A Robust Image Encryption Framework Using Deep Feature Extraction and AES Key Optimization

Abstract

This article presents a novel framework for encrypting color images to enhance digital data security using deep learning and artificial intelligence techniques. The system employs a two-model neural architecture: the first, a Convolutional Neural Network (CNN), verifies sender authenticity during user authentication, while the second extracts unique fingerprint features. These features are converted into high-entropy encryption keys using Particle Swarm Optimization (PSO), minimizing key similarity and ensuring that no key is reused or transmitted. Keys are generated in real time simultaneously at both the sender and receiver ends, preventing interception or leakage and providing maximum confidentiality. Encrypted images are secured using the Advanced Encryption Standard (AES-256) with keys uniquely bound to each user’s biometric identity, ensuring personalized privacy. Evaluation using security and encryption metrics yielded strong results: entropy of 7.9991, correlation coefficient below 0.00001, NPCR of 99.66%, UACI of 33.9069%, and key space of 2²⁵⁶. Although the final encryption employs an AES-256 key (key space of 2²⁵⁶), this key is derived from a much larger deep-key space of 2⁸¹⁹² generated by multi-layer neural feature extraction and optimized via PSO, thereby significantly enhancing the overall cryptographic strength. The system also demonstrated robustness against common attacks, including noise and cropping, while maintaining recoverable original content. Furthermore, the neural models achieved classification accuracy exceeding 99.83% with an error rate below 0.05%, confirming the framework’s reliability and practical applicability. This approach provides a secure, dynamic, and efficient image encryption paradigm, combining biometric authentication and AI-based feature extraction for advanced cybersecurity applications.

1. Introduction

We rely more and more on digital media and data transmission across modern networks, thus it is important to protect digital information from unauthorized access [1]. To keep visual data safe, encryption is necessary. The idea is to make it impossible to read the original image until the proper key is pressed. Because of this [2], the data stays secret and cannot be changed or stolen. AES, DES, and XOR are examples of traditional encryption methods that have a lot of problems. The most important thing about them is that they employ fixed or randomly generated keys that do not rely on the picture’s main features. Because of this constraint [3], the system may not be as safe against pattern analysis and brute-force attacks. Some older encryption algorithms may have had problems with data loss or worse image quality following encryption and decryption [4]. To make encryption safer, you should look at new AI and deep learning techniques [5]. We can make photographs more resistant to cryptographic assaults by using CNNs to extract features and the PSO approach to improve encryption keys. Because of this, each picture will have a high entropy and be one of a kind [6]. This article presents a unique method for photo encryption and decryption that maintains image quality via the integration of CNNs with PSO. The objective is to create a strong and unique AES key for each photo. We may look forward to new scientific discoveries on how to protect digital data, a better encryption method that works with more types of photos, and a big step forward in security compared to prior methods [7].

AES is one of the most popular systems of its type because it is so hard to break using brute-force attacks. Why? Because its base is built on methods that employ permutations and substitutions [8]. The XOR approach is straightforward and fast, but it does not work well with short keys or patterns that repeat [9]. The DES algorithm, which was formerly an important part of early encryption technologies, is not good enough for today’s security demands since its key length is too short and it is vulnerable to parallel computing assaults [10]. Traditional methods work, but they put the security of certain mission-critical applications at risk because they employ static or random keys that do not take into consideration the unique features of the encrypted pictures [11].

CNNs, on the other hand, are great at processing pictures because they can recognize patterns and features very well [12]. This capability has been employed in security applications like fingerprint identification and face recognition, but it is still not widely used for generating encryption keys [13]. Identifying unique traits using CNNs might lead to better and more data-connected encryption keys, which could make the data safer [14]. But when it comes to hard areas, the PSO approach has been quite good at finding the best solutions and optimizing parameters [15]. Some of its uses are to make neural networks operate better, tweak algorithm settings, and create hybrid encryption systems [16]. PSO is a suitable option for improving encryption keys because it can adapt to different space exploration needs [17]. This lets it keep a lot of randomness while making the keys less alike. The literature does not present a cohesive methodology that amalgamates the advantages of CNNs for feature extraction, PSO for feature optimization to produce optimal encryption keys, and the subsequent incorporation of these keys into the prevalent AES algorithm for enhanced security [6]. This clearly shows that further study needs to be done in this area. We believe that this gap calls for the creation of a new research paradigm for photo encryption that makes full use of AI and deep learning methods. Table 1 shows the main results and shows how this research is better than and different from earlier ones.

Table 1. Summarizes the most relevant studies and highlights the features and innovations that distinguish the current research from them.

Reference	Technique Used	Strengths	Weaknesses
[18]	Uses a CNN to extract image features, then encrypts the resulting blocks with AES using multiple keys derived from a master key.	Offers enhanced security via multi-key block encryption, leveraging AES efficiency and CNN feature representation.	Involves higher computational overhead than single-key methods; block-based processing may reduce performance for large images; lacks PSO-based optimization.
[19]	Combines PSO, AES, and GAN to generate high-entropy encryption keys and evaluate performance on medical images.	Provides strong security through high-entropy keys, enhanced diversity via GAN, and demonstrates superior performance for medical image encryption.	High complexity, slower encryption/decryption, no direct CNN feature integration, and high computational demands.
[20]	Provides a comprehensive overview of encryption methods, emphasizing AES, Twofish, and key evaluation metrics.	Provides a solid foundation of key metrics, highlights research gaps, and offers a comparative benchmark for new studies.	Primarily theoretical, lacking practical CNN + PSO + AES implementation and not always covering the latest innovations.
[21]	Uses PSO to select parameters and initial values for a chaotic system, with Scrambling/Diffusion/Confusion techniques applied to encrypted images.	Improves entropy and enhances chaotic system properties; good performance in image encryption; relatively efficient speed if PSO is not applied to each individual image.	Does not employ CNN for feature extraction; key or chaotic system is not directly tied to the image features; may not suit applications requiring data-dependent keys.
[22]	Utilizes a 3D hyper-chaotic map + CNN + image encryption through scrambling, along with key sensitivity analysis.	High security against small key variations; good noise resistance; comprehensive analysis of entropy and distributions.	Does not employ PSO for key optimization; computations with chaotic maps may be complex; AES is not directly applied.
[23]	Employs a CNN-autoencoder to extract features from multimedia files, then encrypts them using AES.	Direct integration of CNN and AES; supports multimedia file processing for greater flexibility; solid experimental evaluation.	No optimization algorithms like PSO for key enhancement; entropy level and similarity across multiple keys not reported.
Current Study (2025)	Integrates CNN for extracting unique image features with PSO to optimize AES keys.	Combines CNN, PSO, and AES to create dynamic, high-entropy keys with strong attack resistance.	Not yet tested on a large scale (still under development and evaluation in this research).

This study may utilize a person’s fingerprint to build an encryption key, which would let them communicate private photographs to someone else. The first thing you should do to verify the sender’s identity is to look it up in the main CNN model. The second model employs fingerprint data to produce an encryption key once authentication is done. To protect the secret picture, an AES key is created and utilized. This guarantees the greatest degree of data protection and privacy. Combining the speed of AES encryption with the capacity of deep learning to find unique fingerprint traits makes dynamic and user-specific keys. Because of this, the data that was delivered is kept hidden, and it is difficult to attack. Even if past attempts have made encryption better, the problem of producing picture-specific AES keys utilizing a mix of CNN feature extraction, PSO optimization, and direct application has not been addressed. This initiative is new because it wants to fill a gap in knowledge.

This study also has these additional things:

(1)

Proposing a dynamic mechanism for AES key generation based on deep features extracted from images using Convolutional Neural Networks (CNNs), thereby directly linking the encryption key to the image content.

(2)

Integrating the Particle Swarm Optimization (PSO) algorithm to optimize the generated encryption keys, ensuring high entropy levels and reduced statistical correlation between successive keys.

(3)

Introducing a key management model that does not require key storage, transmission, or reuse, where a unique key is generated for each transmission, thereby enhancing security against key interception attacks.

(4)

Adding an independent security layer on top of the standard AES framework without affecting its internal structure or proven cryptographic efficiency.

