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This investigation delineates an innovative approach to fortify the secure key exchange process by integrating the robustness of the RSA algorithm with the unpredictability of a chaotic system, thereby advancing the security framework for color image encryption. Within this scheme, encryption keys are derived from a chaotic system, the initial conditions of which are dynamically modulated by the delta feature extracted from the source image. Such a design ensures that the system's behavior inherently adapts to the input image. The initial values and parameters governing the fivedimensional chaotic system are securely transmitted from sender to recipient via the RSA algorithm. Subsequently, diffusion and confusion processes are orchestrated through the application of two uniquely computed key matrices, which operate on the image at the column and row levels, respectively. This mechanism is instrumental in altering pixel values throughout the image. Performance evaluation of the proposed algorithm is quantified by several metrics: a high Number of Pixels Change Rate (NPCR) value of 99.621% illustrates its efficacy in pixel value modification, while a Peak SignaltoNoise Ratio (PSNR) value of 8.898 implies the retention of image quality postencryption. Furthermore, an Unified Average Changing Intensity (UACI) value of 33.823% signifies the algorithm's proficiency in introducing substantial variations in pixel intensities. The results corroborate the algorithm's competency in encrypting color images, underpinning its utility in diverse applications that necessitate stringent data and image protection measures against unauthorized access.
chaotic system, correlation, decryption, delta feature, encryption, initial conditions, RSA, sensitivit
Image encryption has emerged as a pivotal tool for the preservation of privacy across various domains, particularly within realms handling sensitive data such as medical imaging or personal photographs [1]. The application of encryption methodologies precludes unauthorized access to visual content, thereby ensuring the integrity of privacy [2, 3]. Cryptographic techniques are broadly categorized into symmetric and asymmetric systems. Symmetric Key Cryptography utilizes a singular key, which is consensually established between the sender and receiver. In contrast, Asymmetric Key Cryptography assigns unique public and private keys to each user [4]. Public keys are disseminated among all conversational participants, whereas private keys remain confidential to the individual user. The encryption process leverages the receiver's public key for message encryption, and the recipient uses their private key for decryption [5]. In the pursuit of heightened data security, researchers have advocated for the use of extensive keys within various cryptographic algorithms. While an enlarged key size is synonymous with fortified data protection, the complexity inherent in key management cannot be overlooked [6]. The RSA algorithm, a cornerstone in publickey cryptography, was introduced to the public domain in 1978 and represents a significant advancement in the field [7]. The fusion of chaotic systembased encryption with the RSA key exchange mechanism harnesses the intrinsic benefits of both systems. Chaotic systems are distinguished by their inherent stochasticity and unpredictability [8], whereas RSA offers a strong cryptographic framework predicated on publickey encryption techniques. By implementing a duallayered security strategy, the integrity of image transmission and storage is substantially reinforced [9]. Therefore, the proposed research seeks to amalgamate the RSA algorithm with a chaosbased encoding system for color image encryption. The RSA framework, which employs a dualkey system, facilitates secure key exchanges. This integration strives to strike an optimal balance between the efficacy of protection measures and the security of key exchange protocols.
In the domain of image encryption, significant strides have been made to enhance the security of visual data. In 2018, a novel encryption system was introduced, leveraging the virtual optical approach of phaseshifted digital holography in conjunction with RSA public key exchange [10]. The encryption keys are composed of multiple parameters, including the wavelength of the laser beam, the focal length of the test lens, the defocusing distance, and a scaling factor. The encryption process is executed by employing a holographic function that incorporates phase shifting, transforming a plaintext image into its encrypted counterpart. The RSA key exchange protocol is then employed to securely transmit cryptographic keys between the communicating parties.
The following year, a groundbreaking image encryption technique was proposed that merges the robust principles of RSA with chaotic maps [9]. This innovative method was designed to handle images of various sizes, initiating the encryption process with a permutation applied via 1D Skew tent maps and 1D Sin maps. This process served to rearrange the pixels of the input image, thereby contributing to the encryption's complexity.
