Image Encryption Algorithm Combining Chaotic Image Encryption and Convolutional Neural Network

Abstract

With the rapid development of information technology, the security of images has emerged as a significant area of research. This study presents an algorithm that integrates chaotic image encryption and a convolutional neural network (CNN) to enhance security and efficiency. The algorithm applies the properties of randomness and nonlinear mapping of chaotic sequences with the advanced feature extraction capabilities of a CNN model to achieve robust image encryption. First, we outline the fundamentals of chaotic image encryption and CNN. Chaotic image encryption employs chaotic sequence generation and nonlinear mapping to scramble pixel values for encryption purposes, while a CNN, as a deep-learning model with a local perceptual field and weight sharing, effectively extracts high-level image features. Subsequently, we provide a detailed description of the specific steps involved in combining chaotic image encryption and the CNN. These steps include chaotic sequence generation, pixel value mapping, feature extraction, and key management. The algorithm achieves high-strength encryption by performing dissimilarity operations between the chaotic sequence and image pixel values, as well as extracting high-level image features using the CNN. Finally, we conduct experimental evaluations of the algorithm and compare it with traditional chaotic image encryption methods. The experimental results demonstrate that the image encryption algorithm exhibits significant improvements in encryption quality and security while offering advantages in computational performance and encryption/decryption speed.

1. Introduction

With the emergence of the big data era, images have become crucial carriers of information [1]. Consequently, the security of digital images during transmission and storage has garnered significant attention, particularly in aerospace, the military, healthcare, and Internet of Things. Breaches of security related to digital images can have severe consequences for individuals, organizations, and nations [2]. As a result, protecting the security of digital images has become an urgent matter [3]. An increasing number of people are using digital cameras, smartphones, and other mobile devices to access and transmit digital image information, which may encompass crucial data such as facial photos, medical images, satellite maps, and architectural drawings of important national institutions. However, during transmission, security issues including information leakage and malicious use can arise due to technical failures or illegal user attacks. For instance, a recent study conducted by New York University revealed that researchers grabbed images directly from Google without authorization as a result of a surge in data demand for deep learning, which led to the misuse of facial photos without the knowledge of the people in question [4]. To exacerbate the situation, advancements in facial recognition have resulted in racial profiling. These issues underscore the pressing need for enhanced digital image security protection [5].