(5)

Demonstrating the effectiveness of the proposed framework through experimental evaluations and benchmark comparisons, showing improved resistance to brute-force attacks and pattern analysis compared to conventional approaches.

The article is organized as follows: Section 1 provides the introduction, which includes Section 2, the background, and Section 3, the research objective, outlining the motivation, problem statement, and purpose of the study. Section 4 describes the methodology, detailing the theoretical framework, model architecture, and implementation procedures adopted in the proposed encryption framework. Section 5 presents the results and analysis, including the performance evaluation of the neural models, encryption metrics, and comparative assessments demonstrating the system’s effectiveness. Finally, Section 6 delivers the conclusion, summarizing the key findings and offering recommendations for future research directions aimed at enhancing the proposed system’s scalability and adaptability to emerging security challenges

2. Theoretical Background

This section reviews the theoretical foundations of the proposed image encryption framework, focusing on classical techniques and the integration of artificial intelligence to enhance security.

2.1. Image Encryption

Image encryption is a basic part of information security since it changes original images into a format that cannot be understood and can only be put back together with the right decryption key. In this case, traditional algorithms like AES, DES, and XOR have been used [24]. But these methods have problems since they use fixed key structures and may find patterns, which makes the overall security weaker. So, there has been a rising demand to combine encryption with artificial intelligence approaches to make randomness and privacy better [25].

2.2. Convolutional Neural Networks (CNNs)

This is because they can learn features from visual input on their own, thus there is no need for humans to do feature engineering [26]. CNNs commonly link convolutional layers that can find edges, textures, and basic forms in pictures so that they can find local patterns. After that, pooling layers maintain the most important information and make the data less complex. Because of this, the model is stronger and easier to figure out as the items in the image move about [27]. You can make an accurate feature vector that shows the picture’s properties by putting the derived representations into fully connected layers that combine the features you got [28]. CNNs may help with picture identification and classification, but they can also build encryption keys by looking at each image’s unique features. The features taken from the photographs are always changing, thus it is hard to guess what keys will be made. This strategy is less likely to lead to repetition or key prediction than more traditional methods [14]. This study employs two CNN models to decipher fingerprint images. Check out Figure 1 to see how many levels there are, what sorts of layers there are, and how each layer takes features from the image. It also gives a summary of how all the models utilized in this research were made.

Figure 1. Components of CNN models used.

The initial model figures out who someone is by looking at their ID number. The second model gets the detailed fingerprint attributes when the identification check is done. They both use convolutional layers to automatically and progressively pull out essential features from the input data. This makes things more efficient and helps build strong encryption keys by looking at minor visual patterns. The two models are trained using the backpropagation method, using loss functions that are specific to each task. This idea uses the unique identifier in the file name to accurately identify the fingerprint’s owner.

2.3. Theoretical Background on PSO

PSO is one of the most widely recognized swarm intelligence algorithms, initially introduced in 1995 by Kennedy and Eberhartp [29]. The fundamental idea of PSO is inspired by collective behaviors observed in nature, such as bird flocking or fish schooling during migration or foraging, where particles cooperate to converge toward the global optimum [30]. In this algorithm, each potential solution is represented as a particle that moves within the search space. The movement of each particle is guided by two main factors:

(1)

Personal Best (pBest): The best solution identified by the particle itself.

(2)

Global Best (gBest): The best solution found by the entire swarm [31]. The velocity and position of each particle are updated using dynamic mathematical equations, most notably

v_i(t + 1) = w × v_i(t) + c1 × r1 × (pBesti − x_i(t)) + c2 × r2 × (gBest − x_i(t))

(1)

x_i(t + 1) = x_i(t) + v_i(t + 1)

(2)

In this case, xi is the particle’s position, vi is its speed, and www is the inertia weight that controls the balance between exploration and exploitation. Parameters c1 and c2 control how individual and group experiences affect the movement of particles on the solution space and progressively move toward the best placements when the position update is included in the iterative process. This is possible because they learn both individually and as a group [32]. PSO improves key generation for image encryption by changing the positions of particles, which stand for potential encryption keys, over and over again until it finds the optimum safe solution [33]. This makes the recommended encryption method stronger and protects it from both classic and new cryptographic attacks [34]. Figure 2 displays the flow diagram of the process for optimizing encryption keys using the PSO approach.

Figure 2. Flowchart of the PSO-based encryption key optimization process.

2.4. Fitness Function for PSO in Key Generation

In the proposed PSO-based optimization for image encryption, the fitness function is defined as the Shannon entropy of the generated encryption key. This ensures that each key is highly random, unpredictable, and resistant to statistical attacks. The entropy (H) is calculated as follows:

$$H\left(X\right) = -{\sum }_{i=1}^{n}p\left(xi\right) log2 p\left(xi\right)$$

(3)

where p(xi) is the probability distribution of the value xi in the key. If the entropy equals 8 bits, it means the key is completely random. The PSO algorithm iteratively updates particle positions, each particle representing a potential key to maximize the entropy-based fitness function. This process ensures that the selected keys are adaptive, unique for each transmission, and not permanently stored, thereby enhancing the overall security of the encryption system.

3. Research Objective

This research aims to develop a robust framework for digital image encryption based on deep learning and artificial intelligence, with the goal of enhancing data security and achieving a high level of confidentiality without relying on traditional key exchange. The proposed system employs two neural models: the first for user authentication, and the second for extracting fingerprint features and converting them into high-entropy encryption keys using Particle Swarm Optimization (PSO), which are then applied with the Advanced Encryption Standard (AES-256) [35] to secure images. The main objective is to integrate artificial intelligence with traditional encryption methods to generate dynamic and unique keys in real time, preventing interception or reuse while providing strong resistance to differential and statistical attacks. The research also seeks to enhance performance and classification accuracy, as the neural models achieved an accuracy exceeding 99.83% with an error rate below 0.05%, confirming the system’s reliability and practical applicability. This framework aims to establish an intelligent and dynamic encryption model that combines biometric identity, deep learning, and optimization algorithms, making it applicable to diverse fields such as cloud systems, the Internet of Things (IoT), and military communications, while being resilient to future quantum computing threats. It represents a significant step toward a new generation of secure, self-learning encryption systems.

4. Proposed System

The proposed encryption system consists of two main stages: the encryption stage and the decryption stage. Each stage represents a fundamental component in the system’s operation to ensure data confidentiality and integrity. Below, the details of each stage are presented, and their steps are explained in a systematic and precise manner.

4.1. Encryption Stage

Figure 3 below illustrates the constituent stages of the encryption phase in the proposed system and the sequence of operations within it. Figure 3 consists of several interconnected stages, providing a comprehensive view of the methodological sequence of this phase. These stages begin with data loading, followed by preprocessing, analysis, and segmentation, then model building, training, and performance evaluation, proceeding to key verification, generation, and optimization using the PSO algorithm, and finally image encryption using the AES algorithm. Each of these stages will be explained in detail in the following sections. This stage represents the core pillar of the proposed system, as it involves generating the encryption key based on a CNN built on fingerprint data, which is then used in the encryption process. The flowchart in the first stage of the system illustrates the constituent phases of this process, which can be summarized as follows:

Figure 3. Flowchart illustrating the steps of the proposed system.

4.1.1. Database Loading Stage

One of the most important things to do before starting is to make sure that the right data is ready to make key creation as accurate and secure as possible. The SOCOFing database utilized in this analysis has six thousand unique fingerprints from six hundred persons (ten fingerprints apiece). To provide additional variety to the training data, around 49,270 fake fingerprints are made with three degrees of variation: easy (very little variation), medium (moderate variation), and hard (very high variation). For model training, we utilize the synthetic fingerprints, and for testing, we exclusively use the actual fingerprints.

4.1.2. Data Preprocessing Stage

This stage aims to prepare the images in a way that makes them suitable for processing by the CNN model and includes the following steps:

A. Image Dimension Standardization

All images are resized to uniform standard dimensions (96 × 96 pixels) to ensure compatibility with the model requirements and processing efficiency. Equation (4) represents the resizing process as follows:

I′(x′,y′) = I (y/Sy,x/Sx)

(4)

where

• I(x,y): The original image.
• I′(x′,y′): The image after resizing.
• Sx and Sy: Scaling factors for the image dimensions [36].

