPCR, and entropy values remain consistent across all images, indicating the proposed method's stability concerning changing intensity, pixel alterations, and entropy levels. These findings contribute valuable insights into the effectiveness of the proposed encryption method, providing a foundation for further exploration and optimization in the field of cryptographic research. For future research direction, it is recommended to explore the impact of varying image sizes and types on the proposed method's performance. Additionally, by focusing on the area of cryptographic threats, further analysis of the algorithm's resistance against advanced attacks and its computational efficiency would be beneficial.
Keywords:
Encryption quality
Fractal Tromino
Image encryption
Polynomial Chebyshev
Substitution S-box
ABSTRACT
Image encryption is a critical process aimed at securing digital images, safeguarding them from unauthorized access, tampering, or viewing to ensure the confidentiality and integrity of sensitive visual information. In this research, we integrate polynomial Chebyshev, fractal Tromino, and substitution S-box methods into a comprehensive image encryption approach. Our evaluation focuses on standardized 256·256-pixel images of Lena, Peppers, and Baboon, assessing key performance metrics like mean squared error (MSE), peak signal-to-noise ratio (PSNR), unified average changing intensity (UACI), number of pixel changes rate (NPCR), and entropy. The results reveal varying encryption quality across images, with Lena exhibiting the highest MSE (4702) and the lowest PSNR (12.89 dB). However, UACI, NPCR, and entropy values remain consistent across all images, indicating the proposed method's stability concerning changing intensity, pixel alterations, and entropy levels. These findings contribute valuable insights into the effectiveness of the proposed encryption method, providing a foundation for further exploration and optimization in the field of cryptographic research. For future research direction, it is recommended to explore the impact of varying image sizes and types on the proposed method's performance. Additionally, by focusing on the area of cryptographic threats, further analysis of the algorithm's resistance against advanced attacks and its computational efficiency would be beneficial.
(ProQuest: ... denotes formulae omitted.)
1. INTRODUCTION
Image encryption is a process of securing digital images to protect them from unauthorized access, modification, or viewing. This is typically done to ensure the confidentiality and integrity of sensitive visual information [1], [2]. Implementation of various cryptographic techniques and algorithms, image encryption transforms digital images into obscured formats, making it challenging for unauthorized entities to decipher or manipulate the original content [3], [4]. This protective measure plays a vital role in diverse fields where the privacy and security of visual data are paramount. The essence of image encryption lies in the utilization of a 'key', a confidential parameter that must remain undisclosed to unauthorized individuals [5]. This key serves as a critical element in the encryption process, ensuring that only those with the correct key can decrypt and access the original visual content [6]-[8]. The security of the encrypted images hinges on the secrecy of this key, emphasizing the need for robust key management practices. By restricting knowledge of the key to authorized parties, the encryption mechanism establishes a protective barrier, fortifying the confidentiality of sensitive visual information against potential breaches. This stringent control over access to the decryption key is paramount in upholding the overall security and effectiveness of image encryption techniques [9]. Based on the review, the evolution of image encryption techniques by [8]-[ 14] has been shaped by ongoing advancements in cryptographic research and technology. Researchers and practitioners continually explore novel approaches to enhance the resilience of image encryption against evolving cyber threats. Recent developments have seen the integration of machine learning algorithms to reinforce encryption processes, providing an additional layer of defense against sophisticated attacks [15]. The intersection of image encryption with other cybersecurity measures, such as secure transmission protocols and multi-factor authentication, contributes to creating a comprehensive and robust security framework for visual data [16], [17]. Moreover, the adoption of quantumresistant encryption algorithms is gaining attention as a proactive measure to address the potential vulnerabilities posed by quantum computing in the future. In addition to technological advancements, the widespread adoption of image encryption standards and protocols further underscores its significance. Industry-wide acceptance of standardized encryption practices ensures interoperability and facilitates seamless collaboration across different platforms and applications. Standardization not only enhances the compatibility of image encryption solutions but also fosters trust among users by adhering to established security benchmarks. Collaborative efforts among researchers, industry stakeholders, and policymakers are instrumental in developing and promoting these standards, fostering a more secure digital landscape.