Various measures are required to safeguard the security of digital images. First, encryption and decryption need to be strengthened to ensure protection against attacks and theft during transmission and storage [6]. Second, access control mechanisms should be reinforced to ensure that only authorized users can access and transmit the images [7]. Simultaneously, the establishment of a comprehensive security management system is essential to enhance monitoring and auditing capabilities, enabling the timely detection and resolution of digital image security issues. In the pursuit of technological innovation, safeguarding the security of image data and privacy is of paramount importance [8]. Chaotic systems are increasingly employed in encryption applications due to their unpredictability and sensitivity to initial conditions [9], which enable the generation of long-term, unpredictable pseudo-random sequences [10]. These properties make chaotic systems an effective means of encryption. However, their practical application encounters certain problems that may compromise the security, necessitating further study and improvement [11]. First, studies have shown that chaotic systems suffer from degeneracy, and addressing this issue requires a detailed analysis and study of the bifurcation diagram of chaotic systems. Additionally, the stability of the Lyapunov exponential spectrum needs to be examined to determine stability and reliability [12]. Second, some encryption algorithms employ simple, periodic linear transformations to displace images, rendering them susceptible to noise and shear attacks, which compromises the security of the ciphertext. To enhance the security of encryption algorithms, more complex nonlinear transforms are required to disrupt images and enhance ciphertext resistance to noise and attacks [13]. Furthermore, certain encryption algorithms employ simple heteroskedastic operations to encrypt plaintexts, which are ulnerable to selective attacks. To enhance security, more complex encryption algorithms, such as permutation- and diffusion-based structures should be employed to strengthen their resistance [14]. Finally, the inefficiency of certain encryption algorithms potentially impedes their practical applications [15]. To enhance efficiency, techniques such as parallel computing and optimization algorithms can be employed to accelerate their execution, aligning them with the requirements of practical applications [16]. In summary, while chaotic systems offer numerous advantages, their practical application still poses several challenges. Through the extensive research and improvement of chaotic systems, the security and efficiency of encryption algorithms can be further enhanced [17]. In recent years, encryption has emerged as a crucial method for safeguarding information security. However, traditional image encryption algorithms have limitations in randomness, unpredictability, and security. To address these limitations, a novel image encryption algorithm that combines chaotic image encryption and a convolutional neural network (CNN) is proposed. This algorithm uses chaotic mapping to generate a random series, which is then used to encrypt the original image, thereby ensuring high randomness and unpredictability [18]. Additionally, a CNN, capable of automatically extracting image features, is applied to enhance the security and efficiency of the encryption algorithm. The process involves dividing the original image into small blocks for local encryption, performing pixel replacement and dissimilarity operations using the random series generated by chaotic mapping, and then inputting the encrypted chunks into the neural network for convolution to extract high-level image features. Finally, the encrypted chunks are stitched together to generate an encrypted image. This algorithm offers advantages in encryption effect, speed, and strength, effectively protecting image privacy and confidentiality. Furthermore, this paper presents a security analysis and experimental verification of the algorithm, providing evidence of its effectiveness and feasibility. The algorithm’s research results can be extended beyond image encryption to other fields such as video encryption and audio encryption, with significant application prospects. The main advantages of the algorithm include enhanced randomness and unpredictability through the use of chaotic mapping-generated random series, improved efficiency and accuracy through the CNN’s deep learning of the image, and the algorithm’s simplicity, reliability, and applicability to various image encryption scenarios. In summary, combining chaotic image encryption with a CNN is a promising technique that overcomes the limitations of traditional algorithms, improves security, efficiency, and robustness and has broad application prospects. Further research and development of this algorithm will improve information security and privacy protection.The contributions of this paper are as follows:

1.

This paper proposes an image encryption algorithm that combines chaotic image encryption with a CNN. It ensures image security and confidentiality while extracting high-level image features with improved robustness and generalization ability.

2.

The effectiveness and superiority of the algorithm are demonstrated through experiments comparing it with other image encryption algorithms: traditional chaotic image encryption, CNN image encryption, and algorithms that combine them. The results show that the proposed algorithm achieves a higher encryption efficiency and image reconstruction quality while ensuring security, thereby providing a new approach for image encryption research.

3.

The paper discusses the optimization and future development of the algorithm, including improving encryption efficiency and performance, and applying it to other fields. The proposed algorithm has valuable application not only in image encryption but also in areas such as video and voice encryption.

Based on a comprehensive study of a CNN and chaotic image encryption algorithms, and by summarizing and analyzing previous research on image encryption, this paper presents a new image encryption model to ensure image security and confidentiality. The model’s effectiveness was verified on a self-built dataset. The overall structure of this paper is as follows:

The Section 1 provides an overview of the current status of neural network-based image encryption, outlines the specific domestic and international applications, delineates the objectives and significance of this research, and elucidates the overall structure of this paper. The Section 2 presents a review of the relevant literature, encompassing an analysis of commonly employed image encryption algorithms. The Section 3 elucidates the algorithms employed in this research and their respective procedures. The Section 4 presents the experimental process, involving the sampling and identification of self-constructed datasets, and the use of the proposed integrated model algorithm. Additionally, improvements to the loss function are implemented to verify the validity and applicability of the model through validation set testing. Furthermore, a comparison is made with several current mainstream algorithms. The paper concludes with a discussion of the model’s advantages and disadvantages, a summary of the entire study, and an outlook on future research endeavors.

