Enterprise Resource Planning (ERP) systems underpin the operational fabric of modern enterprises, yet their predominantly rule-based, static architectures constrain adaptability in dynamic market conditions. This paper proposes and formalizes the concept of AI-native ERP—an architectural paradigm in which artificial intelligence is not an optional overlay but a foundational, deeply integrated layer spanning data ingestion, intelligent decision-making, autonomous workflow execution, external integration, and human interaction. We present a five-layer reference architecture, a formal decision-engine model combining Bayesian-calibrated machine learning prediction, constraint-satisfaction rule validation, and multi-objective utility optimization, and a risk-aware escalation mechanism parameterized by a composite risk function. Six enterprise use cases—spanning logistics, accounts payable, tax compliance, procurement, financial operations, and cross-functional intelligence—are analyzed to demonstrate practical applicability. Comparative analysis suggests the proposed architecture has the potential to substantially reduce manual process dependency and improve decision quality relative to AI-augmented ERP systems. Challenges including model governance, adversarial robustness, explainability, and organizational change management are critically examined. Future directions encompassing agentic ERP, federated enterprise learning, and self-healing architectures are delineated.

Daily usage of cyberspace and many telecommunication technologies like the Internet of Things (IoT), data transmission through clouds and wireless networks have proliferated. Substantial amounts of data are getting transmitted every day and the number is astronomically huge. The data contains textual data, images, videos and audio. Securing this data which is transmitted through channels of cyberspace is essential. The presented work discusses securing data of the type videos and images. The inspiration behind this research is to furnish a proficiently assembled three-channel image encryption scheme. The proposed work presents a dynamic encryption method for three-channel images built on key generation using the Hankel transform matrix, geometric transformation matrix and hyper-chaotic map to achieve triple security. Computer-simulated results show satisfactory output towards statistical tests. The sustainability of the work proposed in this research, against diverse attacks like differential, injection of noise attacks and cutting channel attacks, is tested and the proposed encryption scheme proves it promisingly. The robustness and effectiveness of the proposed scheme are decently compared with other existing schemes and it demonstrates the practical usability of the proposed encryption scheme.

The motivation for this article stems from the fact that medical image security is crucial for maintaining patient confidentiality and protecting against unauthorized access or manipulation. This paper presents a novel encryption technique that integrates the Deep Convolutional Generative Adversarial Networks (DCGAN) and Virtual Planet Domain (VPD) approach to enhance the protection of medical images. The method uses a Deep Learning (DL) framework to generate a decoy image, which forms the basis for generating encryption keys using a timestamp, nonce, and 1-D Exponential Chebyshev map (1-DEC). Experimental results validate the efficacy of the approach in safeguarding medical images from various security threats, including unauthorized access, tampering, and adversarial attacks. The randomness of the keys and encrypted images are demonstrated through the National Institute of Standards and Technology (NIST) SP 800-22 Statistical test suite provided in Tables 4 and 14, respectively. The robustness against key sensitivity, noise, cropping attacks, and adversarial attacks are shown in Figs. 15–18, 22–23, and 24. The data presented in Tables 5, 6, and 7 shows the proposed algorithm is robust and efficient in terms of time and key space complexity. Security analysis results are shown (such as histogram plots in Figs. 11–14 and correlation plots in Figs. 19–21). Information Entropy ( $$7.9993 \pm 0.0001$$ ), correlation coefficient ( $$\pm 0.09$$ ), Mean Square Error (MSE) ( $$4166.3107 \pm 1645.2980$$ ), Peak Signal to Noise Ratio (PSNR) ( $$12.2643 \pm 1.7032$$ ), Number of Pixel Change Rate (NPCR) ( $$99.60\% \pm 0.2\%$$ ), and Unified Average Changing Intensity (UACI) ( $$33.47\% \pm 0.1\%$$ ) underscore the high security and reliability of the encrypted images, are shown in Tables 8–11. Further, statistical NPCR and UACI are calculated in Tables 12 and 13, respectively. The proposed algorithm is also compared with existing algorithms, and compared values are provided in Table 15. The data presented in Tables 3–15 suggest that the proposed algorithm can opt for practical use.

In this chapter, we have discussed optimized image encryption techniques, which have been inspired by bio-optimization. An optimized-based image encryption algorithm is an essential tool in this modern world to keep the image secure, meet real-time demand (fast communication or processing) and prevent unauthorized access. This review chapter is categorized into four sections. Firstly, we briefly discuss the encryption and decryption model, and then the classification of the bio-optimization methods along with their flowcharts. Secondly, we have reviewed optimized image encryption algorithms in sequential order. Optimization techniques that use a mixture of different algorithms have been given a separate section as miscellaneous. Thirdly, we have provided a table for discussion in which we have listed the advantages and disadvantages of these algorithms. Finally, we have provided a conclusion and future work to be done in the last section.