B. Image Enhancement via Histogram Equalization

To enhance the clarity of fine fingerprint details, the histogram equalization technique is applied. This method aims to improve the distribution of gray levels within the image, thereby increasing contrast and enhancing pattern distinguishability. In low-contrast images, gray values are often confined to a narrow range, causing loss of fine details in dark or bright areas. Histogram equalization redistributes these values over a wider range, contributing to clearer visualization of fingerprint details. Equation (5) [37] mathematically represents this process.

$$H\prime \left(I\right)={\displaystyle \frac{CDFmin-CDF\left(I\right)}{\left(NXM\right)-CDFmin}(1-L)}$$

(5)

where

• H′(I): Represents the new gray value after the transformation.
• CDF(I): The Cumulative Distribution Function (CDF) of gray levels at intensity I.
• CDFmin: Denotes the smallest non-zero value of the cumulative distribution function.
• N × M: Refers to the total number of pixels in the image (its size).
• L: The number of available gray levels in the image, typically 256 for 8-bit depth images. The purpose of this equation is to map the original intensity values to new values that are approximately uniformly distributed over the gray scale range [0, L−1], thereby enhancing contrast and improving the input image quality before it is used in subsequent encryption stages. Figure 4 illustrates the effect of applying histogram equalization on fingerprint images. It shows that the enhanced images exhibit higher contrast, highlighting fine details such as edges and linear patterns, which contributes to better feature extraction and increases the efficiency of fingerprint recognition systems.

Figure 4. (a) Original fingerprint images. (b) Images after applying histogram equalization.

4.1.3. Database Analysis Stage

At this essential point in the proposed system, each enhanced fingerprint is carefully examined to find unique features like patterns and significant places inside the fingerprint. This method aims to create a database rich in intrinsic information so that the models can pick up on the unique traits of each fingerprint. To get basic information like the person’s identity, finger type, and hand (right or left), you look at the file names. This design makes it simpler to get the data ready since one model learns to identify the individual, and the other learns to tell what sort of finger it is. After doing these things, the data is split into two groups: one for testing and one for training. The synthetic fingerprints are utilized for practice, while the real fingerprints are only used for testing. This lets us know that we are judging the models’ performance fairly and appropriately.

4.1.4. Model Construction Phase

After completing the database preparation, image preprocessing, and enhancement, the process transitions to the model construction phase using CNNs. In this phase, two independent models are developed to achieve specific objectives:

• The first model is dedicated to identifying the individual’s identity (SubjectID) through deep learning of the unique fingerprint characteristics.
• The second model focuses on determining the finger number (FingerNum) and extracting distinctive features related to the internal fingerprint structure, such as patterns and minutiae.

Each model consists of a set of carefully organized layers to ensure high performance in feature recognition and optimal accuracy, as illustrated in Figure 2. To further enhance learning efficiency and stabilize the models, hyperparameters are meticulously fine-tuned according to the criteria presented in Table 2. This phase ensures that each model is capable of systematically and accurately extracting essential information from fingerprints, thereby paving the way for the subsequent stage of generating encryption keys and employing them for data protection.

Table 2. Hyperparameter settings of the CNNs used in the system.

Hyperparameter	Value
Number of Convolutional Layers	3
Batch Size	64
Filter Size	3 × 3, 5 × 5
Filters per Layer	32–64–128
Activation Function	ReLU, Softmax, tanh
Optimizer	Adam
Learning Rate	0.0001
Epochs	20
L2 Regularizer	regularizers.l2 (0.001)
Loss Function	Categorical Crossentropy
Dropout	0.3, 0.4
MaxPooling	MaxPooling2D (pool_size = (2, 2))

4.1.5. Model Training and Evaluation Phase

The training and evaluation phase of the two models is one of the most critical steps to ensure the efficiency and accuracy of the system in fingerprint recognition and encryption key generation. The performance of each model is evaluated using standard performance metrics such as Accuracy, Validation, and Error Rate, in order to guarantee the reliability of the results. The first model is validated for its ability to accurately recognize the identities of authorized individuals when requesting an encryption key, thereby ensuring a high level of system security. The second model is assessed based on its performance in correctly identifying the finger associated with the verified identity provided by the first model. This ensures accurate feature extraction and alignment with the individual’s identity. These evaluations are conducted using the test set to verify the models’ performance in a simulated real-world environment, thus guaranteeing the reliability and robustness of the system before proceeding to the key generation and data encryption phase.

4.1.6. Identity Verification and Encryption Key Generation

The individual and fingerprint are verified against the registered name using two deep learning models. This step represents a fundamental stage in the process of generating the encryption key from fingerprints, as illustrated in Figure 5.

Figure 5. Biometric identity verification and key generation process.

4.1.7. Key Optimization Using PSO Algorithm

To strengthen the initial encryption key and ensure higher security, the PSO algorithm is employed as an optimization mechanism. This algorithm enhances the random distribution of the key and improves its cryptographic robustness, thereby making it highly resistant to prediction or compromise. The optimization process relies on iteratively updating the positions and velocities of particles derived from individual fingerprints, as illustrated in Figure 2. Through continuous refinement based on both local and global best positions, the algorithm produces encryption keys with greater complexity and resilience. This raises a critical research question: “How effectively can the proposed system withstand statistical attacks?” The approach is specifically designed to minimize the likelihood of repetitive patterns that could otherwise be exploited by such attacks. The set of hyperparameters adopted for this optimization process, determined through extensive experimental trials, is summarized in Table 3.

Table 3. Optimization algorithm hyperparameters adopted in the system.

Unit/Explanation	Description/Value	Parameter
Lower bound of the range	0	lb
Upper bound of the range	255	ub
Number of particles in the swarm	len(keys)	num_particles
Maximum number of iterations	200	num_iterations
Inertia weight	0.9	w
Cognitive coefficient (personal best focus)	0.5	c1
Social coefficient (global best focus)	0.5	c2
Random factor for cognitive component; varies per particle	0.5	r1
Random factor for social component; varies per particle	0.5	r2
Initial positions of the particles	keys	particle_positions
Initial velocities of the particles	zeros	particle_velocities
Personal best positions	Updated based on the best performance of each particle	personal_best_positions
Best scores achieved by each particle	Calculated through fitness evaluation	personal_best_scores
Global best position	Updated based on the global best performance	global_best_position
Global best performance	Updated based on the global best value	global_best_score

4.1.8. AES-Based Image Encryption Phase

After completing the previous steps, during which a 1024-element key vector is generated using the CNN and then optimized via the PSO algorithm to enhance randomness and entropy, the encryption phase begins using the AES with a 256-bit key. The integration of neural networks and swarm algorithms makes the key unpredictable and computationally hard to break, as illustrated in Figure 6, which shows the encryption phase using the AES algorithm.

Figure 6. Flowchart of the AES-based image encryption phase.

The following provides an explanation of each step of the AES algorithm:

Step 1: Key Derivation

The optimized key from CNN + PSO is denoted as K_CNN+PSO = [x₁, x₂, …, x₁₀₂₄]

First, this vector is converted into a byte representation.

Then, a hash function (SHA-256) is applied to extract a 256-bit key as follows: K_AES = SHA-256(K_CNN+PSO)

Step 2: Image Partitioning

The image data is divided into equal-sized blocks, each 128 bits (16 bytes) long.

Each block is denoted as B_i, where B_i ∈ {0, 1}¹²⁸, i = 1, 2, …, n

Step 3: Initial Round (AddRoundKey)

Each block B_i is combined with the initial round key K_round0 using XOR: S₀ = B_i ⊕ K_round0

Step 4: AES Rounds

Since the key is 256 bits long, the algorithm performs 14 iterative rounds. Each round (except the last) includes the following:

• SubBytes: Replace each byte using the substitution box (S-Box): S′_ij = S − Box(S_ij)
• ShiftRows: Row r is shifted left by r positions: Row_r → Row_r ≪ r
• MixColumns: Each column (C_j) is multiplied by a fixed matrix (M) in GF(2⁸): C′_j = M × C_j
• AddRoundKey: The state matrix (S) is combined with the round key: S = S ⊕ K_round

The final round includes only SubBytes + ShiftRows + AddRoundKey (without MixColumns).

