A key research challenge in modern cryptography is the construction of robust nonlinear components that simultaneously achieve high nonlinearity, resistance to linear and differential cryptanalysis, and efficient implementation for real-time systems. Existing S-box construction methods—whether chaos-based or algebraic—struggle to balance these requirements, especially in RGB image encryption where large data size, high redundancy, and inter-pixel correlations complicate security. To address these challenges, this paper presents a novel technique for constructing block cipher nonlinear elements and developing an RGB image encryption scheme by integrating Gaussian integer rings with Mordell elliptic curves. The proposed method generates strong n× n S-boxes by first establishing a Mordell elliptic curve on a finite field, selecting unique y- values, and applying Gaussian integer transformations to construct nonlinear substitution boxes. The resulting S-boxes exhibit high nonlinearity and effective resistance to linear and differential attacks. Building on this, a new RGB encryption system is designed using a Substitution–Permutation Network (SPN) framework that applies input preparation, S-box substitution, a secondary permutation, and XOR operations to ensure confusion and diffusion across color channels. Experimental evaluation shows that the scheme achieves high entropy, low pixel correlation, and strong robustness against statistical, brute-force, and differential attacks. The integration of Gaussian integer rings with Mordell elliptic curves advances cryptographic security by providing an efficient algebraic framework for image encryption. The proposed methodology is well-suited for real-time applications, including cloud security, IoT data protection, and secure medical image handling. The main originality of this study lies in combining Gaussian integers with elliptic curves to construct secure nonlinear components, offering a new algebraic paradigm for modern encryption systems.
Lignin-derived hard carbon has shown considerable promise as an advanced anode material for sodium-ion batteries, owing to its renewable nature and cost-effectiveness. However, conventional carbonization yields hard carbons with unsatisfactory initial coulombic efficiency (ICE) and limited rate capability because of poorly controlled pore architecture. Herein, we present a molecular engineering strategy for effective regulation of the closed-pore structure of lignin-based hard carbon to enhance sodium ion storage. The cross-linking of lignin plays a pivotal role in directing microstructure evolution, which subsequently facilitates the formation of closed pores during high-temperature treatment. The optimized porous architecture significantly improves the Na+ storage performances, with a remarkable reversible capacity of 361.4 mAh g-1 at 0.02 A g-1 and even 167.4 mAh g-1 at a high current density of 4.0 A g-1, along with a high ICE of 90.8%. The full cell achieves an energy density of 257.8 Wh kg-1. This work provides a fundamental insight into the molecular-level effect of lignin on pore formation and establishes a practical pathway for transforming lignin into high-performance energy storage materials through rational structural design.
In this work, the application of Levenberg-Marquardt backpropagation scheme is used to demonstrate the importance of viscous dissipation, Joule heating, and magnetic field on the stagnation point Darcy-Forchheimer flow of ternary hybrid nanofluid around a rotating sphere containing oxytactic and gyrotactic microorganisms. The present analysis additionally includes higher-order biochemical reactions and heat generating effects. In this paper, the performance of each nanofluid is compared using the Hamilton-Crosser model. This model can be using to optimize and construct complex cooling systems. The result is a statistical matrix data set and a linear graphical representation of the established model on several parameters. The results are thoroughly verified and cross-checked until they align with the Levenberg-Marquardt backpropagation model, utilizing a stochastic, artificial intelligent driven neural network approach. This blend of artificial intelligence allows for precise predictions of nonlinear flow parameters and is beneficial for applications in both biomedical and industrial heat transfer systems. An analysis of the findings indicates that an increase in the Forchheimer and Darcy parameters lowers primary velocity and that a stronger magnetic field boosts the velocity. Changing the Prandtl number leads to temperature decreasing in the profile and changing the Schmidt and chemistry parameters tends to reduce the concentration profile. The profiles of gyrotactic and oxytactic microorganisms are reduced as the Schmidt numbers grow larger. The model is very accurate, reaching values close to zero regression and having a mean square error of 10-6, confirming it is effective for predicting complicated fluid movements.
Efficient heat management is essential for improving the performance of renewable energy systems, particularly in solar-based thermal technologies. To address this challenge, the present study investigates the exergoeconomic performance and thermophysical behavior of a magnetohydrodynamic Williamson hybrid nanofluid (WHNF) flowing over a continuously moving thin needle under the influence of a magnetic field, porosity, and nonuniform heat flux. The hybrid nanofluid, composed of AA7075-AA7072 nanoparticles dispersed in methanol, is analyzed to enhance heat transfer and energy conversion efficiency. The governing partial differential equations are transformed into ordinary differential equations using similarity variables and solved parametrically to examine variations in velocity, temperature, and entropy generation profiles. A machine learning framework based on Artificial Neural Networks (ANNs) is integrated to predict and optimize the thermophysical properties and exergy efficiency of the WHNF system. The graphical results are obtained by varying number of parameters like; M, W e , C, Pr, and B, for discussions of numerical results on f (y) (i) and 8(i) profile. A total of 76 datasets were generated, with 54 used for training, 11 for testing, and 11 for validation. The ANN results show strong predictive accuracy, with mean square error (MSE) values and absolute error (AE) within acceptable limits. The analysis reveals that increasing the magnetic parameter and porosity tends to reduce velocity while enhancing temperature gradients and entropy generation. Moreover, The f (y) (i) profile declines with growing differences of M and W e while f (y) (i) increases growing differences of C. 8(i) profile declines with raising values of P r and AE noted between -2 to 3 x 10-4 . Moreover, 8(i) profile increases due to increment in B and C. The MSE penalties (testing, training, validation) WHNFs flow on thin moving needle lies between 10-10 to 10 00 . The gradients values lie around 10-8 for WHNFs on thin needle. EHA of WHNFs flow on thin moving needle recorded around 10-07 to 10-06 . The AE WHNFs flow on thin moving needle by using LMBNNs is noted between -6 x 10 0 to 8 x 10-05 for all six scenarios. This study thus bridges computational fluid dynamics, nanofluid science, and artificial intelligence for advancing energy-efficient and sustainable heat transfer technologies.
This research accounts bioconvection influence in convectively heated magnetized couple-stress material confined by cylindrical stratified regime. The mathematical modeling includes Brownian diffusive together with thermophoretic aspects, while suspension stability is ensured by considering bioconvection features owing to gyrotactic microorganisms. Robin-type thermosolutal conditions are deployed to elaborate heat–mass transmission at the magnetized cylindrical surface subject to suction/injection (wall transpiration). The investigation further considers radiation impact in energy expression. The governing mathematical (partial differential) expressions are transmuted into nonlinear ordinary differential equations (ODEs) by implementing apposite variables. These ODEs are computed analytically by utilizing homotopy scheme, assuring convergence via selection of suitable auxiliary variables. The influences of key variables on non-dimensional profiles are systematically scrutinized. The velocity exhibits an increasing trend when curvature, mixed convection and injection parameters are escalated. However, it demonstrates opposite behavior when Reynolds number, Hartman number, couple stress, and bioconvection variables are increased. The outcomes provide valuable perception into nanofluidic transportation in state-of-the-art coating technologies, bio-microsystems, and thermal energy mechanisms where magnetized nanomaterials are considered subject to bioconvection phenomena.
