Enhancing image data security using the APFB model

Abstract

Ensuring the confidentiality of transmitting sensitive image data is paramount. Cryptography recreates a critical function in safeguarding information from potential risks and confirming the identity of authorised individuals, thereby addressing the growing demand for enhanced image security. This paper presents a novel AES-permuted Feistel Blowfish (APFB) model that aims to improve image data security cost-effectively and enhance data protection by incorporating AES and Blowfish algorithms. The proposed model's utility over existing approaches stems from its computational efficiency and speed. The proposed model's resilience and security against several attack modalities are validated through a comprehensive range of methods, including extensive experimentation, histogram analysis, PSNR, entropy, MSE, CC, computational time, and NIST statistical tests. The outcomes yielded a PSNR of 67.26, NPCR of 99.6354, and UACI of 33.412. Additionally, the applicability of the proposed model is validated by utilising a practical case analysis. The outcomes exhibit the relevance of the proposed model in real-world applications.

KEYWORDS:

• Cryptography
• image security
• cryptographic techniques
• AES permuted feistel blowfish

1. Introduction

The enhancement of communication technology and availability have profoundly impacted all areas of our business, enterprise, and day-to-day work. These advancements have facilitated the production of substantial quantities of data with greater ease and at a reduced expense. In addition to these progressions, the past two decades have witnessed the extensive integration of mobile technology, resulting in images becoming the predominant form of data (Ben Slimane et al., 2018). Digital images have become important in our everyday life. However, the extensive usage of digital images also poses a potential threat to the confidentiality and integrity of several types of visual content, including personal photographs and secret business documents (Ullah et al., 2023). The importance of image encryption in today's interconnected world cannot be overstated. It converts image data into an incomprehensible and nonsensical format for individuals who lack the appropriate decryption key, thereby safeguarding sensitive information (Veera et al., 2024). Given the increasing risk of data breaches, cyber-threats (Barik et al., 2022), adversarial attacks (Barik et al., 2024), and unauthorised access, ensuring digital image security throughout storage, transmission, and retrieval is mandatory (Güvenoğlu, 2024).

Techniques for encryption and decryption are critical to achieving this objective. Image encryption is the process of using cryptographic methods to convert the pixel values of an image into an incomprehensible and senseless format, rendering it indecipherable to anyone who does not possess the correct decryption key (Wen et al., 2024). Encrypting digital images makes it possible to securely communicate and retain sensitive information within them without the threat of interception or unlawful dissemination. Image encryption techniques can be classified into three basic types: symmetric, asymmetric, and hybrid (Elkandoz & Alexan, 2022). Symmetric encryption utilises a solitary secret key for all the encryption and decryption procedures, offering a comparatively uncomplicated and effective option (Chowdhary et al., 2020). Asymmetric encryption employs a set of keys, consisting of a public key for encryption and a private key for decryption, which offers heightened security but requires more computing complexity. Hybrid encryption is a cryptographic technique that leverages the advantages of symmetric and asymmetric encryption to balance security and efficiency (Pourjabbar Kari et al., 2021).

Encrypting image data presents greater challenges than encrypting text data (Hasan et al., 2021). Firstly, in practical scenarios, the size of image data is greater than that of text data. Encrypting images within a reasonable timeframe becomes challenging due to this. In the second scenario, significant correlations exist between neighbouring pixels in the image data, which attackers can exploit using statistical attacks to access the original images (Feng et al., 2024). Encryption techniques are only effective if they provide sufficient strength. Hence, standard encryption methods like Data Encryption Standard (DES) (Mehta et al., 2024), Triple DES (TDES), Advanced Encryption Standard (AES), and Rivest-Shamir-Adleman (RSA) (Ahmad & Hasan, 2021), which are extensively employed for encrypting text data, are not appropriate for encrypting image data. Encrypting image data requires incorporating many methods. Over time, many image encryption techniques have been presented to cater to digital images’ distinctive features and needs. Image encryption has seen the adaptation and optimisation of traditional encryption methods, such as DES and AES. Furthermore, there have been advancements in encryption algorithms that utilise chaotic systems, Substitution boxes, DNA sequences (Akkasaligar & Biradar, 2020), and RNA (Cun et al., 2023). These algorithms provide enhanced security features and are resistant to attacks.

Image encryption algorithms are typically based on standardized structure and comprise confusion and diffusion (Man et al., 2021). The objective of the confusion phase is to disrupt the relationship between neighbouring pixels in the original image by rearranging their positions while keeping their values unchanged. During diffusion, pixel values are systematically altered to change the image's statistical characteristics (Toktas et al., 2024). For thorough literature on image encryption and decryption, interested readers are encouraged to review the works of (Singh & Singh, 2022; Pourasad et al., 2021; Zhang et al., 2023). In addition, there are different methods, such as (Gao et al., 2023; Rakheja & Khurana, 2023; Yu et al., 2023; Mansoor & Parah, 2023; Soppari & Chandra, 2023).

1.1. Motivation

Considering the advancements in image encryption, some limitations remain (Gull & Parah, 2024; Chai et al., 2022). Distributing and storing encryption keys securely remains a major difficulty in key management. The intricacy of encryption methods and the requirement for instantaneous encryption can present practical constraints. Also, the existing models require high computing resources and processing time and are complex while implemented in the real world. Moreover, the resilience of encryption systems against other types of attacks, such as brute-force and statistical attacks, necessitates ongoing monitoring and enhancement (Herbadji et al., 2024). Our work is motivated by the need to address the existing challenges by presenting cost-effective, reduced computing resources, fast processing, easy-to-implement, and efficient hybrid encryption and decryption techniques. Blockchain technology is used for secure data storage.

1.2. Contributions

The work presents a novel cryptographic model, APFB (AES-permuted Feistel Blowfish), that integrates AES (Hadj Brahim et al., 2024) and Blowfish algorithms (Nampalle et al., 2023) during encryption and decryption. When encrypting image data, special encryption needs are considered. The proposed solution is a hybrid system that utilises the Feistel structure to resist different cryptographic catalysts, allowing for mixing more complex data through substitution and permutation operations. Despite its multi-layered nature, the encryption and decryption techniques are easily implemented, which makes it well-suited for real-world issues due to its low computing resources. The significant contributions of the study are as follows:

1. This study proposed a novel hybrid APFB model to enhance image security during transmission. The presented model is simple to implement with low compute resource requirements.

2. The proposed model takes an average of 0.011 s to encrypt and 0.073 s to decrypt a standard 256 *256 image. This reduced time complexity allows the approach to be applicable in practical scenarios where efficiency is crucial.

3. Encrypting an image using hybrid methods entails the creation of in-between secret keys from the cryptographic process and the real image. Even the smallest alteration to the original image or the secret key results in a completely distinct encrypted image, making differential attacks ineffective. It possesses an extensive range of possible keys and is highly responsive to alterations in the key. Additionally, the data is stored using a hashing algorithm in the blockchain.

4. The proposed model's randomness is validated utilising the National Institute of Standards and Technology (NIST) SP 800-22 statistical tool.

5. Different systematic experiments are performed to validate the proposed model's outcome and compare it with existing studies.

6. A practical case study further depicts the proposed model's applicability.

This theoretical contribution aligns with the fundamental ideas of cryptography by demonstrating the significance of confusion and dispersion for enhanced encryption with reduced computing resources, low processing time, and ease of implementation. Additionally, using blockchain technology for secure storage enhances data security with a cost-effective and efficient option.

The remaining paper is formulated as follows: Section 2 concerns related works with different methods and algorithms. Section 3 demonstrates in detail the methodology of the proposed model, including encryption and decryption. Section 4 demonstrates systematic experimentation, statistical tests, and validation using practical case studies. Section 5 presents the discussion, limitations, and future research. Finally, the paper is concluded in Section 6.

2. Literature review

This section highlights the existing research studies focusing on image security and cryptographic techniques. Singh and Sunitha (2022) proposed a secure method for exchanging images using blockchain and pallier map-based authentication. It is based on the cloud and ensures the integrity and security of image data. The authors demonstrated authentication accuracy by 23%; the analysis showed a 32% reduction in the false positive rate and a 22% decrease in the computational cost. Hafsa et al. (2022) presented an improved AES (IAES) technique that enhances the ciphered video's diffusion and confusion. The chaotic attractor's beginning conditions are created using the SHA-3 hash algorithm. For real-time video transmission, this activity is crucial since it reduces the run time. The chaotic attractor's initial conditions are built using the SHA-3 hash algorithm. The presented outcomes boost the encrypted video's entropy by 15% and reduce the complexity time for encryption and decryption. Daoui et al. (2022) proposed a novel 2D chaotic system sensitive to any change in its control parameters. A novel encryption system is built using QFrMMs to uncover the signal and image processing applications of the suggested FrMP map. Its primary use is the encryption of several types of biomedical data, including various grayscale and colour medical images. The authors demonstrated that sage exchanges image data over the publicly available communication system. El Azzaoui et al. (2022) proposed that using quantum computing and blockchain technology makes smart healthcare systems effective, scalable, and secure. The experimental findings show that the architecture is feasible and that the implemented Q-OTP encryption is secure.

Gupta et al. (2023) proposed an effective solution for encrypting images that combines cryptography and watermarking. It depends on two-tiered security to provide safe and error-free image data transfer. Patel and Thanikaiselvan (2023) presented a study on the image encryption method using neural networks, Latin squares, and other machine-learning methods. The authors suggested creating a chaotic sequence for various uses using a fresh pseudo-random number generator based on neural networks. Sarosh et al. (2023) developed two new two-dimensional chaotic maps, the Logistic Regulated Quadratic map (LRQ) and the Quadratic Regulated Quadratic map (QRQ) for healthcare systems. These maps display compound chaotic features and a large chaotic range. Guo et al. (2024) proposed the ACGAN-FTL federated transfer learning system, built on an auxiliary classifier generative adversarial network, which could fix this. An internal transfer learning process moves data from the system's global model to a user-specific one using a small sample size. Lin et al. (2024) presented a study using an M-based cryptography scheme and a symmetric cryptography technique to safeguard information medical images.