The primary aim of this research is to advance the quality measurement techniques for image encryption through the integration of innovative methodologies, specifically employing the fractal Tramino and polynomial Chebyshev transformations based on chaotic matrices. The goal is to enhance the precision and reliability of quality metrics such as the mean squared error (MSE), peak signal-to-noise ratio (PSNR), number of pixel changes rate (NPCR), and unified average changing intensity (UACI) in assessing the effectiveness of image encryption algorithms. By leveraging the unique properties of fractal Tramino and polynomial Chebyshev transformations within the framework of chaotic matrices, the research seeks to develop a more robust and sensitive quality measurement mechanism. This approach aims to provide a comprehensive evaluation of the encryption algorithms, offering insights into their capacity to induce significant pixel changes and alterations across images while maintaining the desirable properties of encryption, such as confidentiality and resistance against unauthorized access.
This research is structured to comprehensively explore and enhance quality measurement in image encryption, leveraging the innovative integration of fractal Tramino and polynomial Chebyshev transformations within the framework of chaotic matrices. Section 1 introduces the problem of securing digital images and the importance of robust encryption methods, providing a background on existing approaches and their limitations. Section 2 presents a detailed literature review on current encryption techniques, particularly focusing on chaos-based encryption, fractal geometry, and polynomial transformations. In section 3, the proposed method is discussed, outlining the integration of fractal Tramino and polynomial Chebyshev transformations within chaotic matrices, explaining how this combination improves encryption quality and security. Section 4 analyzes the results obtained from implementing the proposed method, evaluating its performance using metrics such as PSNR, SSIM, entropy, and comparing it to traditional methods. Finally, section 5 concludes the research by summarizing the findings, highlighting the improvements achieved, and suggesting future work.
2. LITERATURE REVIEW
2.1. State of the art
The utilization of fractal Tramino and polynomial Chebyshev in the context of image encryption is relatively uncommon. However, a discernible number of research studies have demonstrated the efficacy of employing either one of these methods as part of their image encryption strategies. Moreover, some researchers have taken an innovative approach by combining these less conventional techniques with other established methods to enhance the overall security and robustness of their data protection mechanisms.
The research, as represented by [18], introduces a novel approach to ensure highly secure data transmission through the proposition of a hybrid encryption technique. In this method, encryption and decryption processes are intricately designed by incorporating a hybrid fractal-chaos technique, which comprises four essential modules: key generation, fractal encryption, chaos encryption, and decryption. Initially, a generated key is employed to facilitate both the encryption and decryption of images or data. Subsequently, the fractal encryption process is executed through the application of the L-shaped Tramino. Simultaneously, chaos encryption is carried out using the discrete cosine transform (DCT), culminating in the production of the final encrypted image. The decryption process involves the utilization of chaos decryption and fractal decryption algorithms. Research by Khan et al. [19], proposed encryption scheme is built upon a foundation of fractal Tromino and a Chebyshev polynomial-based generated chaotic matrix. The scheme prioritizes two fundamental aspects of encryption: diffusion and confusion. To achieve confusion, highly nonlinear, pre-defined S-boxes are strategically incorporated. Rigorous testing of the proposed scheme has been conducted using key performance indicators such as differential analysis, statistical analysis, information entropy analysis, MSE, and NIST-based randomness analysis. The findings reveal that the encrypted images exhibit the highest practically achievable entropy of 7.9999. Importantly, the time analysis demonstrates the feasibility of real-time implementation for the proposed system. In the research conducted by [20], the researchers devised an algorithm that combines the digital wavelet transform with fractal encryption to enhance image security. The process initiates with the transformation of a host image into the frequency domain through the discrete wavelet transform. The resulting encrypted watermark is then embedded into the host image in the frequency domain, culminating in the creation of a watermarked image.
The current study adopts a hybrid approach by incorporating elements of the proposed method, specifically integrating the innovative techniques of fractal Tromino and polynomial Chebyshev. This novel combination aims to further enhance the encryption process, leveraging the unique properties of each method to fortify the security measures employed. The forthcoming section will delve into a detailed exploration of the application and intricacies of the fractal Tromino and polynomial Chebyshev methods within the context of this research, elucidating their roles in optimizing image encryption and contributing to the overall efficacy of the proposed algorithm. By synergizing these methods, the study aims to provide a comprehensive understanding of their collective impact on image security, thereby advancing the current state-of-the-art cryptographic practices.