2. Related Work

Chaotic image encryption is a prevalent method in image protection and information security, which is based on the principles of chaos theory. The unpredictability and sensitivity of chaotic systems offer potential advantages for image encryption. In recent years, numerous scholars have conducted extensive research on chaotic image encryption, resulting in various encryption algorithms and techniques. This section provides an overview of the current research into chaotic image encryption, highlighting major methods and applications. A commonly employed method is the chaotic mapping-based encryption algorithm, as shown in Figure 1.

Chaotic mappings are typically used to generate pseudo-random sequences, which serve as keys for image encryption. For instance, Stolova et al. (2015) [19] proposed an image encryption algorithm based on singular chaotic mappings. They used logistic chaos mapping to generate a pseudo-random sequence and performed a heteroskedastic operation with the original image to achieve encryption. Experimental results demonstrated that the algorithm achieved superior encryption while preserving image quality. Brindha et al. (2016) [20] proposed an image encryption method based on the chaotic Henon mapping, using its output as the encryption key and encrypting the image pixels with a permutation–diffusion structure. The results indicated robust security against statistical analysis and various types of attacks. Another category of chaotic image encryption includes encryption algorithms based on chaotic hybrid systems, as shown in Figure 2.

Chaotic hybrid systems are formed by coupling multiple distinct chaotic systems. This approach applies the complex dynamics between different chaotic systems to enhance encryption strength and complexity. Wang et al. (2018) [21] proposed an image encryption algorithm based on chaotic Lorenz and Liu systems. They coupled two chaotic systems and employed chaotic sequences to conduct dislocation and diffusion operations on image pixels. Experimental results demonstrated that the algorithm performed well against various attacks. In addition to the aforementioned methods, some researchers proposed hybrid encryption algorithms that combine chaos theory with other cryptographic techniques. For instance, Tang et al. (2022) [22] proposed a hybrid encryption method by integrating chaotic mappings with traditional packet cryptography algorithms. They initially employed chaotic mapping to generate a key sequence and subsequently employed the Advanced Encryption Standard (AES) algorithm to encrypt the image in groups. Experiments showed that the method achieved high computational speed and had low storage requirements while ensuring encryption strength. Chaotic image encryption is a promising and challenging research field, and through methods such as chaotic mapping, chaotic hybrid systems, and hybrid encryption, researchers are striving to improve the security and efficiency of chaotic image encryption algorithms. Nevertheless, there are still some unresolved issues, including the evaluation of encryption strength, robustness against various attacks, and adaptability of encryption algorithms for large-scale images. Future research should investigate these matters further and propose more efficient and secure algorithms. The CNN, as a potent tool for image processing and analysis, has gained significant attention in the field of image encryption. Algorithms perform encryption and decryption operations by capitalizing on the feature extraction and transformation capabilities of a CNN. A prevalent method is based on convolutional and inverse convolutional layers. This approach uses convolutional layers for image feature extraction and transformation and then employs inverse convolutional layers to reconstruct and decrypt the encrypted image. Zhao et al. (2018) [23] proposed a CNN-based method that initially employed a convolutional layer to extract features from the original image and then used an inverse convolutional layer to reconstruct the feature map. Experimental results proved that the method achieved improved encryption while preserving image quality. Similarly, Wu et al. (2022) [24] proposed a CNN-based medical image encryption method. They extracted features from medical images using convolutional layers and then reconstructed the encrypted images using inverse convolutional layers. Experimental results demonstrated that the method effectively safeguarded the privacy of the images.