Xie et al. (2023) proposed a medical image encryption technique that uses deoxyribonucleic acid encoding in conjunction with a quick and reliable fuzzy C means clustering image segmentation algorithm. The study demonstrates robust encryption and safety against various attacks. Zhu et al. (2023) proposed a system model that uses a one-dimensional piece-wise quadratic polynomial chaotic map (PWQPCM) to enhance its chaotic properties. It is especially suitable for cryptography applications as it displays strong decentralised conduct across a broader set of continuous parameters. A secure image encryption method that utilises the presented model and a strong S-box construction. Elmoasry et al. (2022) presented a dual-layer data strategy consisting of a data concealing technique after the encrypted medical images. The encryption system has two components: diffusion and confusion. To create confusion, it uses logistics and tent maps to create S-boxes. Al-Hyari et al. (2022) presented a safe and effective method for storing digitally coloured images. This method offers a high level of protection using a complicated secret key that the sender and the recipient have agreed upon. Arif et al. (2022) addressed problems in current image encryption methods by presenting a novel method that relies on chaos theory and uses a single substitution box to perform permutations and substitutions. John and Kumar (2023) presented encrypting images using a linear feedback shift register. It shuffles the pixel location and produces pseudo-random integers. The original image can be recovered by the receiver side node decrypting the data after the encrypted image has been delivered via a cloud platform.

Abd-El-Atty et al. (2023) suggested a unique logistic mapping and quantum walk-based double medical image encryption method. The proposed method splits the two plain images in half, with one copy containing each image's high-bit and the other the low-bit versions. Abdelfatah et al. (2023) presented an image encryption method that overcomes these limitations using innovative multi-chaotic map design and adaptive DNA code bases. DNA coding is a powerful tool for improving computational efficiency and data transport capabilities. A multi-chaotic map of the Henson Gaussian logistic was combined to create more chaotic pseudo-random sequences. El-Shafai et al. (2023) offered that the hybrid optical-based solution securely transmits colour and grayscale medical images over unreliable networks by utilising efficient hashing, steganography, and encryption techniques. Patil et al. (2016) proposed an algorithm based on the user's needs. They presented the comparisons by implementing and analysing the cost and performance of used cryptographic algorithms such as DES, 3DES, AES, RSA, and blowfish.

Sahlabadi et al. (2022) presented a novel image encryption algorithm, combining Cycling 3D Chaotic Map with DNA sequences. The study aimed to enhance security by using aggressive violence and genetic design. The method enables strong encryption in image communication and storage applications. Lin et al. (2023) presented a novel method for extracting recognisable watermarks from images using DL technology. Their method demonstrates an efficient removal method and offers versatile applications where watermark removal is required. Saberikamarposti et al. (2024) discussed classification, challenges, and future directions and examined image storage in detail. It examined different approaches to image storage, identified existing challenges, and proposed avenues for future research to improve it. It provided valuable insights into enhancing image security. Arian et al. (2024) presented a new approach to image storage by combining DNA sequences with excess chaos. It introduced an approach that used the chaotic dynamics of hyperchaotic systems to enhance encryption security. Integrating DNA sequences adds robustness and complexity to the encryption process, promising better protection of sensitive image data. Ghorbani et al. (2022) presented a novel image storage system combining ribonucleic acid (RNA) and Hénon maps. Taking advantage of RNA's unique properties and the Henan map's chaotic nature, the system provides enhanced security for image storage. The authors demonstrated promising results regarding encryption efficiency and resistance to attack.

Ali et al. (2024) presented a study on medical image encryption techniques to enhance textual confusion using s-box and novel techniques based on linear fractional transformation. They presented the usefulness of image security by encrypting using an S box. The authors evaluated the proposed method using different evaluation parameters. Huang et al. (2022) proposed image encryption using SHA 3 and sensing an embedded image using asymmetric cryptography. The integer wavelet transform is employed to transform the courier image. The study results demonstrate that the proposed technique has robust imperceptibility and key sensitivity. The author presented a PSNR value of 43 dB and a carrier image value of 0.9999. Alexan et al. (2023) proposed a novel image encryption algorithm using Chaos and KAA maps. The authors presented an extensive mathematical analysis to exhibit the method's robustness. It is effective and can address statistical, differential, and brute-force attacks. The study was further validated using the NIST SP 800 statistical test. Inam et al. (2024) presented an image encryption study using a blockchain-based framework. The authors proposed a novel method using chaotic Arnold's cat map encryption. The data is stored after encryption into the blockchain for enhanced security. They evaluated the method using various parameters and found it effective compared to existing studies. Ahuja et al. (2023) proposed a hybrid encryption method based on Lorenz-Gauss-Logistic image encryption. The authors validated the method using the NIST statistical test. The outcome illustrates the impressive scrambling impact of the presented method, which can significantly enhance image security. The summary of existing studies is outlined in Table 1.

Table 1. Summary of existing studies.

Reference	Cryptography methods	Outcome	Limitations
Kitran et al. (2022)	Encrypt images by encrypting certain regions.	Enhanced security for chaotic encryption technique.	Not focused on security aspects during the encryption process.
Azzaoui et al. (2022)	Blockchain technology, quantum terminal machines	The model is feasible and implemented Q-OTP encryption is secure.	The lowest possible quantum noise level.
Patel et al. (2023)	Latin square, machine learning techniques	The proposed model outperforms and is resistant to communication channel attacks	Latin square methods may lack robustness,
Sarosh et al. (2023)	Deep learning	The model can independently find suitable testing models combined with the best available prior cryptographic knowledge.	Deep learning based on encryption is limited by its susceptibility to adversarial attacks.
Abdelfatah et al. (2023)	DNA, Chaotic map	The outcomes yielded high and low entropy values and can address all types of attacks.	Not focused on processing, encryption, and decryption time.
Nampalle et al. (2023)	Blowfish, Signcryption	The proposed model has a high PNSR value of 57.12 and a low processing time of 42 s.	Dependability on the certificate.
Huang et al. (2022)	Asymmetric encryption, SHA 3, Integer wavelet transform	The proposed model has high imperceptibility and yielded an NCC value of 0.9999 and a PSNR value of 43.	Not focused on reducing encryption time
Alexan et al. (2023)	Chaos, KAA map	The proposed model can address different types of attacks, such as visual, statistical, differential, and brute-force.	Not focused on encryption and decryption times.
Ahuja et al. (2023)	Gauss-Logistic, Lorenz system	The novel technique achieved UACI and NPCR values of 99.63 and 33.35, which indicates an enhanced encryption method.	Not focused on creating a lightweight system.

The literature review identifies different gaps and limitations in the existing research. Though multiple encryption techniques have been proposed, further evaluations are demanded to ensure data integrity, lower computing costs, and robustness against the exponential growth of various attacks. The present systems often rely on specific encryption algorithms, ignoring the potential advantages of hybrid encryption approaches and integration with prospective technologies such as blockchain. The efficiency of encryption systems can vary based on image type, size, and complexity, emphasising the importance of adaptable and scalable encryption solutions customised to a wide range of imaging settings. Cryptographic techniques that reduce computing resources, fast processing, cost-efficient, and easy-to-implement practical solutions are highly demanded. The presented APFB model aims to enhance robust encryption and decryption with reduced computing resources, low processing time, and ease of implementation to address the existing research gap. The private key of APFB is the advancement and fusion of two advanced encryption techniques, AES and Blowfish. Fusing different cryptographic methodologies presents a complex model for protecting confidential data. A theoretical development is represented by the APFB model's combination of Blowfish and AES. By fusing the effectiveness of AES with the Feistel network topology of Blowfish, this hybridisation makes the most of the benefits of both algorithms. By reducing possible flaws brought about by using a single encryption method, the synergy between these cryptographic primitives seeks to provide a greater degree of security. The Feistel network included in the Blowfish segment of the APFB facilitates improved confusion and dispersion. The Feistel structure resists different cryptographic catalysts, allowing for mixing more complex data through substitution and permutation operations. Further, blockchain technology is employed for secure storage to enhance data security with a cost-effective and efficient option.

3. Proposed methodology

This section depicts the proposed methodology employed in this study. First, Kaggle datasets are collected and then pre-processed using Histogram of Oriented Gradients (HOG). Subsequently, the proposed AES-permuted Feistel Blowfish method is performed to protect the confidentiality of sensitive data sent using image data. Blockchains, a distributed database updated by network nodes, are used in this study to safeguard data. Figure 1 illustrates the proposed model.

Figure 1. The proposed model.

3.1. Dataset

This study uses the datasets collected from Kaggle (https://www.kaggle.com/datasets/sachinkumar413/covid-pneumonia-normal-chest-xray-images). The medical image data contains chest X-ray images in three subfolders: COVID-19, NORMAL, and PNEUMONIA. COVID has 1626 images, NORMAL has 1802 images, and PNEUMONIA has 1800 images. All images are preprocessed and are downsized to 256 by 256 PNG format.

3.2. Pre-processing using histogram of oriented gradients

The image contrast and quality can be increased for improved analysis and diagnosis of chest disorders with data pre-processing that employs histograms of gradients. Initially, individuals are identified using a histogram of oriented gradient (HOG) algorithm (Zhou et al., 2020). The data is pre-processed before the gradient can be calculated, oriented, and normalised, as shown in Figure 2.

Figure 2. Histogram equalisation.