Step 5: Producing the Encrypted Image

After completing all rounds, the encrypted blocks C_i are obtained. By combining them, the final encrypted image is formed: I_enc = ⋃ C_i, where i = 1 to n.

Advantages of the Proposed Method

• Increased entropy of the encryption key: H(K_AES) → maximum value
• High resistance against brute-force and statistical attacks.
• Homogeneous distribution of the encrypted image histogram.
• Strong balance between computational efficiency and security level.

4.2. Decryption Phase

This phase is critical for verifying the overall reliability and robustness of the encryption-decryption framework. This phase is similar to the stages described in the encryption section, with the main difference being that the models are not rebuilt or retrained but loaded from previously saved copies. The encryption stage is replaced by the decryption phase to ensure accurate recovery of the original data. Figure 7 illustrates this phase and its sub-stages.

Figure 7. Stages of the decryption process.

• Data loading phase: Limited to loading only the encrypted data produced during the previous encryption phase.
• Data preprocessing phase: The encrypted data is prepared and processed for the subsequent decryption stage.
• Data analysis phase: The encrypted data is analyzed to extract the necessary information for key matching and ensure accurate retrieval.
• Loading the previously saved models: Models trained during the encryption phase are loaded for use in the decryption process.
• Verification and key generation: The data is verified, and the decryption key is regenerated.
• Key optimization stage using PSO: The key is optimized using the PSO algorithm to enhance randomness and retrieval accuracy.
• Image decryption phase using AES: Decryption is performed using the AES algorithm, restoring the original image with high quality and precision. This framework ensures the integrity of the decryption process while maintaining model stability and reliable data recovery, thereby enhancing security and efficiency in the proposed system.
• Performance evaluation and comparison: The decrypted images and keys are evaluated against security and quality metrics to ensure consistency with the encryption phase and to benchmark the framework against conventional methods. All operations in this phase are designed to maintain consistency and minimize potential errors during the decryption process.

5. Analysis and Results

This section aims to evaluate the efficiency and reliability of the proposed encryption system through a series of carefully designed experiments. The evaluation includes testing the strength of the generated keys, the security level against statistical, visual, and brute-force attacks, and the system’s ability to accurately recover the original images after decryption without any loss of quality. To demonstrate the effectiveness of the proposed hybrid model, benchmark images from widely recognized datasets are utilized, along with visual and graphical examples illustrating the encryption and decryption processes. All experiments are implemented in Python (3.11) using the Kaggle cloud environment, which provides advanced resources for machine learning applications. The experimental setup included an NVIDIA Tesla P100 GPU (16 GB), dual Intel Xeon processors (2.0 GHz), and 32 GB RAM. This infrastructure enabled efficient execution of experiments within the allocated computational time. For practical evaluation, two primary databases are employed: the SOCOFing Fingerprint Database, which is used to generate encryption keys based on data from 600 individuals and 49,270 synthetic fingerprints, and the USC-SIPI Image Database, which is used to assess encryption effectiveness through metrics such as entropy and pixel correlation, in addition to testing system resistance against statistical, visual, and differential attacks. The analysis is conducted on two complementary levels: neural key analysis, to assess randomness and entropy strength, and encryption analysis, to evaluate the system’s efficiency and security in protecting and recovering data. To avoid any ambiguity, it is important to note that the comparative evaluation presented throughout the experimental analysis is entirely quantitative. For each security evaluation metric, including entropy, correlation, NPCR, UACI, and key sensitivity, numerical comparison tables with recent state-of-the-art methods are provided. These quantitative results enable an objective, measurable, and fair assessment of the proposed framework, rather than a qualitative or descriptive comparison.

5.1. Neural Key Analysis

This section consists of four main components:

• The performance of the CNN model.
• Results of the encryption key evaluation and related metrics.
• Results of applying the PSO algorithm to enhance the encryption key.
• Comparison of the accuracy of the proposed models with other systems.

5.1.1. The Performance of the CNN Model

The results of each component are presented and explained in detail. The dataset is split into 80% for training and 20% for testing to ensure neutrality and avoid bias. After training, the models’ performance is evaluated using the Accuracy function from the TensorFlow library, with TensorBoard employed to continuously monitor performance accuracy and loss values during both training and testing. The results showed high accuracy and gradual improvement in performance across different epochs. Table 4 and Figure 8, Figure 9 and Figure 10 displayed the accuracy and loss values. The false-positive rate reached 0.000185, confirming the reliability of the proposed models and their efficiency in generating strong and effective encryption keys.

Table 4. Model performance comparison: accuracy and loss.

ID_Name Fingerprint Example	Model No	Training Accuracy (%)	Testing Accuracy (%)	Training Loss	Testing Loss
331 right little	1	99.73334	0.9943	0.0563811	0.0947
331 right little	2	99.833333	0.9856	0.1004451	0.1387

Figure 8. Accuracy (a) and loss (b) curves of the subjectID model.

Figure 9. Accuracy (a) and loss (b) curves of the FingerNum model.

Figure 10. Confusion matrix and accuracy metric.

The testing and training loss values are very low, indicating that the model learns efficiently and generalizes well to new data. The testing and training accuracy values are very high, exceeding 99 percent, which shows that the model provides highly accurate and reliable fingerprint classification results. Overall, the model demonstrates strong and stable performance with excellent efficiency on both training and testing data. The SubjectID and FingerNum recognition models achieved perfect or near-perfect ac-curacy, with precision, recall, and F1-score reaching 1.00 across all classes, confirming the effectiveness of the proposed recognition framework. Figure 8 illustrates the accuracy (a) and loss (b) curves of the subjectID model. It can be observed that both training and validation accuracy increased rapidly from the beginning of training, reaching approximately 100%, indicating that the model learned the patterns with high precision. Moreover, the loss values gradually decreased for both training and validation data until approaching zero, demonstrating that the model has excellent learning efficiency and a high ability to generalize without signs of overfitting.

Figure 9 shows the accuracy (a) and loss (b) curves for the FingerNum model, where the training and validation accuracy gradually increased until they approached 100%, while the loss clearly decreased until it neared zero, indicating that the model has strong performance and excellent stability in the process of finger type recognition.

The confusion matrix in Figure 10 shows that the model correctly recognizes most classes, with very few errors between some classes, reflecting high accuracy and strong performance in finger type classification.

5.1.2. Results of the Encryption Key Evaluation and Related Metrics

The neural key generated from the CNN model is evaluated using specialized metrics to ensure its quality and effectiveness against cyberattacks, including key size and randomness tests such as entropy and repetition. Experiments are conducted in the Kaggle environment using fingerprint images sized 96 × 96.

(1)

Key Space Analysis

The designed key consists of 1024 values (0–255), yielding a total size of 1024 bytes and an extremely large key space (2⁸¹⁹², providing strong resistance against brute-force attacks). Despite this high theoretical security, practical performance evaluation is essential to ensure compliance with modern security requirements.

(2)

Privacy, Template Security, and Key Revocability Considerations

The proposed framework relies on deep features extracted from biometric images without using or storing raw biometric data, thereby reducing privacy risks. These features are transformed through nonlinear mechanisms using the Particle Swarm Optimization (PSO) algorithm, making the generated encryption keys non-invertible and difficult to reconstruct. To support key revocability, multiple encryption keys can be derived from the same biometric input by introducing controlled randomness during the key generation framework, which avoids permanent storage of biometric templates, further enhancing template security and resistance to biometric-specific attacks.

(3)

Encryption Key Tests

Six fingerprint samples are used to generate six encryption keys, each evaluated across eight metrics to assess quality and randomness. All keys successfully passed the tests, demonstrating high unpredictability and suitability for high-security encryption applications.