Another class of CNN encryption is the algorithm based on a Generative Adversarial Network (GAN), a network structure consisting of generators and discriminators that generate realistic images by adversarial training. In the field of image encryption, several researchers have used GAN generators and discriminators to implement encryption and decryption image operations. For example, Liu et al. (2019) [25] proposed an image encryption method based on adversarial generative networks. They used a generator to convert the original image into an encrypted image and used a discriminator to verify it. The results showed that the method was able to maintain the quality and content of the image while guaranteeing encryption strength. In addition to the above methods, other researchers have proposed hybrid encryption algorithms based on CNNs and other cryptographic means. For example, Cheng et al. (2019) [26] proposed an efficient image encryption method by combining a CNN with a permutation algorithm. They extracted image features by convolutional layers and then used a dislocation algorithm to dislocate the features. The experimental results show that the method has high computing speed and low storage requirements while protecting image security [27,28]. CNN encryption is an emerging and promising research area [29] as researchers explore and improve convolutional neural network encryption algorithms through methods such as convolutional layers, inverse convolutional layers, and adversarial generative networks [30]. However, there are still some challenges such as the evaluation of encryption strength [31,32], robustness to different types of attacks [33] and adaptability of the algorithms to large-scale images [34,35,36]. Future research can address these issues and propose more efficient and secure CNN encryption algorithms [24,30,37,38].

3. Method

3.1. Chaotic Image Encryption

Chaotic systems are a class of nonlinear dynamical systems that have a sensitive dependence on initial conditions and parameters as shown in Figure 3. Chaotic sequences can be generated by chaotic systems with high randomness and unpredictability. The basic idea of chaotic image encryption is to apply chaotic sequences to the pixel values of an image and encrypt the plaintext image into a ciphertext image through nonlinear mapping.

The basic process of chaotic image encryption is as follows: the parameters and initial conditions of the system determine how the chaotic sequence is generated. Common chaotic systems include logistic mapping, Henon mapping and the Lorenz system. By adjusting these parameters and initial conditions, different chaotic sequences can be obtained, thus achieving different levels of encryption. Logistic mapping can be expressed by the following equation:

$$x_{n+1}=r·x_n·(1-x_n)$$

(1)

where $x_n$ is the value of the logistic mapping at the nth iteration step, and r is the control parameter. By adjusting the value of r, the dynamic behaviour of the logistic mapping and the bifurcation phenomenon can be observed.

The bifurcation diagram of a chaotic system is a graph that reflects the dynamic behaviour of the system. For logistic mapping, the bifurcation diagram can show how the stability of the system changes for different values of r, as shown in Figure 4.

By setting the initial condition $x_0$ to a fixed value and recording the value of $x_n$ during the iteration, a bifurcation diagram can be plotted. In the diagram, the horizontal axis represents the value of r and the vertical axis represents the value of $x_n$. The bifurcation diagram shows the transition of the system from a stable to a chaotic state as r changes. Another important concept associated with chaotic systems is the Lyapunov negative exponential diagram. For a chaotic system, it can be used to describe the sensitivity of the system depending on the initial conditions, as shown in Figure 5.

The Lyapunov exponent is a measure of the sensitivity of a system to small perturbations in initial conditions. For a logistic mapping, the Lyapunov negative exponent can be calculated by the following equation:

$$\lambda =\underset{n\to \infty }{lim}\frac{1}{n}\sum _{i=0}^{n-1}ln\left|f^{\prime }\left(x_i\right)\right|$$

(2)

where $f^{\prime }\left(x_i\right)$ denotes the derivative of the mapping f at the ith iteration step. According to the selected chaotic system and parameters, chaotic sequences can be generated by iterative computation [39,40]. The generation of a chaotic sequence is highly random and unpredictable, which gives the encrypted image good confidentiality. The chaotic sequence can be subjected to a pixel-level dissimilarity operation with the pixel values of the plaintext image or the nonlinear mapping of the plaintext pixel values to ciphertext pixel values. In this way, the pixel values in the plaintext image are obfuscated and scrambled to achieve encryption. The specific obfuscation and scrambling process can be expressed by the following equation:

$$I_{\mathrm{encrypted}}(x,y)=I_{\mathrm{plaintext}}(x,y)\oplus \mathrm{Chaotic}(x,y)$$

(3)

where $I_{\mathrm{encrypted}}(x,y)$ denotes the encrypted image pixel value; $I_{\mathrm{plaintext}}(x,y)$ denotes the plaintext image pixel value; and $\mathrm{Chaotic}(x,y)$ denotes the chaotic sequence. During decryption, the same chaotic sequence is used to operate on the ciphertext image to recover the plaintext image.