Noises are diminished first through preprocessing. If the reduction is present, the gradient matrices are returned correctly. Filters are used for preprocessing by convolving the signal with them. The result of applying the filter to an image and multiplying it would be a kernel or a mask. It only takes a simple filter slide over an image to reproduce or convolve the signal. The Gradient computation is utilised in image feature extraction to obtain correct shape and appearance gradients. The resulting compounds of functions $\mathrm{\partial }\text{e}/\mathrm{\partial }\text{w}$ and $\mathrm{\partial }\text{e}/\mathrm{\partial }\text{z}$ are computed at each pixel coordinate to produce this function. The magnitude can be calculated using equation 1(1) $\begin{array}{r}(\text{Magnitude}{)}^2=[\text{H}{\text{w}}^2+\text{H}{\text{z}}^2]\end{array}$(1) . (1) $\begin{array}{r}(\text{Magnitude}{)}^2=[\text{H}{\text{w}}^2+\text{H}{\text{z}}^2]\end{array}$(1) The direction can be specified once the gradient is determined using equation 2(2) $\begin{array}{r}\text{ta}{\text{n}}^{-1}\mathrm{\varnothing }=\text{where}=\frac{\text{Hz}}{\text{Hw}}\end{array}$(2) . (2) $\begin{array}{r}\text{ta}{\text{n}}^{-1}\mathrm{\varnothing }=\text{where}=\frac{\text{Hz}}{\text{Hw}}\end{array}$(2) where $\mathrm{\varnothing }$ denotes the resulting angle $\text{Hz and}$ $\text{Hw}$ components that are called components along $\text{z}$ and $\text{w}$ directions.

Equations 3(3) $\begin{array}{rl}\text{k}2-\text{norm}:\text{u}& \to \text{u}/\sqrt{{\text{u}}_2^2}+{ϵ}^2\end{array}$(3) to 5(5) $\begin{array}{rl}\text{k}1-\text{sqrt}:\text{u}& \to \text{u}/\left({\text{u}}_1+\in \right)\end{array}$(5) are used for normalisation, where $\text{u}$ is an integer corresponding to the block's histogram after merging $\in$, an insignificant variable. Users can determine the HOG normalised featured vector. Figure 3 presents the flow of HOG. (3) $\begin{array}{rl}\text{k}2-\text{norm}:\text{u}& \to \text{u}/\sqrt{{\text{u}}_2^2}+{ϵ}^2\end{array}$(3) (4) $\begin{array}{rl}\text{k}1-\text{norm}:\text{u}& \to \text{u}/\left({\text{u}}_1+\in \right)\end{array}$(4) (5) $\begin{array}{rl}\text{k}1-\text{sqrt}:\text{u}& \to \text{u}/\left({\text{u}}_1+\in \right)\end{array}$(5)

Figure 3. The flow of the HOG

3.3. AES permuted feistel blowfish (APFB) model

The popular symmetric encryption technique AES (Advanced Encryption Standard) offers robust protection for sensitive data, including image security. Sensitive information is often included in images, and protecting this information is essential to adhering to privacy laws (Abu-Faraj et al., 2022). AES encryption is a dependable technique for protecting these images during transmission and storage (Nadhan & Jeena Jacob, 2024). The AES encryption uses a symmetric key to translate the image's pixel data into cipher text. This symmetric key is essential for decryption and encryption, enhancing security. The cipher text can quickly identify a change in the key since the AES Sub Bytes transformation was changed to be round key-dependenthe round key matrix's 16 bytes are used to XOR all the bytes in the corresponding $\left(\text{Ro}{\text{w}}_{\text{i}}\right)$ to create 4 eight-bit keys, $\text{XORke}{\text{y}}_1,\text{ XORke}{\text{y}}_2$, and $\text{XORke}{\text{y}}_{3,}$ by $\text{XORing}$ as shown in equations 6(6) $\begin{array}{rl}\mathrm{XORke}{y}_l& =K_{i,0}\oplus K_{i,1}\oplus K_{i,2}\oplus K_{i,3}\mathrm{where}i=0\mathrm{to}3\end{array}$(6) and 7(7) $\begin{array}{rl}\text{XORke}{\text{y}}_0& ={\text{K}}_{0,0}\oplus {\text{K}}_{0,1}\oplus {\text{K}}_{0,2}\oplus {\text{K}}_{0,3}\end{array}$(7) . Each ${\text{XORkey}}_{\text{i}}$, It is appended to every byte using equations 8(8) $\begin{array}{rl}\text{XORke}{\text{y}}_1& ={\text{K}}_{1,0}\oplus {\text{K}}_{1,1}\oplus {\text{K}}_{1,2}\oplus {\text{K}}_{1,3}\end{array}$(8) to 1(1) $\begin{array}{r}(\text{Magnitude}{)}^2=[\text{H}{\text{w}}^2+\text{H}{\text{z}}^2]\end{array}$(1) 1 in the appropriate (Rowi) values in the S-Box, and the state matrix is substituted after the acquisition of the XOR keys. The given a round key K and a state S, which are represented as 4 × 4 matrices: $\begin{array}{rl}\text{S}& =\begin{array}{c}{\text{S}}_{0,0}\\ {\text{S}}_{1,0}\\ \begin{array}{c}{\text{S}}_{2,0}\\ {\text{S}}_{3,0}\end{array}\end{array}\begin{array}{c}{\text{S}}_{0,1}\\ {\text{S}}_{1,1}\\ \begin{array}{c}{\text{S}}_{2,1}\\ {\text{S}}_{3,1}\end{array}\end{array}\begin{array}{c}{\text{S}}_{0,2}\\ {\text{S}}_{1,2}\\ \begin{array}{c}{\text{S}}_{2,2}\\ {\text{S}}_{3,2}\end{array}\end{array}\begin{array}{c}{\text{S}}_{0,3}\\ {\text{S}}_{1,3}\\ \begin{array}{c}{\text{S}}_{2,3}\\ {\text{S}}_{3,3}\end{array}\end{array}\mathrm{and}\text{K}=\begin{array}{c}{\text{K}}_{0,0}\\ {\text{K}}_{1,0}\\ \begin{array}{c}{\text{K}}_{2,0}\\ {\text{K}}_{3,0}\end{array}\end{array}\begin{array}{c}{\text{K}}_{0,1}\\ {\text{K}}_{1,1}\\ \begin{array}{c}{\text{K}}_{2,1}\\ {\text{K}}_{3,1}\end{array}\end{array}\begin{array}{c}{\text{K}}_{0,1}\\ {\text{K}}_{1,2}\\ \begin{array}{c}{\text{K}}_{2,2}\\ {\text{K}}_{3,2}\end{array}\end{array}\begin{array}{c}{\text{K}}_{0,3}\\ {\text{K}}_{1,3}\\ \begin{array}{c}{\text{K}}_{2,3}\\ {\text{K}}_{3,3}\end{array}\end{array}\end{array}$ (6) $\begin{array}{rl}\mathrm{XORke}{y}_l& =K_{i,0}\oplus K_{i,1}\oplus K_{i,2}\oplus K_{i,3}\mathrm{where}i=0\mathrm{to}3\end{array}$(6) (7) $\begin{array}{rl}\text{XORke}{\text{y}}_0& ={\text{K}}_{0,0}\oplus {\text{K}}_{0,1}\oplus {\text{K}}_{0,2}\oplus {\text{K}}_{0,3}\end{array}$(7) (8) $\begin{array}{rl}\text{XORke}{\text{y}}_1& ={\text{K}}_{1,0}\oplus {\text{K}}_{1,1}\oplus {\text{K}}_{1,2}\oplus {\text{K}}_{1,3}\end{array}$(8) (9) $\begin{array}{rl}\text{XORke}{\text{y}}_2& ={\text{K}}_{2,0}\oplus {\text{K}}_{2,1}\oplus {\text{K}}_{2,2}\oplus {\text{K}}_{2,3}\end{array}$(9) (10) $\begin{array}{rl}\text{XORke}{\text{y}}_3& ={\text{K}}_{3,0}\oplus {\text{K}}_{3,1}\oplus {\text{K}}_{3,2}\oplus {\text{K}}_{3,3}\end{array}$(10) (11) $\begin{array}{rl}{{\mathrm{S}}^{\mathrm{\prime }}}_{\text{i},\text{j}}& ={\text{S}}_{\text{i},\text{j}}\oplus \text{XORke}{\text{y}}_{\text{i}}\text{ where j}=0\text{ to }3\text{ where i ranges from }0\text{ to }3\end{array}$(11) $\begin{array}{rl}{\mathrm{S}}^{\mathrm{\prime }}& ==\begin{array}{c}{\text{S}}_{0,0}\oplus \text{ke}{\text{y}}_0\\ {\text{S}}_{1,0}\oplus \text{ke}{\text{y}}_1\\ \begin{array}{c}{\text{S}}_{2,0}\oplus \text{ke}{\text{y}}_2\\ {\text{S}}_{3,0}\oplus \text{ke}{\text{y}}_3\end{array}\end{array}\begin{array}{c}{\text{S}}_{0,1}\oplus \text{ke}{\text{y}}_0\\ {\text{S}}_{1,1}\oplus \text{ke}{\text{y}}_1\\ \begin{array}{c}{\text{S}}_{2,1}\oplus \text{ke}{\text{y}}_2\\ {\text{S}}_{3,1}\oplus \text{ke}{\text{y}}_3\end{array}\end{array}\begin{array}{c}{\text{S}}_{0,2}\oplus \text{ke}{\text{y}}_0\\ {\text{S}}_{1,2}\oplus \text{ke}{\text{y}}_1\\ \begin{array}{c}{\text{S}}_{2,2}\oplus \text{ke}{\text{y}}_2\\ {\text{S}}_{3,2}\oplus \text{ke}{\text{y}}_3\end{array}\end{array}\begin{array}{c}{\text{S}}_{0,3}\oplus \text{ke}{\text{y}}_0\\ {\text{S}}_{1,3}\oplus \text{ke}{\text{y}}_1\\ \begin{array}{c}{\text{S}}_{2,3}\oplus \text{ke}{\text{y}}_2\\ {\text{S}}_{3,3}\oplus \text{ke}{\text{y}}_3\end{array}\end{array}\end{array}$