Entropy Test

Entropy is used to measure the randomness of the key, where the ideal value is 8 bits, indicating complete randomness. The entropy of the key is calculated using Equation (3) in Section 2.4.

The results, summarized in Table 5, confirm the robustness of the proposed keys against security threats.

Table 5. Entropy test results for the generated keys.

ID	5	3	1	173	174	175
Finger Print							Ideal Value
Entropy Test	7.782	7.763	7.748	7.778	7.774	7.87	8
Uniformity Test (Chi-Squared)	262.0	215.0	271.5	295.5	226.5	327.0	293
Repetition Test(Adjacent)	0.59	0.2932	0.6842	0.293	0.586	0.977	0
Average Pearson Correlation	0.0062	0.0062	0.0062	0.0062	0.0062	0.0062	0.05
Stability Test(2)	0.068	0.093	0.060	0.057	0.049	0.039	<0.1
Range Test	passed	passed	passed	passed	passed	passed	0.255
Key strength without PSO	4.682	4.804	3.975	5.093	4.700	4.843	8
Key strength with the use of PSO	7.782	7.707	7.687	7.762	7.774	7.703	8

Repetition Test

The repetition test is conducted to evaluate the presence of repeated segments within the key sequence, whether adjacent or non-adjacent, ensuring no patterns reduce randomness or compromise security. The repetition index (R) is calculated as follows [38]:

R = Number of repeated segments in the key/Total number of segments

(6)

A value of (R) close to zero indicates high key randomness. The results for all generated keys confirm low predictability and strong security, with all values obtained from the test being zero when executed.

Uniformity Test Using the Chi-Squared Method

The uniformity test is a key statistical approach to evaluate the homogeneity of encryption key values. It compares the observed distribution of key values with the expected ideal distribution using the Chi-squared test, calculated as

$${\chi }^2={\sum }_{i=0}^{k-1}\left({\displaystyle \frac{(Qi-Ei)^2}{Ei}}\right)$$

(7)

where:

• χ²: Represents the Chi-Square statistic.
• Qi: The observed frequency or value for category i.
• Ei: The expected frequency or value for category i.
• k: The total number of categories.
• If the chi-square (χ²) value is low, it indicates that the actual distribution of values is close to the ideal distribution, meaning the key is evenly distributed [39]. At a significance level of 0.05, keys with χ² < 293.25 are considered to have passed the test, confirming a uniform distribution. The detailed outcomes are presented in Table 5: Results of the uniformity test.

Adjacent Repetition Test

The Adjacent Repetition Test is a fundamental tool for assessing the randomness of encryption keys, as it measures the occurrence of consecutive repetitions between bits or segments. The metric is calculated as follows:

$$R = {\displaystyle \frac{1}{N-1}}{\sum }_{i=1}^{N-1}\delta \left(x_i,x_{i+1}\right)$$

(8)

where $\delta \left(x_i,x_{i+1}\right)=\{\begin{array}{c}1 if x_i=x_{i+1} \\ 0 otherwise\end{array}$

N denotes the key length, and $x_i$ represents the bit or segment at position (i). High values of (R) indicate weak randomness due to repeated patterns, whereas values approaching zero reflect minimal repetition, signifying a stronger key with enhanced security. The practical results of this test, presented in Table 5, confirm the high randomness of the generated keys, with values close to zero indicating minimal adjacent repetition.

Pearson Correlation Test

The Pearson Correlation Test is a statistical measure used to assess the degree of linear dependence between two variables. In the context of encryption keys, it evaluates the correlation between consecutive segments, where a coefficient close to zero indicates minimal correlation, reflecting high randomness and strong resistance against analytical attacks. The test is calculated as

$$R={\displaystyle \frac{\sum (Xi-X^{-})(Yi-Y^{-})}{\surd \sum {(Xi-X^{-})}^2\cdot \surd \sum {(Yi-Y^{-})}^2}}$$

(9)

where:

• R: Pearson correlation coefficient.
• Xi: Individual values in the first series.
• Yi: Individual values in the second series (e.g., lagged values in time series).
• X⁻: Mean of the Xi values.
• Y⁻: Mean of the Yi values [40]. The results demonstrate that the generated keys achieve coefficients close to zero, confirming minimal linear dependence and enhanced cryptographic strength, as presented in Table 5.

Stability Test

The stability test is designed to verify the reliability of the key generation process by ensuring that identical input data consistently produces the same key. Conversely, even minor variations in the input must result in significantly different keys, thereby strengthening the system’s resistance to potential attacks. For a fixed input I, the system should always generate the same key K: F(I) = K. Repeated key generation using the same input I must yield identical results across all trials:

K1 = K2 = ⋯ = Kn

(10)

The practical results of this evaluation are summarized in Table 6, confirming the stability and security efficiency of the generated keys.

Table 6. Stability and security evaluation of generated keys.

The Key Generated from Attempt 5	The Key Generated from Attempt 4	The Key Generated from Attempt 3	The Key Generated from Attempt 2	The Key Generated from Attempt 1	Finger Print
[95 39 243 220 42…]	[95 39 243 220 42…]	[95 39 243 220 42…]	[95 39 243 220 42…]	[95 39 243 220 42…]		5
[143 24 107 86 110…]	[143 24 107 86 110…]	[143 24 107 86 110…]	[143 24 107 86 110…]	[143 24 107 86 110…]		3
[127 6 38 182 127….]	[127 6 38 182 127….]	[127 6- 38 182 127….]	[127 6 38 182 127….]	[127 6 38 182 127….]		1
[188 224 208 191 161….]	[188 224 208 191 161…]	[188 224 208 191 161…]	[188 224 208 191 161…]	[188 224 208 191 161…]		173
[77 115 56 243 251….]	[77 115 56 243 251….]	[77 115 56 243 251…]	[77 115 56 243 251…]	[77 115 56 243 251…]		174
[106 30 245 143 52….]	[106 30 245 143 52….]	[106 30 245 143 52….]	[106 30 245 143 52….]	[106 30 245 143 52….]		175

Sensitivity to Minor Changes (Inclusivity Effect)

The sensitivity test assesses the encryption system’s response to slight input variations. A minor modification applied to input (I) produces a new input (I’), generating a different key (K’) such that

F(I′) = K′

(11)

The difference between the original key (K) and the modified key (K’) is quantified using the Bit Change Rate (BCR). For a secure encryption system, the BCR should exceed 50%, ensuring that even minimal changes in the input lead to significant differences in the generated keys, thereby reinforcing resistance against analytical attacks. The outcomes of this evaluation are presented in Table 5, while the encryption results using both original and modified keys are shown in Table 7.

Table 7. Results of encryption with original and modified keys.

Original Image	Encryption with the Original Key	Encryption with the Modified Key	Difference Between the Encrypted Images

Range Test

The range test measures the variability of key values, where a wider range indicates stronger exploration of the key space, while a narrower range reflects weaker randomness. It is calculated as

Range = max(K) − min(K)

(12)

where (K) denotes the generated key values, and (max(K)) and (min(K)) represent the maximum and minimum values, respectively [41]. A wider range serves as a key indicator of value diversity, enhancing encryption strength and reducing the likelihood of repetitive patterns. The outcomes of this test are presented in Table 5.

Autocorrelation Test:

The autocorrelation test measures the similarity between a sequence and its shifted version. Low autocorrelation across different shifts indicates high randomness and minimal predictability. It is defined as

$$R\left(d\right) ={\displaystyle \frac{1}{n-d}}{\sum }_{i=1}^{n-d}\left(X_i·X_{d+i} \right)$$

(13)

where (R(d)) is the autocorrelation coefficient at lag (d), (X_i) and (X_d+i) are sequence values, and (n) is the sequence length. Values of (R(d) approximately 0) confirm strong randomness in the encryption key [42]. The outcomes of this test are reported in Table 8.

Table 8. Results of the autocorrelation test.