2.2. Substitution S-box
Substitution S-boxes are integral components in cryptographic systems, particularly block ciphers [21], [22]. Their primary function is to facilitate the nonlinear transformation of input data during the encryption process, contributing significantly to the overall security of the algorithm. The substitution of values within these boxes introduces a layer of confusion and diffusion, thereby complicating the ability of adversaries to discern patterns or relationships between the plaintext and ciphertext. Pseudocode-based S-boxes substitution logic can be seen in Algorithm 1. The provided S-box substitution algorithm employs a predefined substitution table, S - box_table, to substitute input bytes. The algorithm ensures that the input_byte is within a valid range (0 to 255) by applying the modulo operation with 256. This modular operation is represented by (1), where mod denotes the modulo operation. This equation ensures that the input_byte remains within the valid byte range, preventing overflow. The algorithm then proceeds to substitute the input _byte with the corresponding value from the S - box_table, producing the output _byte.
2.3. Fractal Tromino
Fractal Tromino processing involves the recursive application of a mathematical algorithm to create intricate patterns known as fractals, specifically focusing on the construction of a geometric shape known as a Tromino. The Tromino is a type ofpolyomino consisting of three connected squares [19], [20]. In this process, a base shape, often a single square, is repeatedly divided into smaller Trominos through a set of recursive rules. This recursive subdivision leads to the emergence of self-similar patterns on different scales within the overall structure. Based on the fractal Tromino algorithm, can be seen in Algorithm 2. The fractal Tromino algorithm aims to generate a matrix, denoted as R, from an input image matrix using a series of mathematical operations. The matrix R is constructed through iterations over the dimensions of the input image, incorporating randomly generated keys kl and k2 and a computed value c based on the mean of the input image. In (3) illustrates the updating of each element in R by applying a combination of the existing value, kl multiplied by c, and k2, followed by modulo 256. The computed value c in (4) and (5) is determined by summing the absolute differences between each element of the input image and its mean, divided by the product of the image dimensions. The final step involves performing an XOR operation in (6) between the original image and the generated fractal Tromino, resulting in a modified image, refened to as the resulting image.
2.4. Polynomial Chebyshev based on chaotix matrix processing
Polynomial Chebyshev based on chaotix matrix processing in cryptography refers to a novel approach that integrates Chebyshev polynomials with the concept of chaotix matrices for enhancing cryptographic operations [19], [23]. Chaotix matrices are characterized by their chaotic and unpredictable properties, and when combined with the mathematical elegance of Chebyshev polynomials, they provide a platform for creating robust cryptographic protocols. The synergy of Chebyshev-based polynomial processing and chaotix matrices can be leveraged for tasks such as secure key generation, encryption, and authentication. Based on the Polynomial Chebyshev equation can be seen in (7). The provided algorithm outlines a Chebyshev-based image-processing function in cryptography. The algorithm initializes keys p and q along with a constant c derived from the input image matrix as shown in Algorithm 3. It then iteratively updates a matrix R based on conditional rules involving kl and k2. Subsequently, Chebyshev polynomials are applied to update p and q in a nested loop that runs for M · N iterations, where M and N are the dimensions of the image. Two matrices, matrixl, and matrix?., are generated by processing p and q using a modulus operation. The final result is obtained by XORing these matrices.
Algorithm 1. S-boxes substitution algorithm
Function SubstitutionSB ox (input „matrix):
M, N = s ize (input _matr ix)
binMat = convertToBinary (input„matrix, M, N)
partitioned = partitionMatrix (binMat, M, N)
for i from 1 to M :
for j from 1 to A:
partitioned [i,y] = SubByte (partitioned [t,;])
reassembled = reassemble at (partitioned, M, N)
return reassembled
End
Function SubByteOperation (partition):
for i from 1 to size (partition, 1):
for;' from 1 to size (partition, 2):
partition [i,j] = SboxSubstitution (partition[i,;])
return partition
End
Function Substitution(input_byte):
S - box_table = [
0x63, 0x7C, 0x77, 0x7B, 0xF2, 0x6B, 0x6F
0x30, 0x01, 0x67, 0x2B, OxFE, 0xD7, OxAB
OxCA, 0x82, 0xC9, 0x7D, OxFA, 0x59, 0x47
OxAD, 0xD4, 0xA2, OxAF, 0x9C, 0xA4, 0x72]
input_byte = input_byte mod 256 (1)
outpu tbyte S boxtable
[input_byte]
return outputjoyte
End
Algorithm 2. Fractal Tramino algorithm
Function generateFractalT r omino (imag e Matrix) :
M,N,_ = size (imageMatrix)
R = createMatrix (M, 3 · N)
kl, k? = generateRandomKey ()
m = mean(imageMatrix)
for i from 1 to M:
for j from 1 to 3 · N:
c = computeC (imageMatrix.m)
... (3)
fractalTr omino = reshapeMatrix (R,M,N, 3)
return fractalTr omino
End
Function computer (matrix, me an):
sum = 0
for each element in the matrix:
... (4)
... (5)
* size (matrix, 2)))
return c
End
Function generateRandomKey ():
return randomlnteger(0, 255)
End
Function xorWithFr actai (orimage, fractalTrominof.