The resultant state matrix ${\text{S}}^{{}^{\mathrm{\prime }}}$ $\begin{array}{rl}{\mathrm{S}}^{\mathrm{\prime }}& =\begin{array}{c}{{\mathrm{S}}^{\mathrm{\prime }}}_{0,0}\\ {{\mathrm{S}}^{\mathrm{\prime }}}_{1,0}\\ \begin{array}{c}{{\mathrm{S}}^{\mathrm{\prime }}}_{2,0}\\ {{\mathrm{S}}^{\mathrm{\prime }}}_{3,0}\end{array}\end{array}\begin{array}{c}{{\mathrm{S}}^{\mathrm{\prime }}}_{0,1}\\ {{\mathrm{S}}^{\mathrm{\prime }}}_{1,1}\\ \begin{array}{c}{{\mathrm{S}}^{\mathrm{\prime }}}_{2,1}\\ {{\mathrm{S}}^{\mathrm{\prime }}}_{3,1}\end{array}\end{array}\begin{array}{c}{{\mathrm{S}}^{\mathrm{\prime }}}_{0,2}\\ {{\mathrm{S}}^{\mathrm{\prime }}}_{1,2}\\ \begin{array}{c}{{\mathrm{S}}^{\mathrm{\prime }}}_{2,2}\\ {{\mathrm{S}}^{\mathrm{\prime }}}_{3,2}\end{array}\end{array}\begin{array}{c}{{\mathrm{S}}^{\mathrm{\prime }}}_{0,3}\\ {{\mathrm{S}}^{\mathrm{\prime }}}_{1,3}\\ \begin{array}{c}{{\mathrm{S}}^{\mathrm{\prime }}}_{2,3}\\ {{\mathrm{S}}^{\mathrm{\prime }}}_{3,3}\end{array}\end{array}\end{array}$ (12) $\begin{array}{rl}{{\mathrm{S}}^{\mathrm{\prime }}}_{\text{i},\text{j}}& =\text{ Substitution Box }\left[{{\mathrm{S}}^{\mathrm{\prime }}}_{\text{i},\text{j}}\right],\text{ here j}=0\text{ to }3\text{ for each i}=0\text{ to }3\end{array}$(12)

Equation 12 illustrates replacing bytes in the S-Box replacement table using the standard Sub Bytes technique operations upon receiving the new state matrix S′.

3.3.1. Modified inverse sub-bytes transformation

Equation 13 illustrates that the Sub bytes translation is invertible, allowing the inverse Sub Bytes operation to be modified. (13) $\begin{array}{r}\text{f }\left(\text{h}\right)=\text{f}\left(\text{x}\right)\oplus \text{f }\left(\text{J}\right),\text{ and f }\left(\text{x}\right)=\left(\text{f }\left(\text{x}\right)\oplus \text{f }\left(\text{J}\right)\right)\oplus \text{f }\left(\text{J}\right)=\text{f }\left(\text{h}\right)\oplus \text{f }\left(\text{J}\right)\end{array}$(13) To get the value $\left(x\right)$, that is, two hexadecimal values can be supplied, the outcome of adding BF to ED using a special OR procedure. ED is represented by the binary integers 11101101 and BF by 10111111. Below is an illustration of the operation:

In Galois Field $2^8$ (GF $\left(2^8\right)$), it is possible to express ED and BF using the polynomials $\text{f}\left(\text{x}\right)$ and $\left(\text{J}\right)$, respectively. (14) $\begin{array}{rl}\text{f}\left(\text{x}\right)& ={\text{x}}^7+{\text{x}}^6+{\text{x}}^5+{\text{x}}^3+{\text{x}}^2+1=\text{ED}\end{array}$(14) (15) $\begin{array}{rl}\text{f}\left(\text{x}\right)& ={\text{x}}^7+{\text{x}}^5+{\text{x}}^4+{\text{x}}^3+{\text{x}}^2+{\text{x}}^1+1=\text{BF}\end{array}$(15)

Therefore (16) $\begin{array}{rl}\text{f}\left(\text{h}\right)& =\text{f}\left(\text{x}\right)\oplus \text{f}\left(\text{J}\right)={\text{x}}^7+{\text{x}}^6+{\text{x}}^5+{\text{x}}^3+{\text{x}}^2+1\oplus {\text{x}}^7+{\text{x}}^5+{\text{x}}^4+{\text{x}}^3+{\text{x}}^2+{\text{x}}^1+1\\ & ={\text{x}}^6+{\text{x}}^4+{\text{x}}^1\end{array}$(16) $f\left(h\right)=x^6+x^4+x^1=01010010$. The binary representation is 52, whereas the hexadecimal representation is 52. Using the polynomials $f\left(h\right)\oplus f\left(k\right)$, it can demonstrate that $f\left(h\right)$ = ($f\left(h\right)\oplus f\left(k\right)$) $\oplus f\left(k\right)$ = $f\left(h\right)\oplus f\left(k\right)$, (17) $\begin{array}{rl}f\left(x\right)& =f\left(h\right)\oplus f\left(k\right)=x^6+x^4+x^1\oplus x^7+x^5+x^4+x^3+x^2+1\\ & =x^7+x^6+x^5+x^3+x^2+1\end{array}$(17)

Since $\left(\text{x}\right)=\left(\text{f}\left(\text{x}\right)\oplus \text{f}\left(\text{x}\right)\right)\oplus \text{x}\left(\text{J}\right)=\text{f}\left(\text{h}\right)\oplus \text{f}\left(\text{J}\right)$, It has been shown that the Sub byte operation is invertible. Prior to performing an XOR operation on the state matrix and the Rkeyb, the replacement is performed during the inverse Sub byte operation. (18) $\begin{array}{r}{{\mathrm{S}}^{\mathrm{\prime }}}_{\text{i},\text{j}}=\text{ Inverse Substitution Box}\left[{{\mathrm{S}}^{\mathrm{\prime }}}_{\text{i},\text{j}}\right]\text{ where j}=0\text{ to }3,\text{ for each j }=0\text{ to }3\end{array}$(18) Afterward, the replacement yields the matrix S′ in this way: ${\mathrm{S}}^{\mathrm{\prime }}=\begin{array}{c}{{\mathrm{S}}^{\mathrm{\prime }}}_{0,0}\\ {{\mathrm{S}}^{\mathrm{\prime }}}_{1,0}\\ \begin{array}{c}{{\mathrm{S}}^{\mathrm{\prime }}}_{2,0}\\ {{\mathrm{S}}^{\mathrm{\prime }}}_{3,0}\end{array}\end{array}\begin{array}{c}{{\mathrm{S}}^{\mathrm{\prime }}}_{0,1}\\ {{\mathrm{S}}^{\mathrm{\prime }}}_{1,1}\\ \begin{array}{c}{{\mathrm{S}}^{\mathrm{\prime }}}_{2,1}\\ {{\mathrm{S}}^{\mathrm{\prime }}}_{3,1}\end{array}\end{array}\begin{array}{c}{{\mathrm{S}}^{\mathrm{\prime }}}_{0,2}\\ {{\mathrm{S}}^{\mathrm{\prime }}}_{1,2}\\ \begin{array}{c}{{\mathrm{S}}^{\mathrm{\prime }}}_{2,2}\\ {{\mathrm{S}}^{\mathrm{\prime }}}_{3,2}\end{array}\end{array}\begin{array}{c}{{\mathrm{S}}^{\mathrm{\prime }}}_{0,3}\\ {{\mathrm{S}}^{\mathrm{\prime }}}_{1,3}\\ \begin{array}{c}{{\mathrm{S}}^{\mathrm{\prime }}}_{2,3}\\ {{\mathrm{S}}^{\mathrm{\prime }}}_{3,3}\end{array}\end{array}$