In 2020, the evolution of image encryption methodologies witnessed the introduction of a technique that utilized the RSA algorithm to generate a pair of public and private keys [11]. During the encryption phase, a transformation map generated the initial key, which was derived from the cipher text key. Subsequently, this original key was input into a fractional hyperchaotic system equation to calculate the keystream, further complicating the encryption process and enhancing security.
In the ongoing quest to safeguard visual data, 2021 witnessed the introduction of a publickey image encryption technique predicated on pixel information and the insertion of random numbers [12]. During this process, two prime numbers were randomly selected and, in tandem with the public key, utilized for the synthesis of the private key. The plaintext data were encrypted via the RSA algorithm and subsequently subjected to key transformation mapping. The culmination of this process, involving diffusion and XOR operations, yielded the final encrypted image.
Concurrently, a distinct approach to image encryption was presented, which amalgamated the RSA algorithm with the dynamics of the Lorenz hyperchaotic system [13]. The RSA method was initially employed to generate starting values, which were then iteratively processed to produce the keystream. Additive mode diffusion was applied to alter the grey scale values and pixel locations, with the ultimate goal of dispersing pixel information uniformly across the encrypted image.
Upon comparison, it is evident that the studies of Abbas et al. [9] and Lin and Li [13] closely align with the system proposed herein; however, notable distinctions exist in the deployment of the RSA algorithm, as shown in Table 1. While both approaches integrate RSA within their respective frameworks, the intricacies of key generation and the subsequent encryption processes diverge, reflecting the unique contributions of each methodology to the field of image encryption. These innovations underscore the significance of RSA as a foundational element in the development of secure image encryption systems.
Table 1. Comparison between the proposed system and related works
References 
Encryption Method 
Key Used 
RSA Algorithm Recruitment Site 
Proposed 
Chaotic mapping system 5D with RSA. 
Shared public and private key with chaotic mapping system 5D. 
Protect the secure key exchange and transfer of initial values and parameters. 
[9] 
Chaotic mapping system with RSA. 
The shared public and private keys with the chaotic mapping system. 
Integrating RSA principles with chaotic maps. 
[10] 
Virtual optical method with RSA. 
Sharing a public and private key with other information such as focal length, laser wavelength, and blur distance. 
RSA public key exchange using virtual optical control, and digital holography. 
[11] 
a hyperchaotic fractal system with RSA. 
Using a transformation map and a chaotic hyperfractal system with a public and private key. 
Image encryption technique using transform map, hyperchaotic fractal system, and RSA algorithm. 
[12] 
Use RSA to insert pixel information and random numbers. 
Using RSA and key transformation with shared public and private keys. 
Image encryption using RSA to insert pixel information and random numbers. 
[13] 
Lorenz Hyperchaotic System with RSA. 
Lorenz Hyperchaotic System with Shared Public and Private Key. 
Image encryption technology using Lorenz Hyperchaotic system and RSA algorithm. 
A unique chaotic system based on a 5D framework was used with fourteen positive parameters and complicated, chaotic dynamics features. This system's fundamental attributes and dynamic properties are examined. According to the conclusions of the research, the new system has five Lyapunov exponents, which means that the system shows nonpredictive behavior and two unstable equilibrium points. Estimated the values for Kaplan Yorke and maximum positive Lyapunov exponent (MLE) are 3.12204 and 4.45994, respectively, which indicates the complexity of the structure of chaos within the system. The novel system demonstrates unpredictably unstable, highly complicated, and inconsistent features. The acquisition of the innovative fivedimensional autonomous system is accomplished by the following:
$\begin{aligned} & \frac{d x}{d t}=a y ub y w+c y\lambda x \\ & \frac{d y}{d t}=b x ze x u+f xg y \\ & \frac{d z}{d t}=h_1 x y+k u wl(zx) \\ & \frac{d u}{d t}=p w(y+z)q ub w \\ & \frac{d w}{d t}=b x yr z u+t_1 ul w\end{aligned}$ (1)
where, x, y, z, u, w, and tЄR^{+} referred to the states of sys a, b, c, λ, e, f, g, h_{1}, k, l, p, q, r and t_{1} are positive system parameters. The chaotic attractor of the 5D system "(1)" is observed when specific values are assigned to the system parameter. a=10, b=2, c=25, λ=40, e=0.5, f=30, g=0.1, h_{1}=9, k=3, l=4, p=15, q=19, r=.3 and t_{1}=34 And we assume that X(0)=1, Y(0)=0.5, Z(0)=5, U(0)=0.6, and W(0)=0.4 are the initial circumstances. The result of the Lyapunov exponent is obtained as follows: L_{1}=4.45994, L_{2}=0.4620, L_{3}=2.75930, L_{4}=17.72055, L_{5}=48.55465 Intricate and plentiful chaotic behaviors characterize the observed dynamics of this nonlinear system. Figure 1 depicts the 3D representation of the peculiar attractor, which resembles the motion of a butterfly in flight, which shows the chaotic nature and complexity of behavior [14]. The system exhibits complex and rich chaotic properties, and it contributes to understanding the nature of highdimensional dynamical systems that exhibit chaotic behavior and instability.