ABSTRACTThe main aim of this work is to develop a theoretical framework for generalized pseudo‐differential operators involving the special affine Fourier transform (SAFT), associated with a symbol . Some important properties of the SAFT are established, and it is proved that the product of two generalized pseudo‐differential operators is shown to be a generalized pseudo‐differential operator. Further, we explore the practical applications of the SAFT in solving generalized partial differential equations, such as the generalized telegraph and wave equations, providing closed‐form solutions. Furthermore, graphical visualizations for these solutions are illustrated via MATLAB R2023b.

In this paper, we propose a novel n - Dimensional Pseudo-Differential Operator ( n - DPDO) constructed using the robust framework of the n - Dimensional Quadratic Phase Fourier Transform ( n- DQPFT). This operator is characterized by a smooth symbol δ (ν _1, … , ν _n; ω _1, … , ω _n) ∈𝒞^∞ (ℝ^n ×ℝ^n) , paving the way for new directions in mathematical analysis. We provide a rigorous study of its fundamental properties within the context of Schwartz space, proving that the composition of two n - DPDOs yields another n - DPDO, thereby establishing its algebraic consistency. Furthermore, we analyze formal adjoint operators with symbols in 𝒮^r , demonstrating their essential boundedness in L^p(ℝ^n) spaces under the n - DQPFT framework. Additionally, the n - DQPFT is applied to solve generalized partial differential equations. Specific cases of these equations include well-known n-dimensional time-dependent generalized Schrödinger-type equations (Types I, II, and III) and the general Schrödinger equation in quantum mechanics for a single particle with a constant potential.

Abstract: Viruses represent a significant health menace due to their rapid transmissibility and potential to cause worldwide pandemics, resulting in substantial loss of human life. Antiviral agents play a pivotal role in mitigating the impact of viral infections. Nonetheless, treating viral infections is a multifaceted process due to the inherent characteristics of viruses, such as their capacity to undergo mutations and rapid evolution. Consequently, the effectiveness of current antiviral therapies can be impeded. This review encompasses the diverse manners in which viruses, emphasizing COVID-19, affect the human body and elucidates the challenges encountered in formulating efficacious antiviral treatments. Moreover, the limitations of conventional antiviral therapies are underscored. Additionally, a comprehensive compendium of 41 antiviral drugs is presented, detailing their mechanisms of action and routes of administration. Subsequently, the discussion includes 9 drugs repurposed for treating COVID-19, delineating their primary use as well as any accompanying side effects. In conclusion, while antiviral drugs remain pivotal in the battle against viral infections, the obstacles associated with their development and usage warrant careful consideration. Ongoing research is imperative to devise more potent and less toxic antiviral interventions against COVID-19 infection.

Internet use and other communications technologies like wireless networks, cloud computing, and the Internet of Things have skyrocketed in recent decades. This research seeks to provide a structured color picture encryption technique for wireless sensor networks (WSNs). The approach uses a 1-D exponential modified chaotic map (1-D EMC), 2-D discrete wavelet transform, and a 1-D modified version of the logistic map (1-D MVL) to reduce data and improve transmission, especially for images. The XOR operator and random permutation of image matrix rows and columns strengthen the technique against numerous attacks. Statistical analyses are performed on the proposed encryption technique, and the values of these statistical tests presented in the tables are satisfactory. A fair comparison with other competitive existing algorithms shows the effectiveness of the proposed encryption algorithm and can be opted for practical use.

In the modern digital era, human face lies at the core and forms the very basis of any social interaction and communication. It embeds highly precious information alongside facial identities and expressions, but at same time this very trait makes it vulnerable to manipulation attacks. The proliferation of large-scale public image databases alongside advancements in AI-driven image synthesis has heightened the prevalence of “DeepFakes”. While conventional fake detection classifiers suffer from low accuracies due to their susceptibility to manipulation techniques, state-of-the-art convolutional neural network (CNN) models offer high accuracies at the expense of extensive training and computational resources. To address these challenges, we introduce MaD-CoRN i.e. Manipulation detection by Convolutional Reservoir Networks. It is a novel and efficient combinatorial architecture that enhances the feature extraction capabilities using pre-trained convolutional networks with lightweight reservoir computing (RC), an improved form of RNN learning. This approach improves the separation and learning of facial features, resulting in notable speedups and a relative increase of over 15% in fake face detection accuracy, F1-score values when simulated using “Real and Fake Face Detection (RFFD)” and “100K-Generated fake image” public datasets. MaD-CoRN offers several advantages: (i) it is lightweight and cost-effective, (ii) leverages transfer learning and RC-based feature extraction, (iii) it achieves enhanced accuracies even with small input datasets ( ≈ 1900 samples) and it boasts a highly flexible and generic architecture. Additionally, we propose a unified framework based on various adaptations of the MaD-CoRN architecture.