The initial state is recovered by using equation 1(1) $\begin{array}{r}(\text{Magnitude}{)}^2=[\text{H}{\text{w}}^2+\text{H}{\text{z}}^2]\end{array}$(1) 9 to XOR the $S^{\mathrm{\prime }}$ matrix with the XOR keyy. (19) $\begin{array}{r}{\text{S}}_{\text{i},\text{j}}={{\mathrm{S}}^{\mathrm{\prime }}}_{\text{i},\text{j}}\oplus \text{ XORke}{\text{y}}_{\text{i}},\text{ where j}=0\text{ to}3\text{ or each from }0\text{to}3\end{array}$(19) The matrix displaying the inverse of the Sub Bytes operation is as under ${\mathrm{S}}^{\mathrm{\prime }}==\begin{array}{c}{\text{S}}_{0,0}\oplus \text{ke}{\text{y}}_0\\ {\text{S}}_{1,0}\oplus \text{ke}{\text{y}}_1\\ \begin{array}{c}{\text{S}}_{2,0}\oplus \text{ke}{\text{y}}_2\\ {\text{S}}_{3,0}\oplus \text{ke}{\text{y}}_3\end{array}\end{array}\begin{array}{c}{\text{S}}_{0,1}\oplus \text{ke}{\text{y}}_0\\ {\text{S}}_{1,1}\oplus \text{ke}{\text{y}}_1\\ \begin{array}{c}{\text{S}}_{2,1}\oplus \text{ke}{\text{y}}_2\\ {\text{S}}_{3,1}\oplus \text{ke}{\text{y}}_3\end{array}\end{array}\begin{array}{c}{\text{S}}_{0,2}\oplus \text{ke}{\text{y}}_0\\ {\text{S}}_{1,2}\oplus \text{ke}{\text{y}}_1\\ \begin{array}{c}{\text{S}}_{2,2}\oplus \text{ke}{\text{y}}_2\\ {\text{S}}_{3,2}\oplus \text{ke}{\text{y}}_3\end{array}\end{array}\begin{array}{c}{\text{S}}_{0,3}\oplus \text{ke}{\text{y}}_0\\ {\text{S}}_{1,3}\oplus \text{ke}{\text{y}}_1\\ \begin{array}{c}{\text{S}}_{2,3}\oplus \text{ke}{\text{y}}_2\\ {\text{S}}_{3,3}\oplus \text{ke}{\text{y}}_3\end{array}\end{array}$The following steps create the resulting matrix S, representing the initial state. $S=\begin{array}{c}{S}_{0,0}\\ S_{1,0}\\ \begin{array}{c}{S}_{2,0}\\ S_{3,0}\end{array}\end{array}\begin{array}{c}{S}_{0,1}\\ S_{1,1}\\ \begin{array}{c}{S}_{2,1}\\ S_{3,1}\end{array}\end{array}\begin{array}{c}{S}_{0,2}\\ S_{1,2}\\ \begin{array}{c}{S}_{2,2}\\ S_{3,2}\end{array}\end{array}\begin{array}{c}{S}_{0,3}\\ S_{1,3}\\ \begin{array}{c}{S}_{2,3}\\ S_{3,3}\end{array}\end{array}$

The argument above shows the inevitability of the Sub Bytes operation.

$\mathrm{SubstitutionBox}\left[S_{i,j}\oplus \mathrm{XORke}{y}_i\right]=\mathrm{InverseSubstitutionBox}\left[{S^{\mathrm{\prime }}}_{i,j}\right]\oplus \mathrm{XORke}{y}_i$ Where $j=0$ to 3, for each i from 0 to 3.

3.3.2. Shift rows transformation

Randomising the method to perform the Shift Rows operation is important. The procedure depends on an integer known as the Ranking Number (RNo) instead of the constant offset (Vandic et al., 2024). This value may be retrieved by finding the state matrix row corresponding to the round key matrices. The state's rows are reorganised using the derived rank number. The first algorithm's rank was determined by two matrices, a circular key matrix K and a state matrix S. The rank detection using state and the round key matrix is presented in Algorithm 1. $S=\begin{array}{c}{S}_{0,0}\\ S_{1,0}\\ \begin{array}{c}{S}_{2,0}\\ S_{3,0}\end{array}\end{array}\begin{array}{c}{S}_{0,1}\\ S_{1,1}\\ \begin{array}{c}{S}_{2,1}\\ S_{3,1}\end{array}\end{array}\begin{array}{c}{S}_{0,2}\\ S_{1,2}\\ \begin{array}{c}{S}_{2,2}\\ S_{3,2}\end{array}\end{array}\begin{array}{c}{T}_{0,3}\\ T_{1,3}\\ \begin{array}{c}{T}_{2,3}\\ T_{3,3}\end{array}\end{array}\mathrm{and}K=\begin{array}{c}{K}_{0,0}\\ K_{1,0}\\ \begin{array}{c}{K}_{2,0}\\ K_{3,0}\end{array}\end{array}\begin{array}{c}{K}_{0,1}\\ K_{1,1}\\ \begin{array}{c}{K}_{2,1}\\ K_{3,1}\end{array}\end{array}\begin{array}{c}{K}_{0,1}\\ K_{1,2}\\ \begin{array}{c}{K}_{2,2}\\ K_{3,2}\end{array}\end{array}\begin{array}{c}{K}_{0,3}\\ K_{1,3}\\ \begin{array}{c}{K}_{2,3}\\ K_{3,3}\end{array}\end{array}$

Table

Algorithm 1 Rank determination using state matrix and round key matrix
Step 1: A State-Key (SKey) vector, consisting of four bytes, was created by adding each row $\left(\mathrm{Ro}{w}_j\right)$ performed an XOR operation on each row in the position medium that corresponds to that row of the circular key matrix.
Step 2: To produce an eight-bit value termed the Ranking Value ($\mathrm{Rva}{l}_j$), XORing specifically, this word describes the first four bits of the State-Key element.
Step 3: Next, the state matrix is used to store the eight-bit Rank Value ($\mathrm{Rva}{l}_j$) in the associated row.
Step 4: Rows 1 through 3 will continue to follow the same pattern as steps 1-3.
Step 5: The lowest rank value should be used first for each state row (rows 0 through 3), and work your way up to the highest rank value, adding a Ranking Number (RNo) to each of the Ranking Values (Ranking Values) collected in Step 3 above

Equation 20 is used to create the state key $\left(\mathrm{SKey}\right)$ vector (20) $\begin{array}{r}\mathrm{Ske}{y}_i=\left(\left(S_{i,0}\oplus K_{i,0}\right),\left(S_{i,1}\oplus K_{\text{i}1}\right),\left(S_{i,2}\oplus K_{i,2}\right),(S_{i,3}\oplus K_{i,3}\right)\end{array}$(20) Further reduction of equation 2(2) $\begin{array}{r}\text{ta}{\text{n}}^{-1}\mathrm{\varnothing }=\text{where}=\frac{\text{Hz}}{\text{Hw}}\end{array}$(2) 1, which in turn allows for (21) $\begin{array}{r}\mathrm{Ske}{y}_i=\left(S{\text{K}}_{i,0,}S{\text{K}}_{i,1,}S{K}_{i,2,}S{\text{K}}_{i,3}\right)\mathrm{where}S{\text{K}}_{i,f}=S_{i,f}\oplus K_{i,f}\end{array}$(21)

Equations 22(22) $\begin{array}{rl}\mathrm{Ske}{y}_0& =\left(S{\text{K}}_{0,0},S{\text{K}}_{0,1},S{\text{K}}_{0,2,}S{\text{K}}_{0,3}\right)\end{array}$(22) to 2(2) $\begin{array}{r}\text{ta}{\text{n}}^{-1}\mathrm{\varnothing }=\text{where}=\frac{\text{Hz}}{\text{Hw}}\end{array}$(2) 5 can be used to break down equation 1(1) $\begin{array}{r}(\text{Magnitude}{)}^2=[\text{H}{\text{w}}^2+\text{H}{\text{z}}^2]\end{array}$(1) 6. (22) $\begin{array}{rl}\mathrm{Ske}{y}_0& =\left(S{\text{K}}_{0,0},S{\text{K}}_{0,1},S{\text{K}}_{0,2,}S{\text{K}}_{0,3}\right)\end{array}$(22) (23) $\begin{array}{rl}\mathrm{Ske}{y}_1& =\left(S{\text{K}}_{1,0},S{\text{K}}_{1,1},S{\text{K}}_{1,2,}S{\text{K}}_{1,3}\right)\end{array}$(23) (24) $\begin{array}{rl}\mathrm{Ske}{y}_2& =\left(S{\text{K}}_{2,0},S{\text{K}}_{2,1},S{\text{K}}_{2,2,}S{\text{K}}_{2,3}\right)\end{array}$(24) (25) $\begin{array}{rl}\mathrm{Ske}{y}_3& =\left(S{\text{K}}_{3,0},S{\text{K}}_{3,1},S{\text{K}}_{3,2,}S{\text{K}}_{3,3}\right)\end{array}$(25)

Equation 26 is used to derive the Rank Values $\left(\mathrm{RVals}\right)$, such that: (26) $\begin{array}{r}\mathrm{RVa}{l}_i=\left(S{\text{K}}_{i,0}\oplus S{\text{K}}_{i,1}\oplus S{\text{K}}_{i,2}\oplus S{\text{K}}_{i,3}\right),\text{where}i=0\mathrm{to}3\end{array}$(26)

Equation 2(2) $\begin{array}{r}\text{ta}{\text{n}}^{-1}\mathrm{\varnothing }=\text{where}=\frac{\text{Hz}}{\text{Hw}}\end{array}$(2) 6 can be divided into four separate equations that reflect each row of the condition shown in equations 27(27) $\begin{array}{rl}\mathrm{RVa}{l}_0& =S{\text{K}}_{0,0}\oplus S{\text{K}}_{0,1}\oplus S{\text{K}}_{0,2}\oplus S{\text{K}}_{0,3}\end{array}$(27) to 30(30) $\begin{array}{rl}\mathrm{RVa}{l}_3& =S{\text{K}}_{3,0}\oplus S{\text{K}}_{3,1}S{\text{K}}_{3,2}\oplus S{\text{K}}_{3,3}\end{array}$(30) . (27) $\begin{array}{rl}\mathrm{RVa}{l}_0& =S{\text{K}}_{0,0}\oplus S{\text{K}}_{0,1}\oplus S{\text{K}}_{0,2}\oplus S{\text{K}}_{0,3}\end{array}$(27) (28) $\begin{array}{rl}\mathrm{RVa}{l}_1& =S{\text{K}}_{1,0}\oplus S{\text{K}}_{1,1}\oplus S{\text{K}}_{1,2}\oplus S{\text{K}}_{1,3}\end{array}$(28) (29) $\begin{array}{rl}\mathrm{RVa}{l}_2& =S{\text{K}}_{2,0}\oplus S{\text{K}}_{2,1}\oplus S{\text{K}}_{2,2}\oplus S{\text{K}}_{2,3}\end{array}$(29) (30) $\begin{array}{rl}\mathrm{RVa}{l}_3& =S{\text{K}}_{3,0}\oplus S{\text{K}}_{3,1}S{\text{K}}_{3,2}\oplus S{\text{K}}_{3,3}\end{array}$(30)

The Rank Number $\left(\mathrm{RNo}\right)$ is appended to each of the Rank Values $\left(\mathrm{Rvals}\right),$ starting with the lowest $\mathrm{RVal}$ and going all the way up to the largest $\mathrm{RVal},$ in ascending order.