Figure 1. Chaotic attractor threedimensional view (xyz)
It is widely recognized that the waveform of a chaotic system exhibits a lack of periodicity. To establish the chaotic nature of the suggested system, it is necessary to provide evidence [15]. The graphic in Figure 2 illustrates the relationship between time and the state variable as generated from the simulation conducted using the MATHEMATICA software. The time domain representation of x(t) is depicted in Figure 2, illustrating its aperiodic nature.
Figure 2. Time versus x of the novel chaotic system
An efficient algorithm for securely encrypting color images using a 5D chaotic system is presented. The encryption keys are generated using differences extracted from the original image, which makes them difficult to predict, and enhances the security of the system. RSA technology is used to encode the different feature and initial parameters of the chaotic system during the transmission process. The process of decrypting the parameters is done using the RSA private key derived from the key values (p and q) chosen from the keys generated by the chaotic system. When conducting a set of experiments using different images using standards such as NPCR, UACI, Correlation Coefficient, MSE, PSNR, Information Entropy, and encryption and decryption time, the results showed the strength of the algorithm in achieving effective and secure encryption of color images. Comparing the performance of the proposed algorithm with some other algorithms, the proposed algorithm achieved superior results in many criteria as shown in Figure 3.
Figure 3. The diagram of the proposed encryption algorithm
Table 2. The algorithm of the delta feature
Algorithm 1. Compute delta feature value 
Input: r(row), image Output: Value of delta E Begin Step1: Extract the reference L*a*b* and measured RGB color values Step 2: Convert the measured RGB colors to the L*a*b* color space I_lab=rgb2lab(image); Step 3: initialize the deltaE variable to 0 dE=0; Step 4: iterate over image rows for i=1: r1 Step 5: compute deltaE for the entire block of pixels block1=I_lab (i: i+1, 1:2, :); block2=I_lab (i:i+1, 2:3, :); deltaE_block = deltaE (block1, block2); Step 6: sum up the deltaE values for this block dE = dE + sum(deltaE_block); Step 7: Normalize the delta features fet = mod(sum(dE),256); End algorithm 
Table 3. Utilize the computed delta feature value
Algorithm 2: Utilization of the computed delta feature value (fet) 
x (1) = initial value x (0) + fet * 0.002 y (1) = initial value y (0) + fet * 0.002 z (1) = initial value z (0) + fet * 0.002 u (1) = initial value u (0) + fet * 0.002 w (1) = initial value w(0) + fet * 0.002 
4.1 Compute delta feature value from image
Delta Features refer to the differences between two images or image regions. This can be calculated as the absolute or relative changes in pixel values, color channels, or texture features [16]. Computing the delta feature from an image and using it to change the initial condition in a chaotic system is an interesting approach to generating encryption keys. Chaotic systems are susceptible to initial conditions, so even a small change can lead to significantly different trajectories [14]. This property can be harnessed to create a unique and unpredictable sequence of values, serving as an encryption key. Algorithm 1 describes steps to extract the feature from an image in Table 2. For implementation, see Table 3.
4.2 Chaotic sequence generator
The state values of chaotic systems are often expressed as floatingpoint integers, and the sequences composed of these state values are not directly applicable in image cryptosystems [13]. In this specific phase, five unordered sequences are generated by employing the initial conditions and attributes linked to the recently established 5D hyperchaotic system (1). The mechanism under test is a hyperchaotic system that generates five sequences (xi, yi, zi, ui, wi) made up of real numbers The given sequences are subsequently converted into five vectors (key1, key2, key3, key4, key5) using the chaotic sequence.
4.3 Encryption image stage
The encryption algorithm employs the exclusive (XOR) operation to generate disorderly sequences within a fivedimensional chaotic environment. The procedure commences by selecting a prominent image, which is subsequently partitioned into blocks of a specified size, denoted as SB. The sequences are created using a confidential key, and the image is partitioned into three vectors (R, G, and B) for every block. The block image undergoes scrambling through the utilization of pseudocode, while the plain image is subjected to encryption via the use of five chaotic sequences formed during step 2. The generation of the encrypted image involves the merging of the red (R), green (G), and blue (B)Components inside each block lead to the creation of the ultimate encrypted image (Table 4).
Table 4. The proposed image encryption algorithm
Algorithm 3: Encryption algorithm 