resultimage = (6)
orilmage XOR fractalTromino
return resultimage
End
Algorithm 3. Polynomial Chebyshev algorithm
Function Chebyshev (imageMatrix,x,y,kl,k2);
M, N = size (imag eMatrix)
p = initializeKey ()
q = initializeKey ()
c = calculateC (imageMatrix)
for i from 1 to M;
for j from 1 to N:
if mod (i,k2 · c) < kl · c:
R[i,j] = mod(j,r)
elseif mod (j,k2 · c) > kl · c;
R[i,j] = mod(i, r)
else:
R[i,j] = mod(c - t, c)
for iteration from 1 to M · N;
p = cos (x · arccos (w · p))
q = cos(y · arccos(q))
matrixl = processMatrix(p, q, M, N, r)
matrix2 = processMatrix(q, p, M, N, r)
resultMatrix = matrixl XOR matrix2
return resultMatrix
End
... (7)
q(l + 1) = Tm(ql) = cos(y x arccos(ql)),
2.5. Quality measuremet
MSE is a widely used metric in cryptography to quantify the difference between an original image and its reconstructed or encrypted version [24], [25]. The MSE is calculated by taking the average of the squared differences between corresponding pixel values in the two images. The equation for MSE based on grayscale images can be seen in (8). Where M and N represent the dimensions of the images, fj denotes the pixel intensity of the original image, and Ktj is the pixel intensity of the encrypted or reconstructed image. A lower MSE value indicates a closer match between the two images, implying a smaller difference between the original and the encrypted image. If MSE approaches 0, it signifies that the encrypted image is nearly identical to the original, suggesting a successful and accurate encryption process. On the other hand, an MSE value approaching 1 implies a significant deviation between the original and encrypted images, indicating a higher level of distortion or error in the encryption process [5]. In summary, a lower MSE is desirable as it reflects a higher fidelity in preserving the content of the original image during encryption, while a higher MSE indicates greater distortion. For red, green, and blue (RGB) images, the MSE calculation is performed independently for each color channel, and the final MSE is the average of the MSE values for each channel. The equation for MSE based on RGB images can be seen in (9). PSNR is especially relevant in cryptography when assessing the fidelity of encrypted images [26]. The PSNR is calculated as the ratio of the peak signal value to the MSE between the original and encrypted images, expressed in decibels (dB). The equation for PSNR can be seen in (9).
... (8)
... (9)
... (10)
UACI is a metric used to assess color distortion in image or video processing applications [23]. A high UACI value indicates a significant chromaticity change between the original and processed images, reflecting a substantial alteration in color information. On the contrary, a low UACI value signifies minimal chromaticity change, indicating that the processed image closely preserves the original color information. The equation based on UACI can be seen in (11):
... (12)
NPCR is a quality measurement metric employed in image processing to assess the effectiveness of cryptographic algorithms by quantifying the extent of pixel change between an original and an encrypted image [27]. A higher NPCR value signifies that a larger proportion of pixels experience changes, indicating a greater sensitivity to alterations in the encryption key. In contrast, a lower NPCR value indicates that fewer pixels are affected by changes in the encryption key. The equation based on NPCR can be seen in (12). Where, M and N represent the dimensions of the images, Uij) denotes the pixel intensity of the original image at coordinates (i,jY K(i, j) is the pixel intensity of the processed or encrypted image at the same coordinates, and L signifies the maximum pixel intensity value. The formula computes the average percentage change in chromaticity between corresponding pixels in the original and processed images, with the XOR (ф) operation used to calculate the bitwise exclusive OR of the pixel intensities. The resulting values are normalized by L and multiplied by 100 to express the percentage change.