Following the acquisition of the Rank Values ($\mathrm{Rvals}$), the values are assigned a Rank Number $\left(\mathrm{RNo}\right)$ in ascending order, wherein the largest $\mathrm{RVal}$ is assigned an $\mathrm{RNo}$ of 4 and the smallest $\mathrm{Rvals}$ is assigned an $\mathrm{RNo}$ of 1.

The state's rows are then all moved. $\mathrm{RNo}-1$ places to the left. The row with $\mathrm{RNo}=1$ is thus not moved, whereas the rows with $\mathrm{RNo}$ = 2 and $\mathrm{RNo}=$3 are shifted one, two, and three bytes correspondingly to the left, and lastly, The highest-ranking row has three bytes shifted to its left, $\mathrm{RNo}=4.$

The modified Shift Rows operation is explained below, using the matrices. $S$ for states and $K$ for round keys. $S=\begin{array}{c}4D\\ \mathrm{EC}\\ \begin{array}{c}4A\\ 8C\end{array}\end{array}\begin{array}{c}87\\ 6E\\ \begin{array}{c}C3\\ D8\end{array}\end{array}\begin{array}{c}F2\\ 4C\\ \begin{array}{c}46\\ 95\end{array}\end{array}\begin{array}{c}97\\ 90\\ \begin{array}{c}E7\\ A6\end{array}\end{array}\mathrm{and}K=\begin{array}{c}11\\ 1\text{F}\\ \begin{array}{c}83\\ D4\end{array}\end{array}\begin{array}{c}55\\ 44\\ \begin{array}{c}E6\\ 31\end{array}\end{array}\begin{array}{c}75\\ 53\\ \begin{array}{c}90\\ 77\end{array}\end{array}\begin{array}{c}A1\\ \mathrm{CA}\\ \begin{array}{c}3D\\ 9F\end{array}\end{array}$Now, it can get the state key $\left(S-\mathrm{Key}\right)$ vectors, the following steps are followed. $\begin{array}{rl}\mathrm{Ske}{y}_0& =\left(\left(4D\oplus 11\right),\left(87\oplus 55\right),\left(F2\oplus 75\right),\left(97\oplus A1\right)\right)=\left(5C,B2,87,36\right)\end{array}$ $\begin{array}{rl}\mathrm{Ske}{y}_1& =\left(\left(\mathrm{EC}\oplus 1F\right),\left(6E\oplus 44\right),\left(4C\oplus 53\right),\left(90\oplus \mathrm{CA}\right)\right)=\left(F3,2A,1F,5A\right)\end{array}$ $\begin{array}{rl}\mathrm{Ske}{y}_2& =\left(\left(4A\oplus 84\right),\left(C3\oplus E6\right),\left(46\oplus 90\right),\left(E7\oplus 3D\right)\right)=\left(C9,25,B6,\mathrm{DA}\right)\end{array}$ $\begin{array}{rl}\mathrm{Ske}{y}_3& =\left(\left(8C\oplus D4\right),\left(D8\oplus 31\right),\left(95\oplus 77\right),\left(A6\oplus 9F\right)\right)=\left(58,E9,E2,39\right)\end{array}$

Next, it gets the Rank Values $\left(\mathrm{RVals}\right)$ by following these steps: $\begin{array}{rl}\mathrm{RVa}{l}_0& =5C\oplus D2\oplus 87\oplus 36=3F\end{array}$ $\begin{array}{rl}\mathrm{RVa}{l}_1& =F3\oplus 2A\oplus 1E\oplus 5A=9C\end{array}$ $\begin{array}{rl}\mathrm{RVa}{l}_2& =C9\oplus 25\oplus D6\oplus \mathrm{DA}=E0\end{array}$ $\begin{array}{rl}\mathrm{RVa}{l}_3& =58\oplus E9\oplus E2\oplus 39=6A\end{array}$

Each row's rank number determines how much room each row needs, which is one less than the row's $\mathrm{RNo}$ value, as presented in Table 2. Row 0 will remain unchanged, row 1 will relocate two bytes to the left, row 2 will move three bytes to the left, and row 3 will move to the left-hand side. These Shift Rows operations are performed on the provided state using the lowest rank value and should be used first for each state row (rows 0 through 3) for the state matrix after the modification. $\begin{array}{r}S=\begin{array}{c}4D\\ \mathrm{EC}\\ \begin{array}{c}4A\\ 8C\end{array}\end{array}\begin{array}{c}87\\ 6F\\ \begin{array}{c}C3\\ D8\end{array}\end{array}\begin{array}{c}F2\\ 4C\\ \begin{array}{c}46\\ 95\end{array}\end{array}\begin{array}{c}97\\ 90\\ \begin{array}{c}E7\\ A6\end{array}\end{array}\mathrm{and}S{}^{\mathrm{\prime }}=\begin{array}{c}4D\\ 4C\\ \begin{array}{c}E7\\ D8\end{array}\end{array}\begin{array}{c}87\\ 90\\ \begin{array}{c}4A\\ 95\end{array}\end{array}\begin{array}{c}F2\\ \mathrm{EC}\\ \begin{array}{c}C3\\ A6\end{array}\end{array}\begin{array}{c}97\\ 6E\\ \begin{array}{c}46\\ 8C\end{array}\end{array}\end{array}$

3.3.3. Inverse shift rows transformation

Decryption uses a backward reading of the round keys, which means that the rank number computation for the Inverse Shift Rows operation is identical to that of the modified Shift Rows operation (Benoit et al., 2024). Aside from the change in direction, both methods involve shifting to the state matrix's rows. When turning the tables around, according to their rank, the rows are moved to the right (Rahman et al., 2024). The AES-128 algorithm is described in Algorithm 2.

Table 2. The RVals, RNos, and state row numbers correlate to the rank values.

S/No	RVals	RNos	State Row No	Value (Dec)	Value (Hex)
1	$\mathrm{RVa}{l}_0$	1	0	63	3F
2	$\mathrm{RVa}{l}_1$	3	1	156	9C
3	$\mathrm{RVa}{l}_2$	4	2	224	E0
4	$\mathrm{RVa}{l}_3$	3	3	106	6A

Table

Algorithm 2 AES-128 Encryption Process
Input: The 128-bit plaintext blocks P and key K.
Output: The 128-bit cipher text blocks C.
Y ← Add Round Key (P, L)
For i ← 1 to 10 do
Y ← Sub Bytes(Y)
Y ← Shift Rows(Y)
If i ≠ 10 Y ← Mix Columns(Y)
End
L ← Key Schedule (L)
Y ← Add Round Key (X, L)
End D ← Y
Return D

Blowfish is a symmetric cipher system that encrypts and protects images (Gadde et al., 2023). It works for safeguarding medical images since it employs a length of the key that might vary between 32 and 448 bits. The Blowfish symmetric block cipher is 64 bits long and uses keys of varying lengths (Abbas et al., 2021). The procedure has two parts: one that encrypts images and another that increases keys. The key extension requires several sub-key arrays totaling 4168 bytes for keys with a maximum of 448 bits. The data is encrypted through a Feistel network of 16 rounds. It is only appropriate for applications such as automated file encryption or communications links when the key is the same. The Blowfish algorithm is presented in Algorithm 3.

Table

Algorithm 3 Blowfish encryption process
Divide Y into two 32-bit halves, Y L and Y R
For i = 1 to 16:
$\mathrm{YL}=\mathrm{YL}\mathrm{Pi}$
$\mathrm{YR}=F\left(\mathrm{XL}\right)\mathrm{YR}$
$\mathrm{Swap}\mathrm{YL}\mathrm{and}\mathrm{YR}$
$\mathrm{End}\mathrm{for}\mathrm{Swap}\mathrm{YL}\mathrm{and}\mathrm{YR}$
$\mathrm{YR}=\mathrm{YR}P17$
$\mathrm{YL}=\mathrm{YL}P18$
Recombine YL and YR Output Y (64-bit data block: cipher text)

This work presents a hybrid cryptography technique using AES Permuted Feistel Blowfish. These symmetric techniques can lengthen the time it takes to encrypt and decode images obtained from medical image directory databases (Nagarajan et al., 2022). Figures 4 and 5 illustrate the proposed model for hybrid encryption and decryption. The proposed APFB model algorithm is illustrated in Algorithm 4.

Figure 4. Encryption process of the proposed model.

Figure 5. The decryption process of the proposed model.