Input 
Image, SB (Size Block), the Secret key: The initial conditions, parameters, and iteration for a 5D chaotic system. 
Output 
Encrypted Image 
Begin 

Step 1 
Compute the feature image using Table 1 and Table 2 
Step 2 
Iterate the proposed hyperchaotic system with a secret key to create five chaotic sequences [{K1},{K2},{K3},{K4},{K5}]

Step 3 
Divide the Image into Blocks and Create Vectors (R, G, B)

Step 4 
Scrambled Block Image sb (start block) eb(end block) Create two matrices for rows and column permutation Scramble Column = [w (sb+1: eb+1) u (sb+1: eb+1) x (sb+1: eb+1)]; first stage Scramble Row = [x(sb+1: eb+1) y(sb+1:eb+1) z(sb+1:eb+1)]; third stage Calculate the MSB (most significant bit) as the XOR of the first two bits of the jth element of the x component of the key as seen in Figure 3 second stage 
Step 5 
Encrypt plain Image with keys from 5D HyperChaotic System using XOR operation Use the five chaotic sequences {K1}, {K2}, {K3}, {K4}, and {K5} generated in step 2 to encrypt the plain image using the XOR operation 
Step 6 
Combine the R, G, and B components for each block into the final encrypted image. Combine the R, G, and B components obtained in step 5 to form the encrypted image. 
Step 7 
Output the encrypted image 
End 

Table 5. Creates an RSA public/private key
Algorithm (4): Generated RSA Key 

Input: Initial condition, parameters, delta feature, (x,y,z): chaotic system keys Ooutput: public &rivate key begin 

Step 1 
Initialization and Setup:

Step 2 
Main Loop to Generate Key Components:

Step 3 
Generate RSA Key Components

Step4 
Storing Key Components

Step 5 
Retrieve user input and RSA key components

End 

This study uses RSA technology to encrypt the delta feature and initial parameters of the chaotic system throughout the transmission process from the transmitter to the receiver. The recipient decrypts the parameters using their RSA key, derived from the prime values (p and q) selected from the keys created by the chaotic system (refer to Table 5). Implementing these steps guarantees the preservation of confidentiality and integrity, hence bolstering the security of color picture encryption.
The decoding procedure is initiated when RSA is used to transfer the original values and parameters of a fivedimensional chaotic system from the sender to the receiver and then reconstruct it at the receiving end. The system can adapt based on the original image. Decrypting the encrypted image involves using the initial values, delta feature, and keys generated within the decryption process and back XOR operation in reverse order. This process ensures security by incorporating precise details and maintaining the privacy of keys and information shared between the sender and the recipient (Figure 4).
Figure 4. Results of the test images: Plain images of (a) peppers, (b) butterfly, (c) village, (d) autumn landscape. Encrypted images of (e) peppers, (f) butterfly, (g) village, (h) autumn) landscape. Decrypted images of (i) peppers, (j) butterfly, (k) village, (l) autumn landscape
To assess the credibility and robustness of the method, a series of simulations were conducted utilizing the Matlab platform on the Windows 10 operating system. The chosen sample photos consist of "Peppers" and "Butterfly," both color images measuring 256×256 in size. The images titled "The Village" and "Autumn" have dimensions of 512×512 pixels. Several metrics and criteria are used to evaluate the effectiveness of the encryption method [10]. As shown in Table 6, reviewing the most common metrics.
7.1 Histogram analysis
A histogram is employed as a visual representation to illustrate pixel intensity distribution within an image. An encrypted image that meets the ideal conditions has a consistent frequency distribution, which means that potential attackers can't use it to learn anything useful about statistics. The histogram distribution of photos before and after encryption is depicted in Figure 5 [15].
7.2 The experiment results of the proposed system
As shown in Table 7, the NPCR value means that the attacker will have difficulty distinguishing patterns between the images and the encrypted images. The ideal UACI value would be close to 33.823%, a positive result indicating effective encryption. The correlation coefficient values indicate a very weak linear relationship, which is a positive result for the coding. A higher PSNR value indicates better image quality because the decoded image closely matches the original image. An ideal encryption process should result in maximum entropy, which indicates that the image is highly random and difficult to predict. The value of entropy 7.6981 indicates good randomness. Execution times are important to evaluate the efficiency of an algorithm, especially in realtime or resourceconstrained applications.
Table 6. Image encryption evaluation procedure
Metric 
Characterizations 
Equations 
Outline 
Number of Changing Pixel Rate (NPCR), Unified Averaged Changed Intensity (UACI) [17]. 
The NPCR technique, with an ideal range of 01, is highly suitable for encryption, while an ideal UACI value of 34 is recommended for a 512×512pixel image. 
$N P C R=\frac{\sum_{i, j} I(i, j)}{M \times H} \times 100 \%$ $\mathrm{UACI}=\frac{1}{\mathrm{M} \times \mathrm{H}}\left[\frac{\sum_{\mathrm{i}, \mathrm{j}} \mathrm{D}(\mathrm{i}, \mathrm{j})\mathrm{D}(\mathrm{i}, \mathrm{j})}{255}\right] \times 100 \%$ D and D’ are encrypted images before and after a single pixel change, with L representing the maximum supported value and T representing the total number of pixels. 
An NPCR value of 0.9 and a UACI value of approximately 0.33 are essential. 
Correlation Coefficient (CC)[14] 
defines the connection between original and encoded image pixels. The analysis includes horizontal, diagonal, and vertical components. CC scale can be negative or positive. 
$c c=\frac{\sum_{i m} \sum_{j n}\left(A A_{i j n}\overline{A A}\right)\left(B B_{m i j} \overline{B B}\right)}{\sqrt{\left(\sum_{i m} \sum_{j n}\left(A A_{i j n}\overline{A A}\right)^2\left(\sum_{i m} \sum_j\left(B B_{i j n}B \bar{B}\right)^2\right)\right.}}$ where, A and B are matrices of comparable dimensions, where (A̅=mean(A), B̅=mean(B)). 
The crosscorrelation (CC) value for an encrypted image is expected to be almost equal to zero. 
Mean Squared Error (MSE)[8] 
Validating error values that distinguish encrypted and plain images The MSE range is 0 to ∞. 
$\operatorname{MSE}=\frac{1}{M \times N} \sum_{i=0}^{m1} \sum_{j=0}^{n1}[A(i, j)B(i . j)]^2$ where, A and B are the encrypted and unencrypted images. In a m×n image size, pixels with coordinates (i, j) 
Images with a low (MSE) are often regarded as superior quality. 
Peak Signal to Noise Ratio (PSNR)[7] 
compare the quality of plain images with their encrypted counterparts. The Range of (PSNR) is quantified in decibels (dB) and spans from zero to infinity (∞). 
PSNR $=\frac{10 \times \log _{10}(2 X X1)^2}{M S E}$ where, X is the number of bits allocated per pixel. 
PSNR between original and decrypted images must be high. 
Information Entropy (IE)[14] 
It's the average data per image pixel. Pixels have different values. IE 0 TO +8. 
$H(m)=\sum_{i=0}^{N1} P\left(m_i\right) \log \left[P\left(m_i\right)\right]$ H(m) is the entropy of a message m, where p(m_{i}) is the probability of the symbol appearing. 
The IE value for an 8bit image should be closer to 8. 
Execution Time (ET) [18] 
It defines imageencryption time. Sum of compile and run times. Measurements are ms, secs, and minutes. 
 