... (12)
Entropy is a statistical measure used in information theory and image processing to quantify the randomness or unpredictability of pixel intensities within an image. In the context of image analysis, entropy represents the level of disorder in the pixel values entropy indicates greater disorder, complexity, and information content, while lower entropy suggests a more ordered and predictable image. A high entropy value implies that the image contains a wide range of pixel intensity values and lacks a discernible pattern, making it more challenging to predict or compress. Based on entropy equation can be seen in (13):
... (13)
3. PROPOSED SCHEME
The proposed scheme involves a combination of substitution S-box, fractal Tramino, and polynomial Chebyshev algorithms for encryption. The encryption process is outlined:
- Step 1 : substitution S-box initialization. Convert the input image matrix into binary form and partition it. Apply the SubByte operation using S-box substitution for each partition.
- Step 2: fractal Tramino initialization. Create a matrix R based on the image dimensions. Generate random keys kl and k2, calculate c using (5), and update R using (3).
- Step 3: Chebyshev initialization. Initialize keys p and q, calculate c and update matrix R based on conditional rules.
- Step 4: fractal Tramino processing. Generate fractal Tramino using the initialized matrix R and random keys kl and k2.
- Step 5: Chebyshev processing. Iterate through Chebyshev processing on the image matrix using keys p, q,x,y, kl, and k2. This involves applying Chebyshev polynomials and updating matrix R.
- Step 6: substitution S-box processing. Perform substitution S-box operation on the encrypted matrix obtained from the fractal Tromino and Chebyshev processing.
- Step 7: XOR operation. XOR the results obtained from fractal Tromino and Chebyshev processing to generate the final encrypted matrix.
- Step 8: output. The encrypted image is obtained as the result of the XOR operation.
Based on steps 1 to 8, the aforementioned process is visually represented in Figure 1, offering a comprehensive illustration of each stage in the encryption workflow as in Figure 1. Based on the fractal Tromino algorithm and Figure 2, the visual depiction clearly illustrates a sequence of steps through a series of processes outlined:
- Step 1 : the process begins by sampling the initialized image, typically represented as a matrix of dimensions M X N X 3 (height, width, and color channels). Subsequently, two random keys kl and k2 are generated using the generateRandomKey function. The mean (m) of the image matrix is computed through the mean (imageMatrix).
- Step 2: for each pixel in the initialized image, the algorithm undergoes M X 3N iterations. The computation of c is executed using the computeC (matrix, mean) function, involving the summation of absolute differences between each matrix element and the mean, as defined in (4). The computed c is then employed to update the fractal matrix R using (3).
- Step 3: the resultant matrix R is reshaped into a M X N X 3 matrix to yield the fractal Tramino. This generated fractal Tramino is subsequently returned.
- Step 4: the final step entails XORing the acquired fractal Tramino with the RGB image using the xorWithFractal (orilmage and fractalTromino) function and (6). This XOR operation finalizes the encryption process.
4. RESULTS AND DISCUSSION
In this experiment, the proposed image encryption method was implemented on a dedicated device with specifications including an Intel Core i? 10th Gen processor, RTX 3050 graphics card, 16 GB RAM, and a 256 GB SSD. The software execution was carried out using MATLAB 2021b. The dataset employed for this research consisted of PNG images widely used in related studies, namely Lena, Peppers, and Baboon. The visual representation of these images is depicted in Figures 3(a)-(d). As illustrated in Figures 3(a)-(d), the outcomes of the image processing procedure revealed distinct transformations in the Lena, peppers, and Baboon images. After the application of the proposed fractal Tromino-based image encryption algorithm, the processed images are visually represented in Figures 4(a)-(d). The testing phase, as depicted in Figures 4(a)-(d), presents a comprehensive evaluation of the proposed image encryption algorithm. The encrypted counterpart is featured in Figure 4(c), providing a visual insight into the transformation induced by the fractal Tromino-based encryption. To quantitatively assess the fidelity of the encrypted image, MSE and PSNR metrics were computed and are visually represented in Figures 5 and 6, respectively.