In the current era, major technology is cloud computing and Internet of Things due to their vast applications in day-to-day life. The major reason behind today’s internet traffic is big data transmission and usage in varied data types like textual, image and video datasets, as well as audio data. Due to widely spread usage of social media, security and authenticity of image data is of utmost priority especially when it comes to applications like medical images, Geographic imaging system, biometric authenticity. The major objective of this research is to provide a sustainable robust encryption algorithm for securing images where data authenticity is of priority like biometric images. Algorithm is lightweight cryptographic algorithm as it uses low dimensional chaotic map Arnold’s CAT map (ACM) and ℒ -System fractal for key generation. The results tabulated show satisfactory output towards statistical tests. Robustness and effectiveness of the proposed algorithm is compared decently with other existing algorithms and it demonstrates practical usability of the algorithm.

AbstractIn this article, we define the octonion quadratic-phase Fourier transform (OQPFT) and derive its inversion formula, including its fundamental properties such as linearity, parity, modulation, and shifting. We also establish its relationship with the quaternion quadratic-phase Fourier transform (QQPFT). Further, we derive the Parseval formula and the Riemann–Lebesgue lemma using this transform. Furthermore, we formulate two important inequalities (sharp Pitt’s and sharp Hausdorff–Young’s inequalities) and three main uncertainty principles (logarithmic, Donoho–Stark’s, and Heisenberg’s uncertainty principles) for the OQPFT. To complete our investigation, we construct three elementary examples of signal theory with graphical interpretations to illustrate the use of OQPFT and discuss their particular cases.

The primary aim is to develop a new class of pseudo-differential operators by incorporating the Special Affine Fourier Transform (SAFT) and some of its fundamental properties in Schwartz and tempered distribution space. The secondary aim is to explore the utility of the SAFT in constructing a new generalized heat equation and derive its analytical solution. Further, we have investigated particular cases of the proposed generalized heat equation. Furthermore, we have visually illustrated solutions of this equation via MATLAB R2023b.

In this paper, we define the Windowed Octonion Quadratic Phase Fourier Transform (WOQPFT) and derive its inversion formula, including its essential properties, such as linearity, anti-linearity, parity, scaling, modulation, shifting, and joint time-frequency shifting, as well as its link to Octonion Quadratic Phase Fourier Transform (OQPFT). Additionally, we derive the Riemann-Lebesgue lemma using this transform. Following the present analysis, we formulated Sharp Pitt’s and Sharp Hausdorff-Young’s inequalities. Further, Logarithmic, Heisenberg’s, and Donoho-Stark’s uncertainty principles are also formulated. The practical application of WOQPFT and the five elementary examples of signal theory are discussed, and their particular cases are analyzed through graphical visualization, including interpretation.

An efficacious mathematical cryptographic algorithm for three-plane RGB images based on an L-shaped fractal and a 1-D chaotic tent map is proposed. Since vast data sets of images and videos are transmitted daily over public channels, the security and authenticity of data are of utmost priority. Fractals are very well suited for image encryption on a large scale due to their randomness property and infinite boundaries. One of the simplest implementations on the hardware of an IoT device is a one-dimensional dynamical system called the 1-D Chaotic tent map. This map is frequently used in encryption techniques because of its sensitivity towards initial conditions and impulsiveness. Due to the low dimensions of the 1-D chaotic tent map, this algorithm is more suited for lightweight cryptographic applications. The computer simulation results on MATLAB 2022a are explained to analyze the capabilities of the proposed algorithm using statistical analysis. The test results of differential attacks, percentage cropping attacks, and noise attacks are tabulated to confirm the wholesomeness of the proposed algorithm for 3-plane image encryption. There is a table that shows how secure the proposed 3-plane image encryption algorithm is by comparing it to other RGB image encryption algorithms that are already out there using entropy, correlation coefficient, and robustness using differential attacks.