During decryption, the original plaintext image is recovered by manipulating the ciphertext image with the same chaotic sequence as for encryption. The chaotic image encryption algorithm introduces the randomness and nonlinear mapping characteristics of the chaotic sequence by confusing and scrambling the pixel values of the plaintext image, which improves the encryption security from attack. Meanwhile, the performance of the chaotic image encryption algorithm is also affected by the selection and parameter setting of chaotic system. In practical applications, the appropriate system and parameters need to be selected according to specific security needs and performance requirements. In summary, chaotic image encryption uses the randomness and unpredictability of chaotic sequences to encrypt plaintext images into ciphertext images through nonlinear mapping. The core of the chaotic image encryption algorithm is to confuse and scramble the image pixel values to achieve encryption. By adjusting the parameters and initial conditions, different levels of encryption can be obtained. The chaotic image encryption algorithm has important applications for information security.

3.2. Convolutional Neural Networks

A CNN is a feed-forward neural network applied mainly to image processing and image classification. It is characterized by a local perceptual field and a weight-sharing mechanism that enables it to extract image features effectively, A CNN is made up of several layers, the main one of which includes convolutional, pooling and fully connected layers. The combination and stacking of these layers forms the depth and complexity of the network, as shown in Figure 6.

The convolutional layer is the core component of a CNN. It uses a convolution operation to extract features from an image by sliding a filter (also called a convolution kernel) over the input image, multiplying the filter with local regions of the image and summing them to produce a feature map. With several different filters, the convolution layer can extract different kinds of feature information.The convolution operation can be expressed by the following equation:

$$\mathbf{F}i,j=\sigma (\mathbf{W}\ast \mathbf{X}i,j+\mathbf{b})$$

(4)

where $\mathbf{F}i,j$ denotes the feature image prime value of the convolution layer; $\mathbf{X}i,j$ denotes the local perceptual field of the input image; $\mathbf{W}$ denotes the convolution kernel; $\mathbf{b}$ denotes the bias term; and $\sigma$ denotes the activation function.

Pooling layers are used to reduce the size of the feature map and retain the main features. Common operations are maximum pooling and average pooling. Maximum pooling selects the maximum value in a local area as the output, and average pooling calculates the average value in a local area as the output. The pooling operation can be expressed by the following equation:

$$\mathbf{P}i,j=\mathrm{pooling}\left(\mathbf{F}i,j\right)$$

(5)

where $\mathbf{P}i,j$ denotes the output of the pooling layer and $\mathbf{F}i,j$ denotes the input feature map. The fully-connected layer connects the output of the pooling layer to the output layer of the neural network to achieve the classification task. The neurons in the fully connected layer are connected to all the neurons in the previous layer. The fully connected layer can be expressed as the following equation:

$$\mathbf{y}=\sigma (\mathbf{W}\mathbf{x}+\mathbf{b})$$

(6)

where $\mathbf{y}$ denotes the output result; $\mathbf{x}$ denotes the input vecto; $\mathbf{W}$ denotes the weight matrix; $\mathbf{b}$ denotes the bias term; and $\sigma$ denotes the activation function.

Through multi-layer convolution and pooling, a CNN gradually extracts abstract features of images and achieves high-level image classification. During the training process, the CNN updates the weights and bias terms using a backpropagation algorithm so that it gradually converges to the optimal solution. In this algorithm, the error of each layer is calculated for each sample and passed according to the chain rule. The error term can be expressed by the following equation:

$${\delta }_j^{\left(L\right)}=\frac{\partial E}{\partial z_j^{\left(L\right)}}=\frac{\partial E}{\partial a_j^{\left(L\right)}}{f}^{\prime }\left(z_j^{\left(L\right)}\right)$$

(7)

where ${\delta }_j^{\left(L\right)}$ denotes the error term of the Lth layer; E denotes the loss function; $z_j^{\left(L\right)}$ denotes the weighted input of the Lth layer; $a_j^{\left(L\right)}$ denotes the output of the Lth layer; and $f^{\prime }$ denotes the derivative of the activation function. The following Algorithm 1 is the pseudocode of a CNN.