Table

Algorithm 4 Proposed APFB model
Encryption
Setup: After entering the security parameter $\lambda$, the master key $s$ and public system parameter ParamsParams are generated via ECDH.
Partial key generation: Set the system's properties. The user's partial private key $\mathrm{PS}{K}_u$ and partial public key $\mathrm{PP}{K}_u$ are generated using ECDH using the user's identification $I{D}_u$ and its parameters (master key $s$).
User key generation: To set the system parameter to produce a full set of public and private keys ($P{K}_u,S{K}_u$), the parameters include consumer $U^{\mathrm{\prime }}s$ identification $I{D}_u$ and partial public and personal keys ($\mathrm{PP}{K}_u,\mathrm{PS}{K}_u$).
Keyword encryption: Set the system's properties to construct the keyword cipher text $C$; the following parameters are required: a keyword$\omega$, the identities of many receivers $\{I{D}_i,P{K}_i\}$, and their public keys
Encode the Keyword: Transform the word $\omega$ into an encryption-ready format. Hashing the keyword or using an appropriate encoding technique could be necessary.
Key Derivation: To generate a symmetric encryption key or keys, use the system parameters Params, the value encoded with keywords, and the public keys of the intended recipients$\{I{D}_i,P{K}_i\}$. A key derivation function is usually used for this purpose.
Symmetric Encryption: Insert the derivation key$\left(s\right)$ into the APFB symmetric encryption algorithm and encrypt the keyword. The output of this process is the $C$-key cipher text.
Decryption
Partial Key Retrieval: For user$U$, utilise the given identification $I{D}_u$ and the system settings. Building the partial private key, $\mathrm{PS}{K}_u$, requires certain parameters and a master key.
Key Agreement: To create a shared secret $\mathrm{SSi}$ between user $U$ and each receiver $i$, execute an elliptic curve Diffie-Hellman (ECDH) key agreement using the partial private key, $\mathrm{PS}{K}_u$, and the public key, $P{K}_i$, or each receiver $i.$
Key Derivation: Gather all the necessary receivers’ shared secrets, $S{S}_i$, and combine them to form a common secret key $K$. A secure key derivation function can do this.
Decryption: Decode the keyword cipher text $C$ using the generated common secret key $K$. The chosen encryption method determines the precise decryption algorithm.
Output: The decrypted term ω.

In blockchain, encrypted data is stored through hashing. When information is added to a block, it undergoes a cryptographic hash function, generating a fixed-size string of characters that uniquely represents the data (Alfrhan et al., 2021). This hash is stored along with the previous block's hash, forming a chain. Encrypted data is transformed using a cryptographic hash function in a stored process through hashing. This hash uniquely represents the encrypted data the blockchain keeps (Barik et al., 2023). The hash serves as a fingerprint for the data and ensures its integrity. The hash changes drastically if the data is altered, even by a single character. Moreover, since each block references the previous block's hash, any interference with a block necessitates altering subsequent blocks, making the stored process secure and resistant to unauthorised modifications. The user should initiate the decryption process by requesting the decryption of data. Data that needs to be decrypted is retrieved in response to user requests. The first step in decoding is getting the encryption keys. The encryption transformations are reversed using the same keys used for encryption. Figure 5 demonstrates the decryption process of the proposed model.

4. Experimental results and analysis

This section discusses the proposed model's outcome. This study is conducted on a laptop with an Intel Core i7 8550 CPU, 1.8 GHz, 4 cores, MS Windows 11 64-bit OS, 32 GB of RAM, and 500 GB of SSD storage. The model is implemented in the Python environment. Different evaluation metrics are considered, i.e., MSE, PSNR, CC, Entropy, NPCR, and UACI, and computed using equations 31(31) $\begin{array}{rl}\text{MSE}& =1/\phantom{1\text{n}}\text{n}\sum _{\text{i}=1}^{\text{n}}({\text{y}}_{\text{i}}-{\text{x}}_{\text{i}}{)}^2\end{array}$(31) and 3(3) $\begin{array}{rl}\text{k}2-\text{norm}:\text{u}& \to \text{u}/\sqrt{{\text{u}}_2^2}+{ϵ}^2\end{array}$(3) 7, respectively. (31) $\begin{array}{rl}\text{MSE}& =1/\phantom{1\text{n}}\text{n}\sum _{\text{i}=1}^{\text{n}}({\text{y}}_{\text{i}}-{\text{x}}_{\text{i}}{)}^2\end{array}$(31) (32) $\begin{array}{rl}\text{PSNR}& =10.\log 10\left(\frac{\text{Peak signal valul}{\text{e}}^2}{\text{Mean square error }\left(\text{MSE}\right)}\right)\end{array}$(32) (33) $\begin{array}{rl}\text{H}\left(\text{X}\right)& =-\sum _{\text{i}}\text{P}\left({\text{x}}_{\text{i}}\right).{\log }_2\left(\text{P}\left({\text{x}}_{\text{i}}\right)\right)\end{array}$(33) (34) $\begin{array}{rl}\text{C}& =\frac{\text{n}(\sum \text{xy})-(\sum \text{x})\left(\sum \text{y}\right)}{\sqrt{\left[\text{n}\sum {\text{x}}^2-{\left(\sum \text{x}\right)}^2-{\left(\sum \text{y}\right)}^2\right]}}\end{array}$(34) (35) $\begin{array}{rl}\text{H}\left(\text{s}\right)& =\sum _{\text{i}=0}^{2^{\text{n}-1}}\text{P}\left({\text{S}}_{\text{i}}\right){\log }_{2}1/\phantom{1\text{P}\left({\text{S}}_{\text{i}}\right)}\text{P}\left({\text{S}}_{\text{i}}\right)\end{array}$(35) (36) $\begin{array}{rl}\mathrm{NPCR}& =\frac{{\sum }_{\text{lm}}\text{C}\left(l,m\right)}{X\ast Y}\ast 100\mathrm{\%}\end{array}$(36) (37) $\begin{array}{rl}\mathrm{UACI}& =\frac{1}{X\ast Y}\sum _{\text{lm}}\left[\frac{\left[{\text{Z}}_1\left(\text{l},\text{m}\right)-{\text{Z}}_2\left(l.m\right)\right]}{255}\right]\ast 100\end{array}$(37)

${\text{Z}}_1$ and ${\text{Z}}_2$ are the chipper images corresponding to two security keys.

Mean Squared Error (MSE) is utilised to evaluate the efficacy of image encryption techniques. It quantifies the average squared difference between an image's pre- and post-encryption pixel values. A lower MSE shows minimum distortion between the original and encrypted images, and a lower MSE presents greater preservation of image quality throughout the encryption process. Figure 6 illustrates the test outcome of the MSE values for five specific images.

Figure 6. MSE for the specific images.

The encryption and decryption durations for specific images are contingent upon several elements, such as the encryption technique employed, the image's dimensions, and the hardware's computing capacity. The original image should be converted into a coded format to safeguard its information. This process is reversed to retrieve the original image during decryption. Fast encryption and decryption times are necessary for efficient data transfer and real-time applications. Processing times can be significantly decreased by using hardware-accelerated advanced encryption methods. However, additional processing power and time might be needed for encryption and decryption of higher image sizes. Figures 7 and 8 illustrate the duration of encrypting and decrypting each of the five images and the image index.

Figure 7. Encryption times for the individual images.

Figure 8. Decryption times for individual images.

The correlation coefficient (CC) indicates the image's pixel redundancy. The plain image has duplication, although the encrypted image should have a high CC value. This signifies the encrypted image with the lowest level of redundancy. It provides the degree of correlation coefficient analysis, the degree to which two adjacent pixels in an image are similar for each of the five images, as pictured in Figure 9.

Figure 9. Correlation coefficients for the specific images.

Entropy is used to access images of unpredictability. In this study, entropy is employed as a criterion for evaluating the relevance of the ciphering approach. Figure 10 illustrates the test outcome of the entropy values for specific image analysis for each of the five individual images.

Figure 10. Entropy values for the specific images.

A common metric for evaluating the effectiveness of image encryption is the PSNR. The ratio of the greatest potential power of a signal (the original image) to the power of the noise created during encryption is known as PSNR. Figure 11 depicts the test results of the PSNR values for a particular image analysis for each of the five distinct encrypted images.

Figure 11. PSNR for the specific encrypted images.

Figure 12 depicts the test results of the PSNR values for a particular image analysis for each of the five distinct decrypted images.

Figure 12. PSNR for the specific decrypted images.

Table 3 illustrates the outcome of the proposed model. The image is encoded using the optimal technique that enables a safe transmission. After two-fold encryption, the image can be sent safely. The last step recovers the original image using a hybrid decryption method. Encryption is obtained twice during transmission. The other user uses the blowfish decryption technique to execute design encryption and decryption after receiving the information.

Table 3. Analysis of the proposed model's outcomes using different input image data.

Original Image	Encrypted Image	Decrypted Image	PSNR	MSE	CC	Entropy	Time
			65.4283	0.01863	0.9993	14.0605	0.0100 sec
			69.7922	0.00682	0.9993	15.0265	0.0190 sec
			66.0190	0.01626	0.9993	15.0353	0.0280 sec
			69.9873	0.00652	0.9999	14.9565	0.0242 sec
			67.2697	0.01219	0.9998	13.8351	0.0080 sec

The five selected images were chosen to compute the encryption and decryption time of the proposed mode, and the outcome is presented in Table 4.

Table 4. Encryption and decryption time of five images.

Image	Encryption Computation time (s)	Decryption Computation time (s)
Image 1	0.006	0.0861
Image 2	0.013	0.0901
Image 3	0.015	0.0931
Image 4	0.016	0.0909
Image 5	0.005	0.008
Average	0.011	0.0736

4.1. Robustness analysis

Robustness refers to encryption systems’ ability to address and remain unaffected against attacks, making it an essential quality. We conducted experiments using plaintext, noise, and JPEG compression attacks using 256 *256 images to evaluate the resilience of the proposed model.

4.1.1 Plaintext attacks

The analysis should include a dedicated segment on the chosen plaintext attack, examining its potential vulnerabilities and countermeasures within the proposed encryption system (Yuan et al., 2024). The model is evaluated using the Number of Pixels Change Rate (NPCR) and the Unified Average Changing Intensity (UACI). Table 5 illustrates the experimental outcomes of NPCR and UACI values in different images. The proposed encryption system can address plaintext attacks, as exhibited in Figures 6, 9, 11, 12, and Tables 3 and 5.

Table 5. Experimental outcomes of NPCR and UACI for different images.