The paper proposes a new hyper-chaotic-discrete-wavelet-packet-transform encryption algorithm for RGB images. The highlight is that the 512-bit hash of timestamp is used to get the initial values of the 4D hyper-chaotic system. The sequences generated by the 4D Lorenz system are used to construct 12 keys for encryption. The proposed encryption algorithm uses a newly designed 3D chaotic diffusion and inter-shuffling of pixels followed by 2D diffusion to improve security levels. The obtained images will go through another deep level of diffusion and shuffling in approximation coefficients (where most of the information is stored) after applying discrete wavelet packet transform at the desired level with a wavelet “name" selected by users. This step resists commonly well-known attacks such as differential, noise, and crop attacks. After that, modified approximation coefficients and other remaining coefficients, namely horizontal, vertical, and diagonal coefficients, are reverted back using the inverse wavelet packet transform. In the end, another layer of chaotic diffusion and row-column matrix shuffling is performed to avoid high redundancy and correlation in the encrypted image. The main advantage of using the hyper-chaotic system in the encryption process is that it gives a vast key space to make brute-force attacks infeasible and provides excellent speed to the proposed algorithm. The randomness of the encrypted image has been verified using the NIST SP800-22 statistical test suite. Several well-known attacks have been used to validate the algorithm’s robustness. The proposed technique has been compared with other existing algorithms, and the data (presented in tables) confirm that the proposed algorithm is competitive and can be used for practical purposes. Finally, a conclusion, including a future scope, has been provided.

An image encryption model is presented in this paper. The model uses two-dimensional Brownian Motion as a source of confusion and diffusion in image pixels. Shuffling of image pixels is done using Intertwining Logistic Map due to its desirable chaotic properties. The properties of Brownian motion helps to ensure key sensitivity. Finally, a diffusion mechanism based upon a Coupled Map Lattice helps to bind image pixels together and provide a chaining effect as diffusion. Key streams used in confusion and diffusion are made input image dependent that follows the symmetric encryption model requirements. The model introduces randomness in the cipher image resulting in negligible correlation coefficients between the cipher image pixels. It leads to uniform distribution of pixels in image histogram representing a high degree of confusion complexity assuring resistance against differential attacks. The NPCR (99.83 % ) and UACI (33.42 % ) values meet the minimum standard requirements for image security. Details of other test results related to entropy (7.9995 % ), Peak Signal to Noise Ratio (8.8751dB), noise and NIST randomness tests are also mentioned which support the model’s resistivity against various known and chosen plaintext attacks.

Due to the proliferation of electronic devices such as mobile phones, tablets, laptops, desktops, e-drives, hard drives, etc., transferring information in the form of images through the Internet has become an essential practice in this digital era. Red, green, blue (RGB) images are used to store or share information, such as medical imaging for disease diagnosis, e-learning, online shopping, defense services, personal images, and much more. Adversaries are trying to steal this critical information from images for their gain or personal interest. Hence, we need to prevent an adversary from misusing this crucial information using encryption algorithms. This chapter aims to provide a new, secure, and fast encryption algorithm for RGB images in deoxyribonucleic acid (DNA)-encoded domain involving random sequences generated by arithmetic progression (AP) and logistic map associated with generalized Vigenere-type table suitable for wireless sensor network (WSN). The randomness of generated sequences is performed using the National Institute of Standards and Technology (NIST) statistical suite test, and the results are provided in Appendix. The proposed encryption algorithm provides a huge keyspace and is robust against brute-force, dictionary, side-channel, correlation, differential, cropping, noise, chosen cipher, and plain image attacks. The various security analysis is performed on standard test images to demonstrate the proposed algorithm's efficiency and security. Further, a comparison with other competing existing algorithms is shown. The analysis results conclude that the proposed algorithm can opt for practical application.

In this work, an n-dimensional pseudo-differential operator involving the n-dimensional linear canonical transform associated with the symbol ?(x1,..., xn; y1,..., yn) ? C?(Rn ? Rn) is defined. We have introduced various properties of the n-dimensional pseudo-differential operator on the Schwartz space using linear canonical transform. It has been shown that the product of two n-dimensional pseudodifferential operators is an n-dimensional pseudo-differential operator. Further, we have investigated formal adjoint operators with a symbol ? ? Sm using the n-dimensional linear canonical transform, and the Lp(Rn) boundedness property of the n-dimensional pseudo-differential operator is provided. Furthermore, some applications of the n-dimensional linear canonical transform are given to solve generalized partial differential equations and their particular cases that reduce to well-known n-dimensional time-dependent Schr?dinger-type-I/Schr?dinger-type-II/Schr?dinger equations in quantum mechanics for one particle with a constant potential.

A 3D-logistic-fraction-sine (3D-LFS) chaotic map and NFSR are used to encrypt sensitive data in a new, secure, and lightweight manner. The algorithm can process data in a variety of formats, including images, random test data streams, and legal PDF documents accessible to the public. Randomness of the encrypted image has been verified using the NIST SP800-22 statistical test suite. Several well-known attacks, such as differential, noise, and crop attacks, have been utilised to validate the algorithm’s robustness. Finally, the proposed technique has been compared with other existing algorithms and the data (presented in tables) confirm that the proposed algorithm is competitive and can be applied in embedded systems (and IoT devices) due to its performance.