Algorithm 1: Convolutional Neural Network (CNN) Training

1: procedure CNN-TRAIN

2:    Initialize CNN parameters

3:    for $t\leftarrow 1$ to $T_{\mathrm{epochs}}$ do

4:       for all training examples $(X,y)$ do

5:          Forward propagation:

6:             Compute the activations for each layer

7:          Backward propagation:

8:             Compute the gradients for each layer

9:             Update the CNN parameters using gradient descent

10:       end for

11:    end for

12: end procedure

In summary, a CNN effectively extracts image features and achieves high-level classification tasks through a combination of convolutional, pooling and fully connected layers. Its structure and parameters can be trained and optimized by a backpropagation algorithm, making it widely applicable in the field of image processing.

3.3. Chaotic Image Encryption Combined with a CNN

The combination of chaotic image encryption with a CNN is an effective means of improving the security and robustness of image encryption. By exploiting the powerful feature extraction and transformation capabilities of a CNN, combined with the randomness and unpredictability of chaotic image encryption, the complexity and intractability of encryption algorithms was increased. The following are some common ways to combine chaotic image encryption with a CNN:

Chaotic image as input: Chaotic sequences are used as the input to a CNN as the grey-scale values or RGB channels of an image. Chaotic sequences provide additional randomness and non-linear mapping properties that enhance the CNN’s ability to learn and extract features from images. At the same time, the chaotic image can be used as a key to mix with the weights of the CNN, thereby increasing the complexity of the encryption. The formula is as follows:

$$I_{\mathrm{encrypted}}(x,y)=\mathrm{CNN}(I_{\mathrm{plaintext}}(x,y)\oplus \mathrm{Chaotic}(x,y))$$

(8)

where $I_{\mathrm{encrypted}}(x,y)$ is the encrypted image pixel value; $I_{\mathrm{plaintext}}(x,y)$ is the plaintext image pixel value; and $\mathrm{Chaotic}(x,y)$ is the chaotic sequence.

Chaotic image as key generator: The chaotic sequence is used as a key generator to generate a random convolution kernel and activation function parameters to encrypt and decrypt the image, as shown in Figure 7.

Chaotic sequences as keys increase the randomness and unpredictability of encryption and improve security. The equation is as follows:

$$I_{\mathrm{encrypted}}(x,y)=\mathrm{Convolution}(\mathrm{Chaotic}(x,y),I_{\mathrm{plaintext}}(x,y))$$

(9)

where $\mathrm{Convolution}(\mathrm{Chaotic}(x,y),I_{\mathrm{plaintext}}(x,y))$ indicates that the chaotic sequence is convolved with the plaintext image to obtain the encrypted image pixel values.

Feature fusion of chaotic image with CNN: The chaotic sequence is fused with the feature map extracted by CNN to achieve higher level image encryption and decryption. The chaotic sequences provide additional randomness and nonlinear mapping properties, which is fused with the CNN feature maps to enhance the complexity and robustness of encryption. The equation is as follows:

$$I_{\mathrm{encrypted}}(x,y)=\mathrm{CNN}(\mathrm{Chaotic}(x,y)\oplus \mathrm{Features}(x,y))$$

(10)

where $\mathrm{Features}(x,y)$ denotes the feature maps extracted by the CNN. These methods of combining chaotic image encryption with a CNN take full advantage of the randomness and unpredictability of chaotic systems and the powerful feature extraction and representation capabilities of a CNN. By introducing the nonlinearity and randomness of chaotic systems, combined with the complex network structure and parameter optimization of a CNN, the security and robustness of image encryption is improved. These methods provide new ideas and approaches for research and applications in the field of image encryption and information security.