Image	NPCR	UACI
Image 1	99.6354	33.412
Image 2	99.5478	33.321
Image 3	99.5632	33.326
Image 4	99.5891	33.432
Image 5	99.6231	33.436

4.1.2. Noise attacks

This experiment employs salt and pepper noise attacks, with the noise strength K for the recommended encryption approach of 0.01 in five images. Figure 13 exhibits the encrypted text visuals and the related decoded images for those visuals under different noise attacks and intensities. Although the quality of the decrypted image deteriorates with increasing noise levels, the approach can resist noise attacks over a wider range of intensities. Table 6 displays the PSNR values of encrypted images subjected to noise attacks. Consequently, the proposed model is more resilient against attacks that rely on salt and pepper noise.

Figure 13. Experimental outcomes of noise attacks.

Table 6. PSNR value of noise attacks.

Image	Density level	PNSR values of encrypted images
Image 1	0.001	45.327
Image 2	0.001	45.658
Image 3	0.001	42.569
Image 4	0.001	40.329
Image 5	0.001	44.852

4.1.3. JPEG compression attacks

It leverages the extensively utilised JPEG compression method, which employs lossy compression techniques to lessen image record sizes (Yuan et al., 2024). The attacks aim to exploit the lossy nature of JPEG compression to degrade the first-rate decrypted images, introducing distortions and artifacts that decrease the image's fidelity and reliability. The JPEG compression is applied, and Figure 14 shows the outcome of five selected images. The proposed model improves defences against JPEG compression attacks. Hybrid encryption techniques strengthen encryption via random key integration inside the Feistel shape.

Figure 14. Experimental outcome of JPEG compression attacks.

4.1.4. Physical brute-force attack

The attacker can access data physically by disassembling the devices and obtaining the disk. Also, the emergency access option can be enabled on most devices, granting access to essential tasks without authentication (Jiang et al., 2024). Therefore, it is important to prevent physical brute force by designing adequate physical defence measures. The proposed model combines the advantages of APFB to strengthen encryption against brute-force attacks. The Permuted Feistel Network adds another layer of complexity to resist brute-force attacks. Combining hybrid techniques produces a robust encryption mechanism with complicated key recovery that makes brute-force attacks challenging.

4.1.5. Man-in-the-middle attack

A Man-in-the-Middle (MITM) attack happens when an unauthorised third party eavesdrops on and manipulates the conversations between two parties. The attackers can steal important information or introduce malicious code by infiltrating the transmission process (Al-Hawawreh & Hossain, 2023). The AES offers robust encryption, and data security is enhanced by the random integration of keys within the permuted Feistel structure. Incorporating Blowfish enhances the encryption diversity, thereby augmenting the level of security. The multilayered technique creates a complex and dynamic cryptographic environment to protect against unauthorised access and tampering, effectively preventing any attempts of MITM attacks.

4.1.6. Insider attack

When authorised users do destructive or accidental things with a company's systems or data, it is known as an insider threat (Randive et al., 2023). While AES ensures strong encryption, permuted Feistel uses permutation functions to offer added protection. Blowfish's complex substitution-permutation network and key-dependent s-boxes strengthen defences against unauthorised access.

4.2. Statistical analysis

The proposed approach involves the sequential application of mixing procedures to pixels. The randomness of the randomised pixel is evaluated. The SP 800-22 test tool consists of 16 components developed by the National Institute of Standards and Technology (NIST) to test the randomness of the model (Yang et al., 2020). In this testing tool, a test is deemed successful if the P-value is greater than or equal to α. Here, α is equal to 0.01 and reflects the significance threshold. The test results from NIST are demonstrated in Table 7. Based on the test results, the P-values exceed the significance level α = 0.01, which indicates a high level of randomness in the pixel arrays developed by the model.

Table 7. NIST test outcome.

Test details	P-value	Outcome	Conclusion
Frequency test	0.912	Pass	Random
Block frequency test	0.892	Pass	Random
Cumulative sums test-forward	0.439	Pass	Random
Cumulative sums test-reverse	0.868	Pass	Random
Runs test	0.298	Pass	Random
Longest run	0.798	Pass	Random
Discrete Fourier transform	0.592	Pass	Random
Rank	0.965	Pass	Random
Non overlapping	1	Pass	Random
Overlapping	0.936	Pass	Random
Universal	0.932	Pass	Random
Approximate entropy	0.612	Pass	Random
Serial	0.498	Pass	Random
Random excursions	0.584	Pass	Random
Random excursions variant	0.401	Pass	Random
Linear complexity	0.431	Pass	Random

4.3. Comparative analysis with existing studies

Table 8 displays the comparative analysis with the existing studies. However, it should be noted that the existing studies were performed in different environments, datasets, and techniques.

Table 8. A comparative study with the existing methods.

Methods	Entropy	PSNR	Correlation coefficient	NPCR	UACI	Encryption computation time (s)
Ali et al. (2024)	7.9996	27.31	−0.0061	99.6	33.46	–
Abdelfatah et al. (2023)	7.9985	7.18	0.0063	99.79	33.447	–
Nampalle et al. (2023)	21.9886	57.52	0.9999	99.6824	33.348	–
Huang et al. (2022)	7.5937	44.9383	0.977	–	–	0.2657
Alexan et al. (2023)	7.9972	8.928	0.000013	99.6254	33.0704	2.75
Inam et al. (2024)	7.9992	6.65	0.9568	99.63	33.21	–
Ahuja et al. (2023)	7.9996	28.4761	−0.0106	99.63	33.35	0.322
Proposed	14.9565	69.9873	0.9993	99.6354	33.412	0.011

4.4. Case study

This case study considers a small health case solution with 30 employees. The organisation manages medical imaging data for patients and shares it with a third party as required. They have branches in two different cities. The organisation needs to enhance image security and transmission quickly, with optimal computing resources, and cost-effectively. The proposed APFB model is implemented to handle the existing challenges and store the image data through blockchain for secure data transmission. Adequate training sessions and awareness programs have been conducted for employees about the significance of image security, the key features, and the model's applicability. The proposed model reduced the encryption and decryption time with enhanced image security and reduced compute resources. The improved cryptographic technique and access controls helped control unauthorised access to patient images, improving confidentiality and privacy. The model prevents attacks like plaintext, noise, man in the middle, JPEG compression, and physical brute-force attacks. The experience of HealthCare Solutions serves as a realistic example of how companies can effectively address image security concerns to protect sensitive image information. This case study illustrates the practical application of the APFB model in enhancing image data security in a healthcare company.

5. Discussion, study limitation, and future studies

This study presented a novel APFB model for enhancing image security using hybrid cryptographic techniques. The effectiveness of this model is illustrated through comprehensive analysis using different evaluation matrices. The proposed model is easy to implement, fast, and reduces computing resources. This study presented a novel APFB model for enhancing image security with cost efficiency and reduced computing resources using hybrid cryptographic methods. The effectiveness of this model is illustrated through comprehensive analysis using different evaluation matrices. The proposed model is easy to implement, fast, and reduces computing resources. Experimental outcomes with PSNR, entropy, MSE, CC, NPCR, UACI, and processing time signify promising results. The proposed model is tested with the NIST randomness test, and the outcomes signify that the sequences utilised have reasonably adequate randomness. It is observed that the proposed model takes an average of 0.011 s to encrypt and 0.073 s to decrypt a standard 256 *256 image. This reduced time complexity makes the approach useful in practical scenarios where efficiency is important. The proposed model is further validated with a practical case study analysis.

5.1. Study limitations

This study has thoroughly examined image data security. However, it is important to note the study's limitations and constraints outlined below.

1. The proposed model is validated using a limited set of data.

2. The study employed limited computing resources for processing. A high-speed computer and different evaluation matrices can be explored for model evaluation.

3. With the proposed model, compatibility between different cryptographic algorithms can be challenging, especially when negotiating with various devices, platforms, or applications.

4. The proposed model may require significant memory for key management, especially in scenarios with large numbers of users or when handling vast datasets.

5.2. Future studies

The future studies are outlined under

1. As technology advances, attackers can employ more complex techniques to compromise encryption systems. Additional research is required to create hybrid encryption methods that resist sophisticated cryptanalysis techniques and adversarial attacks.

2. Encryption algorithms must balance between ensuring security and optimising computational performance. Subsequent future studies can prioritise the development of encryption methods that offer strong security while reducing processing resources.

3. Future studies should analyse the development of effective and flexible key management strategies. This will assist in safely overseeing encryption keys in extensive systems.

4. Future studies can explore the potential collaboration between image encryption and developing techniques, namely deep learning and edge computing, to create innovative methods that offer improved protection and enactment.

6. Conclusion

This study presented the hybrid APEB model for robust security, combining AES and Blowfish algorithms. This primary goal is to present and assess an exclusive method that combines cryptographic algorithms to strengthen data security. The encrypted and decrypted data is stored in the blockchain to ensure security. The proposed model is demonstrated to protect sensitive information during transmission to maintain confidentiality and authenticity for image data. The proposed model achieved a PSNR of 67.2697, an entropy of 14.4321, an MSE of 0.01219, an NPCR of 99.6354, and a UACI of 33.412 and is compared with existing studies. The proposed model is tested with the NIST statistical suite. Additionally, the applicability of the proposed model is validated with a practical case study. The proposed model significantly reduces computation costs and computation time. The proposed model can be further enhanced to improve performance and provide secure multimedia files like audio and video. Incorporating image encryption with the latest technologies can provide new research opportunities.

Acknowledgments

The authors are thankful to their departments for providing the research environments and facilities to perform this research. They also sincerely thank the anonymous reviewers for taking the time and effort to review the manuscript and appreciate all useful comments and recommendations, which helped improve quality.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

The author(s) reported there is no funding associated with the work featured in this article.