Figures 7(a)-(d) provides a comprehensive visual representation of the MSE and PSNR metrics across two significant iteration counts, namely 10x and 100x. The iterative nature of the proposed fractal Tromino-based image encryption algorithm is explored to understand its impact on the quality of encryption. The MSE and PSNR values are depicted in Figures 5 and 6, portray the evolution of dissimilarity between the original and encrypted images as the iteration count increases. In Figure 7(d), the visual representation encapsulates the essence of the proposed method, which amalgamates the distinctive attributes of the fractal Tromino algorithm, polynomial Chebyshev processing, and substitution S-box.
In a histogram, the horizontal axis (x-axis) represents the intensity values or brightness levels of an image. These values typically range from 0 to 255 in grayscale images, where 0 corresponds to black, 255 corresponds to white, and the values in between represent various shades of gray. For colored images, the intensity values for each color channel (red, green, and blue) are represented similarly. Meanwhile, the vertical axis (у-axis) indicates the frequency or the number of occurrences of each intensity value in the image. This frequency shows how many pixels in the image correspond to each specific intensity level, providing a clear representation of the image's overall contrast and brightness distribution.
Another test using UACI and NPCR provides additional insights into the proposed image encryption method. This evaluation is complemented by a comparative analysis with relevant studies, as outlined in Table 1. The juxtaposition of these findings with those from related studies enables a comprehensive assessment of the proposed method's efficacy in terms of pixel-level alterations and overall intensity changes. The comparative analysis presented in the table highlights the performance of the proposed image encryption method in contrast to several existing studies, as measured by the UACI and the NPCR. In terms of UACI, the proposed method demonstrates a value of 33.48, indicating the average changing intensity across encrypted images. This places it near the results obtained by Alghafis et al. [27], Khan et al. [28], He et al. [29], and Norouzi and Mirzakuchaki [30], where UACI values range from 33.44 to 33.50. On the NPCR front, the proposed method achieves a rate of 99.66%, outperforming the counterparts mentioned in the comparison. Khan et al. [19] closely trails the proposed method with a rate of 99.64%, while the others range from 99.57% to 99.63%. The final assessment involves computing the entropy of the encrypted images as a comprehensive measure of information content. Entropy, depicted in Table 1, serves as an essential metric to evaluate the randomness and uncertainty within the encrypted images. Based on the comprehensive quality measurements presented in Table 1, which focus on three benchmark images-Lena, Peppers, and Baboon-the optimal outcomes from each image are compiled in Table 2. The outcomes derived from the comprehensive evaluation presented in Table 2 offer a detailed assessment of the proposed method's performance, considering image datasets standardized to a size of 256x256x3.
5. CONCLUSION
The testing phase results reveal crucial insights into the performance of the proposed image encryption method across various sample images, namely Lena, Peppers, and Baboon, each standardized to a size of 256x256 pixels with three color channels. The MSE values, representing the average squared differences between the original and encrypted images, indicate that Lena has the highest MSE (4702), followed by Peppers (5321) and Baboon (3894). PSNR, a measure of image quality, exhibits corresponding trends, with Lena having the lowest PSNR (12.89 dB), followed by Peppers (11.12 dB) and Baboon (12.31 dB). UACI andNPCR show consistent values across all three images, emphasizing the stability of the proposed method. The entropy values remain constant at 7.9999 for all images, denoting a consistent level of disorder in the encrypted data. Overall, these quantitative metrics provide a comprehensive evaluation of the proposed method's efficacy in securing image data, considering both visual fidelity and encryption robustness. This research has laid a foundation for the integration of fractal tramino, polynomial Chebyshev, and substitution S-box methods in image encryption, showcasing promising results in terms of MSE, PSNR, UACI, NPCR, and entropy. For future endeavors, it is recommended to explore the impact of varying image sizes and types on the proposed method's performance. Additionally, considering the evolving landscape of cryptographic threats, further analysis of the algorithm's resistance against advanced attacks and its computational efficiency would be beneficial. Exploring the integration of other encryption techniques and conducting a comparative study with state-of-the-art methods could provide valuable insights into the proposed method's relative strengths and weaknesses. Furthermore, the research community could delve into optimizing the algorithm for real-time applications and expanding its applicability to diverse multimedia data beyond static images.
ACKNOWLEDGEMENTS
This research is supported by the Research Center for Intelligent Distributed Surveillance and Security, Universitas Dian Nuswantoro.
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