ET should affect the encryption scheme value less. 
Figure 5. The histogram for the original and encryption image using the proposed algorithm
Table 7. The experiment results of the proposed system
Images Metrics 
Peppers 
Butterfly 
Village 
Autumn 

NPCR 
99.617 
99.5911 
99.5977 
99.6202 

UACI 
% 33.82 
% 32.323 
% 34.9335 
% 33.6567 

Correlation Coefficient 
0.00532 
0.0014 
0.0014 
0.0013 

(MSE) 
Encryption 
8651.05 
7555.80 
9273.46 
8394.69 
Decryption 
0 
0 
0 
0 

(PSNR) 
Encryption 
8.7601 
8.0566 
8.4584 
8.8908 
Decryption 
∞ 
∞ 
∞ 
∞ 

Information Entropy 
Original 
7.6981 
7.8353 
7.8307 
7.6681 
Encryption 
7.9991 
7.9990 
7.9998 
7.9997 

Decryption 
7.6981 
7.8353 
7.8307 
7.6681 

Execution Time 
Key generate 
0.380580 
0.34499 
0.93776 
0.90332 
Encryption 
0.52734 
0.52772 
2.16187 
2.02593 

Decryption 
0.52288 
0.53269 
2.21767 
2.09913 
Table 8. A comparison between the proposed study and other systems
Ref. Metrics 
Proposed 
Ref. [7] 
Ref. [19] 
NPCR 
99.621 
100% 
99.706 
UACI 
% 33.65 
% 38.14 
33.461 
Correlation Coefficient 
0.0014 
0.367 
0.0075 
PSNR 
8.8908 
41.27 
8.0132 
Information Entropy 
7.9998 
2.747 
7.9974 
Table 9. Comparison of the proposed system with other systems for Lena (256×256) and (512×512)
Metrics 
Lena 256×256 
Lena 512×512 

Propose 
Ref. [20] 
Ref. [21] 
Propose 
Ref. [20] 
Ref. [21] 

NPCR 
99.615 
99.6114 
99.766 
99.611 
99.608 
99.7470 
UACI 
31.452 
33.4954 
36.7148 
31.352 
33.4558 
36.7368 
CC 
0.0011 
0.0072 
0.0029 
0.0011 
0.0028 
0.0015 
IE 
7.9993 
7.9974 
7.9955 
7.9998 
7.9993 
7.9989 
PSNR 
8.6251 
/ 
36.3461 
8.6262 
/ 
35.3924 
To correctly identify and quantify these leverage points, it's critical to undertake a comprehensive examination and comparison of the proposed encryption method and current systems, as shown in Tables 8 and 9. Several comparison criteria could be employed depending on the objectives and specifications of the encryption system and the environment in which it will be utilized. Additionally, a thorough evaluation of security, performance, and other pertinent variables should be used to determine the best encryption method.
The results of the image encryption algorithm presented in this paper demonstrate its effectiveness in providing secure and dynamic color image encryption. The algorithm leverages a fivedimensional chaotic system with tested features such as unpredictability and sensitivity to initial values, supported by a positive Lyapunov exponential. Key generation dynamically adapts based on delta feature values extracted from the original image, enhancing the system's security. The high NPCR value of 99.621 indicates that the encryption algorithm induces significant changes in pixel values between the original and encrypted images. This is a positive sign of the algorithm's ability to perturb the image data effectively. An ideal UACI value of 33.823% suggests that the encryption algorithm introduces substantial changes in pixel intensities, reinforcing that it effectively obfuscates the image content. A low correlation coefficient value of 0.00532 between the original and encrypted images indicates a minimal similarity, further confirming the algorithm's ability to obscure the original content. The increase in information entropy from the original to the encrypted image (7.6981 to 7.9991) signifies that our encryption algorithm introduces a high level of randomness and unpredictability into the data, a desirable characteristic in encryption. However, the decrypted image also has an entropy value of 7.6981, which indicates the decryption. process effectively restores the original information content, as the entropy value returns to a level similar to that of the original image. Regarding execution time, we observed the following values (in seconds): Key Generation: 0.38058, Encryption: 0.52734, and Decryption: 0.52288. These execution time results indicate that our encryption algorithm is efficient and practical for realworld applications. essential for secure communication. Encryption and decryption times are also reasonably quick, making the algorithm suitable for use in scenarios where realtime or nearrealtime processing is required.
This effort was made possible with assistance from Mustansiriyah University.
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