Result Explanation	Critical Value	Ideal Value	Autocorrelation Test	Finger Print	ID
Pass (close to 0)	0.05	Close to 0	0.0359		5
Pass(close to 0)	0.05	Close to 0	0.0342		3
Pass(close to 0)	0.05	Close to 0	0.032		1
Fail (pattern detected)	0.05	Close to 0	Failed		173
Pass (close to 0)	0.05	Close to 0	0.033		174
Fail (deviation from ideal value)	0.05	Close to 0	0.33		175

5.1.3. Results of Applying PSO to Enhance the Encryption Key

After the predefined iterations, the PSO algorithm converges to the optimal encryption key, identified as the solution achieving the highest fitness value. The fitness function plays a central role in guiding the swarm toward keys with improved randomness and security. The effectiveness of PSO in refining and strengthening the generated key is presented in Table 5.

5.1.4. Comparison of Accuracy Between the Proposed Models and Existing Systems

This section presents a rigorous comparative analysis of the proposed system models against state-of-the-art approaches reported in recent literature. Experimental results show that the proposed models achieve accuracy rates exceeding 99%, underscoring their high effectiveness and reliability. This analysis further highlights the impact of modern deep learning architectures on fingerprint data processing and cybersecurity. The results confirm that advanced neural networks not only enhance encryption accuracy but also consistently outperform traditional methods, demonstrating significant improvements in both efficiency and security. Table 9 provides a detailed comparison of the proposed models relative to other contemporary approaches.

Table 9. Comparative analysis of the proposed models and recent approaches.

Epochs	Data Type	%ACC	Method Using	Reference
100	Fingerprint	99–98	CNN model (VGG-16 Tuned)	[43]
60	Fingerprint	98.89	DeepFKTNet model	[44]
N/A (Not reported)	Fingerprint	98.0	Deep Neural Network (Bio-Key Generation)	[45]
50	Fingerprint	98.00	MCP-FP model	[46]
N/A (Not reported)	Natural image	95.30	B-DCNNs	[47]
30	Fingerprint	96.10	CNN(3 classes of FVC2004)	[48]
20	Fingerprint	98.70	Modified HOG descriptor	[49]
30	Fingerprint	97.40	Statistics of D-SIFT descriptor	[49]
20	Fingerprint	99.73–99.83	CNN and PSO	proposed system

Discussion of the Results of the Key Generated by the CNN Model

The results demonstrate that the key generated by the CNN model integrated with PSO achieved high accuracy, ranging between 99.73% and 99.83% within only 20 training epochs, outperforming most modern models listed in Table 9. For instance, the enhanced VGG-16 model reached 99.98% accuracy but required 100 epochs, while DeepFKTNet 98.89% in 60 epochs. This highlights the efficiency of the proposed approach in achieving high accuracy with reduced training time, attributed to the synergy between CNN and PSO, which enhanced feature extraction and supported the generation of strong, highly random keys. Moreover, the biometric key derived from CNN parameters extracted from fingerprints demonstrated uniqueness, resistance to tampering, and advanced security with low risk of duplication or replication. Overall, the proposed framework provides an effective solution for generating biometric encryption keys that combine computational efficiency, randomness, and robustness.

The Role of the PSO Algorithm in Key Enhancement

The integration of PSO with CNNs plays a pivotal role in enhancing the quality of encrypted keys by optimizing the extracted parameters during generation, thereby improving randomness, independence, and robustness. On one hand, CNNs provide a powerful capability for extracting fine biometric features, while PSO strengthens key security through parameter optimization, increasing their efficiency against cyber threats. As a result of this synergy, the system achieves higher classification accuracy with reduced training time, alongside the generation of strong keys that are difficult to replicate or manipulate. This raises the protection level of biometric data and establishes a comprehensive framework that combines computational efficiency with security resilience. Accordingly, the proposed approach offers an effective solution to address contemporary cybersecurity challenges, including advanced and adversarial attacks.

5.2. Results of the Proposed Encryption Method

The experiments conducted on standard images from the USC-SIPI database confirmed the effectiveness of the proposed color image encryption method, where the encrypted images achieved high randomness based on entropy measurements and low correlation between adjacent pixels. The method also demonstrated strong resistance against brute-force, statistical, differential, and noise attacks. Moreover, it showed remarkable computational efficiency, Moreover, the proposed method demonstrated remarkable computational efficiency across different image sizes, as detailed in Table 10, which presents the execution time analysis of the proposed encryption system for images with varying resolutions, confirming its scalability and suitability for practical applications.

Table 10. Encryption execution time for different image sizes.

Test Image	Image Size (Pixels)	Encryption Execution Time (s)
	256 × 256	4.0382
	512 × 512	4.1939
	1024 × 1024	4.2824

Table 11 presents the details of the adopted images, confirming that the proposed method achieves a balance between security strength and computational efficiency, highlighting its applicability in modern encryption systems.

Table 11. Details of the images utilized in the experiments of the proposed technique.

Image Name	Size	Original Image	Image Name	Size	Original Image
Baboon	463 × 516		Tree	316 × 312
Jelly beans	200 × 200		House	225 × 222
Pepper	463 × 516		Splash	225 × 222
Female	408 × 382		Airplane	395 × 344
Car	231 × 209		Landscape	456 × 496

5.2.1. Information Entropy

Information entropy is a key measure of randomness and thus an important indicator of encryption efficiency. For color images, entropy is calculated for each channel (R, G, B), and values close to the ideal 8.0 signify high unpredictability, making statistical analysis and data recovery without the correct key infeasible. As shown in Table 12, the entropy values of the encrypted images consistently approach 8.0 across all channels, confirming the proposed method’s ability to ensure high randomness, strong confidentiality, and robustness against entropy-based attacks.

Table 12. Entropy values of colored images across different channels.

Image Name	No (ID) Print Finger	R	G	B
Baboon	3	7.9991	7.9990	7.9991
Jelly beans	50	7.9991	7.9990	7.9989
Female	70	7.9989	7.9990	7.9990
Car	300	7.9991	7.9990	7.9991
Tree	55	7.9989	7.9989	7.9990
House	80	7.9990	7.9991	7.9990
Splash	90	7.9991	7.9989	7.9989
Airplane	170	7.9990	7.9991	7.9990
Landscape	120	7.9991	7.9990	7.9990

In an additional experiment, the proposed method is applied to the Baboon color image, as shown in Table 13 The results demonstrated that the proposed algorithm achieved a higher average entropy compared to other recent approaches, with values very close to the ideal 8.0. These findings confirm the efficiency of the method in generating encrypted images with high randomness and ensuring strong confidentiality.

Table 13. Entropy comparison for the encrypted baboon image.

References	R	G	B	Average
Proposed (ID = 33)	7.9989	7.9990	7.9989	7.9989
[50]	-	-	-	7.993
[51]	7.9969	7.9971	7.9969	7.9969
[49]	-	-	-	7.9968
[52]	7.9029	7.9031	7.9033	7.9031
[53]	7.9973	7.9973	7.9974	7.9973

Table 13 shows that the proposed algorithm achieved an entropy value of 7.9989, which is very close to the ideal value of 8.0, indicating strong randomness in the encrypted images. It also outperformed most recent methods and produced results comparable to the best, confirming its efficiency in strengthening resistance against statistical attacks.

5.2.2. Correlation Analysis

Original images exhibit strong correlation between adjacent pixels, while an effective encryption algorithm aims to remove this correlation. In the encrypted images, the correlation coefficients in horizontal, vertical, and diagonal directions for each color channel (R, G, and B) are close to zero, indicating high randomness and preventing statistical prediction. The results in Table 14 show that the proposed algorithm successfully breaks pixel correlation, enhancing the system’s resistance to statistical attacks.

Table 14. Correlation coefficients of color images.