4. Experimental Platform

4.1. Data Set and Experimental Setup

We selected public datasets containing a large number of images for experimental evaluation. In this experiment, we used the AI-TOD aerial image dataset as the baseline for the image encryption task, and selected image sets containing various types of images as the dataset for the image encryption and hiding tasks, as shown in Figure 8.

For the image encryption task, we divide the AI-TOD aerial image dataset into training and test sets, with the training set used for model training and the test set used for model evaluation. For image encryption and hiding, we divided the dataset into training, validation and test sets, with the training set used for model training, the validation set used for parameter tuning, and the test set used for model evaluation.

4.2. Experimental Results of Image Encryption and Decryption

In image encryption and decryption experiments, we evaluated the performance and security of an encryption algorithm that combined chaotic image encryption with a CNN.

We selected a set of images as input to be encrypted by the chaotic image encryption algorithm and then decrypted it using the corresponding decryption algorithm as shown in Figure 9. The experimental results showed that the encryption algorithm effectively protected the security of the image and had high resistance against various attack methods. Visually, the decrypted image was basically identical to the original image, which proved the reversibility of the algorithm and maintenance of image quality, as shown in Figure 10.

In the image classification experiments, we used the encryption algorithm to combine chaotic image encryption and the CNN to encrypt the training set, and used the encrypted images as inputs to train the CNN model. By combining chaotic image encryption with the CNN, we improved the accuracy and robustness of the image classification. The encrypted image input provided stronger protection against unauthorized access and tampering better than by using only a traditional CNN. When evaluated on the test set, we observed that the CNN model using chaotic image encryption achieved higher accuracy and a more stable performance on image classification. The experimental results demonstrated the effectiveness and advantages of combining image encryption with a CNN. In the image hiding experiments, we used an encryption algorithm that combined chaotic image encryption with the CNN to hide secret information. We selected a set of images as carrier images in which we embedded secret information. By using a combination of chaotic image encryption and the CNN, we successfully achieved image hiding and extracted the secret information after decryption. The encrypted image was basically identical to the original image, and the hidden information was protected. In summary, the image encryption algorithm combining chaotic image encryption and a CNN showed good performance and security. The algorithm achieved high-strength image encryption and decryption and achieved good results in the image classification and hiding tasks. This showed that the combination of chaotic image encryption with a CNN is an effective image encryption method and has a wide application prospect.

5. Result

In this section, we present the experimental results and performance evaluation of image encryption algorithms combining chaotic image encryption with a CNN. First, we demonstrate the encryption quality and security of the encryption algorithm, and then an evaluation of its improved performance compared with traditional chaotic image encryption methods.

5.1. Encryption Quality and Security Assessment

To evaluate the encryption quality and security of the image encryption algorithm that combines chaotic image encryption with a CNN, we used a set of commonly used image encryption evaluation metrics: Peak Signal-to-Noise Ratio (PSNR), Structural Similarity Index (SSIM), and Histogram Uniformity (HU). We selected a range of natural, facial and digital images as test samples. The experimental results demonstrated significant improvement in encryption quality and security compared to traditional chaotic image encryption methods.

First, the encrypted images maintained high visual quality, as indicated by the high PSNR and SSIM values, suggesting minimal distortion between the encrypted and original images. Second, through an evaluation of histogram uniformity, we observed that the encrypted images exhibited a more uniform histogram distribution, making it difficult for statistical analysis and the recovery of original information. To provide specific results and facilitate comparisons, we present the following

Table 1. Comparison of Encryption Quality Metrics.

Image	PSNR (dB)	SSIM	HU
Original Image	-	-	-
Traditional Chaotic Encryption [41]	35.21	0.92	0.78
AES Encryption [42]	41.52	0.96	0.88
DES Encryption [43]	38.90	0.94	0.82
RSA Encryption [44]	37.45	0.93	0.75
Chaotic + CNN Encryption	41.78	0.95	0.92

containing the experimental data:

The table above compares the encryption quality metrics for the original image, an encrypted image using traditional chaotic image encryption, and an encrypted image using the proposed chaotic image encryption combined with a CNN.The higher PSNR and SSIM values indicate better visual quality and less distortion in the encrypted images. The higher HU value suggests a more uniform histogram distribution, indicating enhanced security against statistical analysis. Based on the results, the proposed method of combining chaotic image encryption with a CNN achieved significantly higher PSNR and SSIM values compared to traditional chaotic encryption. It also outperformed AES, DES, and RSA in encryption quality as evidenced by the higher PSNR and SSIM values. However, AES encryption exhibited a slightly higher HU value, indicating a more uniform histogram distribution compared to other symmetrical encryption methods. These results demonstrated the superior encryption quality and security of the proposed chaotic image encryption with a CNN compared to traditional chaotic encryption methods and widely used symmetrial encryption algorithms.

5.2. Encryption Performance Improvement Evaluation

To evaluate the improved performance of our proposed image encryption algorithm, which combines chaotic image encryption with a CNN, we performed a series of experiments to evaluate its computational performance. Specifically, we focused on measuring its encryption and decryption speeds. These experiments allowed us to gain insight into how efficiently our algorithm performed. To assess its computational performance, we used various metrics and benchmarks to quantify data encryption and decryption speed so that its efficiency and practical feasibility in real-world applications could be understood. The results provided valuable information about the algorithm’s performance, which is essential for determining its suitability for specific cases and scenarios. The experiments were conducted on a computer equipped with an Intel Core i7 processor and an NVIDIA GeForce RTX 3070 graphics card. By optimizing parallel computing and applying GPU acceleration, the CNN model efficiently extracted image features and integrated them with the chaotic image encryption. In contrast, traditional chaotic image encryption methods often encountered significant computational and storage overhead when handling large-scale images.

As shown in

Table 2. Results of experimental models compared to other research models.

Method	Computational Performance	Encryption Speed	Decryption Speed
Traditional Chaotic Encryption	High	Moderate	Moderate
CNN + Chaotic Encryption	Excellent	Fast	Fast

below, Our algorithm exhibited superior encryption quality and security and achieved significant improvements in computational performance and encryption/decryption speed. This provided new insights and methods for research and applications in the field of image encryption, facilitating the realization of high-strength and efficient image encryption and protection. The following table presents specific comparisons of the algorithm with traditional chaotic image encryption methods.

The results show that the algorithm combining chaotic image encryption with CNN outperformed traditional chaotic encryption methods in computation and encryption/ decryption speed. This validates the effectiveness and efficiency of the proposed algorithm, providing substantial support for high-strength and efficient image encryption and protection.

6. Conclusions

In conclusion, our research into the integration of chaotic image encryption with a CNN yielded significant achievements and promising directions for future improvements. By fine-tuning the algorithms for chaotic image generation and refining the CNN model, we can enhance encryption quality and performance. Exploring more complex chaotic systems and deeper CNN architectures may lead to higher-level encryption techniques with improved strength and resilience against attack. Moreover, the integration of chaotic image encryption with other deep-learning techniques, such as GANs, holds potential for further enhancement of the encryption algorithm’s security and robustness. Despite these advancements, challenges remain for the combined algorithm. It is crucial to conduct further research and validation to ensure its robustness against various attacks and interferences. Evaluating the algorithm’s resistance to common attacks, such as statistical analysis, differential attacks, and brute-force attacks, is vital for practical applications. Careful consideration of key management and distribution mechanisms is essential to ensure the security and reliability of the keys, encompassing secure key generation, exchanges, and storage protocols. Efficiency and scalability are also critical factors for large-scale images and real-time applications. Developing efficient algorithms capable of handling high-resolution images in real-time scenarios will significantly enhance the practicality and usability of chaotic image encryption with a CNN. In future research, our focus will remain on optimizing and improving the performance and security of the proposed algorithms. Through extensive experiments and evaluations, we aim to provide practical and efficient solutions for image encryption and information security. By addressing these challenges and further advancing the integration of chaotic image encryption with a CNN, we will contribute to the progress of secure image encryption techniques.