Images	No (ID) Print Finger	Directions	R	G	B
Baboon	33	V	−0.001281	0.004330	0.004461
		H	0.003778	0.003129	−0.003143
		D	−0.000183	−0.001469	0.008695
Female	70	V	0.002034	−0.004129	−0.003747
		H	−0.005959	0.003615	0.006995
		D	−0.007581	−0.000141	−0.000712
Car	300	V	0.001345	−0.002371	0.000063
		H	0.001102	0.002512	−0.004991
		D	−0.004585	−0.004492	0.002176
Tree	55	V	0.001716	0.000083	0.004725
		H	0.002483	0.004794	0.002511
		D	−0.005072	−0.000074	0.001490
House	80	V	−0.001664	0.004233	−0.002595
		H	−0.000833	−0.003344	−0.001740
		D	0.004233	−0.001804	−0.002005
Splash	90	V	0.001244	0.002332	0.004921
		H	−0.001855	0.011403	−0.007025
		D	−0.003260	−0.000596	−0.003135
Airplane	170	V	−0.004128	−0.009574	−0.001172
		H	0.003797	0.002109	−0.002230
		D	0.000942	0.004130	−0.006901
Landscape	120	V	0.001348	−0.001719	0.003130
		H	−0.001142	−0.001223	0.000480
		D	0.004944	−0.006214	0.007639

The results in Table 15 clearly show that the proposed method outperforms other recent techniques in terms of correlation coefficients.

Table 15. Comparison of correlation coefficients for the baboon image.

References	Directions	R	G	B	Average
Proposed (ID = 33)	H	0.0050	−0.0040	0.0000	_
	V	−0.0011	0.0009	−0.0104
	D	0.0083	0.0021	0.0003
[2]	H	_	_	_	0.0148
	V				0.0042
	D				−0.0070
[54]	H	_	_	_	0.0029
	V				0.0015
	D				0.0016
[49]	H	_	_	_	0.0021
	V				−0.0061
	D				−0.0064
[48]	H	−0.0090	−0.0020	−0.0078	_
	V	0.0018	0.0017	−0.0032
	D	0.0042	−0.0039	0.0073
[55]	H	_	_	_	−0.0030
	V				0.0131
	D				0.0072
[56]	H	−0.0002	−0.0008	0.0017	_
	V	0.0010	−0.0017	0.0010
	D	0.0001	−0.0016	0.0016

We conducted a comparative analysis with the method of F. Saeed et al. [48]. Table 15 highlights the superiority of the proposed approach in terms of correlation coefficients. The proposed method achieved lower values across most directions (H, V, D) and color channels, with significant improvements in the vertical and diagonal orientations. This reduction demonstrates a stronger ability to break inter-pixel dependencies, thereby enhancing randomness and limiting statistical predictability. As shown in Table 15 and Figure 11 and Figure 12, the encrypted image exhibits a clear reduction in pixel clustering compared to the original, confirming the effectiveness of the algorithm in correlation suppression and strengthening encryption robustness.

Figure 11. Correlation analysis of the baboon image across three directions (RGB channels).

Figure 12. Correlation analysis of the encrypted baboon image in three directions for the color channels.

5.2.3. Differential Attack Resistance

Resistance to differential attacks is measured using NPCR (Number of Pixels Change Rate) and UACI (Unified Average Changing Intensity), which quantify how much the encrypted image changes when a minor modification is applied to the input.

$$\mathit{NPCR}={\displaystyle \frac{1}{M\times N}}{\sum }_{i=1}^M{\sum }_{j=1}^{N}D\left(i,j\right)\times 100\left(\%\right)$$

(14)

where D(i, j) is defined as

$$D\left(i,j\right)=\{\begin{array}{c} 0, \mathrm{if} E_1\left(\mathrm{i},\mathrm{j}\right)=E_2(\mathrm{i},\mathrm{j}) \\ 1, \mathrm{if} E_1\left(\mathrm{i},\mathrm{j}\right) \ne E_2\left(\mathrm{i},\mathrm{j}\right) \end{array}$$

$$\mathit{UACI}={\displaystyle \frac{1}{M\times N}}{\sum }_{i=1}^M{\sum }_{j=1}^N{\displaystyle \frac{|E_1\left(i,j\right)-E_2\left(i,j\right)|}{255} \times 100(\%)}$$

(15)

Here, (E₁) and (E₂) are two encrypted versions of the original image generated by altering a single random pixel [57]. High NPCR and UACI values indicate strong resistance to differential attacks, as confirmed by the results summarized in Table 16.

Table 16. NPCR and UACI results for various color images.

Images	No (ID) Print Finger	NPCR			UACI
		R	G	B	R	G	B
Baboon	3	99.6261	99.6276	99.5773	33.8945	33.9069	33.8650
Female	70	99.5941	99.5742	99.5864	33.7221	33.9410	33.9476
Car	300	99.6170	99.5849	99.6124	33.8789	33.8584	33.8774
Tree	55	99.6414	99.6231	99.66583	33.8250	33.8763	33.8167
House	80	99.6246	99.6154	99.6017	33.9067	33.8718	33.8870
Splash	90	99.6063	99.6353	99.6139	33.7854	33.9097	33.8265
Airplane	170	99.6292	99.6063	99.5941	33.8002	33.8913	33.9425
Landscape	120	99.6200	99.6185	99.6032	33.8283	33.9657	33.7674

The results in Table 16 show that NPCR and UACI values for all three color channels (R, G, B) closely match the theoretical benchmarks, with NPCR exceeding 99.5% and UACI around 33%. These high values confirm the proposed method’s strong resistance to differential attacks, as minor input changes produce substantial variations in the encrypted output, enhancing randomness and overall security. A comparative analysis with recent methods is summarized in Table 17.

Table 17. NPCR and UACI comparison for the baboon image using various methods.

References	NPCR				UACI
	R	G	B	Average	R	G	B	Average
Proposed (ID = 3)	99.6261	99.6276	99.5773		33.8945	31.9069	31.8650	31.8888
[51]	-	-	-	99.62	-	-	-	33.48
[58]	99.5937	99.6170	99.6033	99.6063	33.3539	33.4655	33.5937	33.4710
[59]	--	--	--	99.59	--	--	--	33.42
[60]	-	-	-	99.613	-	-	-	33.503
[61]	99.5422	99.6070	99.6765	99.6085	33.2026	33.4944	33.6965	33.464
[62]	--	--	--	99.6084	--	--	--	33.446

Table 17 shows that the proposed method achieves NPCR and UACI values near the ideal, confirming strong resistance to differential attacks and enhanced encryption security.

5.2.4. Histogram Analysis

The histogram of a color image represents the distribution of pixel intensities across grayscale levels. For an encryption algorithm to be effective, the histogram of the encrypted image should differ significantly from that of the original image. While the histogram of the original image typically shows a non-uniform distribution due to its inherent structure and patterns, the histogram of a securely encrypted image should exhibit a nearly uniform distribution, indicating that pixel values have been effectively randomized without bias or distortion. Histogram variance is used as a quantitative measure to assess the degree of uniformity, calculated as follows:

$$\mathrm{Var}\left(\mathrm{Y}\right) = {\displaystyle \frac{1}{n^2}}{\sum }_{i=1}^n{\sum }_{j=1}^n{\displaystyle \frac{1}{2}}({\mathrm{Y}}_{\mathrm{i}}-{\mathrm{Y}}_{\mathrm{j}}{)}^2$$

(16)

where

• (Y): Pixel intensity frequencies (counts of each grayscale level).
• (N): Number of levels in (Y) (usually 256 for grayscale images).
• (Y_i, Y_j): Individual values in the set [62].
• Low variance → uniform histogram → strong resistance to statistical attacks.
• High variance → patterns present → weaker encryption.

As presented in Table 18, the encrypted images obtained using the proposed method achieve significantly lower variance values compared to the original images, confirming their enhanced uniformity. Furthermore, Table 19 provides a comparative evaluation against an existing method, where the proposed scheme demonstrates superior performance. Additionally, Figure 13 shows the histograms of the R, G, and B channels of the original and encrypted baboon image. While the original histograms reveal non-uniform distributions, the encrypted ones display near-uniform behavior. This combination of statistical evidence (Table 18 and Table 19) and visual validation (Figure 13) strongly supports the effectiveness of the proposed encryption algorithm and its robustness against statistical attacks.

Table 18. Histogram variance of images with the proposed method.

Images (256 × 256)	No (ID) Print Finger	Original Image			Encrypted Image
		R	G	B	R	G	B
Baboon	33	24,100	41,000	34,934	269	263	282
Jelly beans	50	50,885	34,061	88,039	223	280	328
Female	70	816,057	905,071	663,413	282	255	279
Car	300	69,732	96,237	77,515	227	279	265
Tree	55	91,749	72,269	121,385	246	276	274
House	80	315,075	384,818	479,840	268	246	267
Splash	90	135,944	129,880	356,887	228	273	314
Airplane	170	146,761	142,392	245,324	259	260	273
Landscape	120	48,915	41,417	92,971	246	242	257

Table 19. Histogram variance comparison between proposed and previous methods.

Comparison Criteria	Proposed	Hussain, M et al., (2022) [44]	Observation
Image Used	Baboon 256 × 256	Baboon 256 × 256	Same input image used
Original Image Variance (R)	24,100	33,300	Lower in proposed method
Original Image Variance (G)	41,000	57,300	Noticeably lower
Original Image Variance (B)	34,934	32,100	Comparable values
Encrypted Image Variance (R)	269	1031.3	Significantly reduced
Encrypted Image Variance (G)	263	1103.4	Significantly reduce
Encrypted Image Variance (B)	282	984.8235	Significantly reduced
Difference Between Original and Encrypted Image	Sharp decrease	Moderate decrease	Better image obfuscation
Value Uniformity After Encryption	More uniform	Less uniform	Indicates higher randomness
Resistance to Statistical Analysis	Harder	Easier	Proposed method offers stronger encryption

Figure 13. Histograms of the original vs. encrypted “baboon” image.

The results in Table 19 show that the proposed method achieves lower variance than both the original images and Hussain, M et al., (2022) [44], ensuring more uniform pixel distribution, higher randomness, and stronger resistance to statistical attacks.

5.2.5. Noise and Data Cropping Attacks

The ability to resist noise and partial data loss is a key criterion for evaluating the strength of any image encryption algorithm. Encrypted images transmitted over networks may be subjected to random interference or partial cropping, which can affect their accurate recovery. To assess the efficiency of the proposed system, the Peak Signal-to-Noise Ratio (PSNR) is employed, calculated as

$$\mathit{PSNR} = 10 \times {\log }_{10}\left({\displaystyle \frac{{255}^2}{MSE}}\right)$$

(17)

where MSE (Mean Squared Error) is defined as

$$\mathit{MSE} ={\displaystyle \frac{1}{MN}}{\sum }_{i=1}^N{\sum }_{j=1}^M\left[I_o\right(i,j)-{I_d(i,j)]}^2$$

(18)

with (I_o) and (I_d) representing the original and decrypted images, respectively. Higher PSNR values indicate more accurate recovery, with values above 35 dB generally signifying near-perfect visual similarity. The experimental results (Figure 14 and Figure 15, and Table 20) demonstrate the robustness of the proposed algorithm against both noise (including “salt and pepper”) and data cropping attacks, confirming its strong performance and reliable recovery even under highly adverse conditions.

Figure 14. Effect of data cropping on the “baboon” image: (a) cropped region 128 × 128, (b) corresponding decrypted image, (c) cropped region 64 × 64, (d) corresponding decrypted image.

Figure 15. Impact of salt-and-pepper noise on the “baboon” image: (a) noise level 0.05, (b) corresponding decrypted image, (c) noise level 0.02, (d) corresponding decrypted image.

Table 20. Assessment of encryption resilience to noise and data cropping.

Attack Type	Density/ Size	R Channel PSNR (dB)	G Channel PSNR (dB)	B Channel PSNR (dB)	Average PSNR (dB)	Evaluation
Salt & Pepper Noise	0.002	51.5941	52.0894	51.7992	51.8276	Excellent– High Quality Restoration
Salt & Pepper Noise	0.005	47.9940	47.8290	47.8329	47.8853	Very Good– Slight differences
Data Cut (Baboon)	128 × 128 pixels	33.8903	33.9369	33.9377	33.9216	Acceptable—Some detail loss
Data Cut (Baboon)	64 × 64 Pixels	39.9494	39.9922	39.9550	39.9655	Good—Good restoration despite cuts

According to standard PSNR benchmarks, image recovery quality can be classified as excellent when PSNR values exceed 45 dB, indicating near-perfect reconstruction; very good when values surpass 42 dB, with negligible visual differences; and acceptable around 34 dB, where minor degradation is observed but main features remain discernible. Based on these standards, the results in Table 20 demonstrate that the proposed encryption scheme exhibits remarkable resistance to various attacks, including noise interference and data loss. Even when subjected to distortion or cropping, the decrypted images retain high visual fidelity and structural clarity. Moreover, the method shows strong resilience against a wide range of cryptographic attacks—KPA, CPA, differential, statistical, and brute-force—due to the generation of a unique key for each transmission, effectively preventing key reuse and pattern prediction. This dynamic key strategy eliminates fixed dependencies exploitable by attackers. The consistently high PSNR values across RGB channels further validate the robustness of the approach, confirming excellent image restoration even under Salt & Pepper noise and cropping conditions, where both image clarity and essential features are effectively preserved.

6. Conclusions

This study demonstrates that integrating biometric techniques with deep learning represents a significant breakthrough in encryption key generation. The proposed system dynamically creates a unique key for each transmission based solely on the recipient’s fingerprint, eliminating the need for key transfer or reuse and ensuring an exceptionally high level of security. The generated keys exhibit high randomness and are resistant to replication or guessing, further strengthened by the PSO algorithm. Activation functions play a crucial role, with the tanh function outperforming ReLU by distributing values more evenly, increasing randomness, and enhancing training stability, while Batch Normalization may reduce key strengths in this context. This research clearly highlights the substantial advantage of using CNNs to enhance traditional methods such as AES. CNNs extract highly distinctive and unique features from biometric data, increasing the strength of the resulting keys and making them more resistant to both traditional and digital attacks. This integration of deep learning and AES not only improves randomness but also enhances personalized protection for each user through keys directly linked to their biometric identity, achieving a level of security unattainable with conventional methods alone.

Table 21 presents the abbreviations used in the proposed image encryption system. Furthermore, this approach has broad applicability across multiple domains, including IoT devices, secure cloud storage, financial transactions, medical imaging, and military communications. It demonstrates system flexibility and adaptability to future developments, including lightweight encryption for embedded systems and resilience against emerging threats such as quantum computing. Despite some limitations related to dataset specificity and computational demands for generating very large keys, the proposed framework proves to be an innovative, robust, and scalable solution, with exceptional potential to strengthen the security and efficiency of conventional digital encryption.

Table 21. Abbreviations of the proposed image encryption system.

Abbreviation	Meaning	Abbreviation	Meaning
AES	Advanced Encryption Standard	KCNN + PSO	Key vector generated by CNN and optimized by PSO
AES-256	Advanced Encryption Standard with 256-bit key	KAES	AES key derived from CNN + PSO output
AES Key	Encryption key generated dynamically from fingerprint features	CNN	Convolutional Neural Network
AI	Artificial Intelligence	CNN + PSO	Combination of CNN for feature extraction and PSO for key optimization
CDF	Cumulative Distribution Function (used in histogram equalization)	Conv	Convolutional layer (extracts edges, textures, patterns)
DeepFKTNet	Deep learning network for fingerprint key generation	FC	Fully Connected layer in CNN
GPU	Graphics Processing Unit, used for computation acceleration	ID	Identification (user identifier)
IoT	Internet of Things	KPA	Known-Plaintext Attack
NPCR	Number of Pixels Change Rate	PSNR	Peak Signal-to-Noise Ratio, measures image recovery quality
PSO	Particle Swarm Optimization	RGB	Red, Green, Blue color channels of an image
Row	Row r of the AES state matrix	ReLU	Rectified Linear Unit activation function
S-Box	Substitution box in AES	TANH	Hyperbolic tangent activation function
UACI	Unified Average Changing Intensity	USC-SIPI	University of Southern California—Signal and Image Processing Institute database
VGG-16	Visual Geometry Group model, deep CNN architecture	XOR	Exclusive OR
Ienc	Final encrypted image	Kround0	Initial round key in AES
CPA	Chosen-Plaintext Attack	–	–