Current improvements in quantum computing present a substantial challenge to classical cryptographic systems, which typically rely on problems that can be solved in polynomial time using quantum algorithms. Consequently, post-quantum cryptography (PQC) has emerged as a promising solution to emerging quantum-based cryptographic challenges. The greatest threat is public-key cryptosystems, which are primarily responsible for key exchanges. In PQC, key encapsulation mechanisms (KEMs) are crucial for securing key exchange protocols, particularly in Internet communication, virtual private networks (VPNs), and secure messaging applications. CRYSTALS-Kyber and NTRU are two well-known PQC KEMs offering robust security in the quantum world. However, even when quantum computers are functional, they are not easily accessible. IoT devices will not be able to utilize them directly, so there will still be a requirement to protect IoT devices from quantum attacks. Concerns such as limited computational power, energy efficiency, and memory constraints in devices such as those used in IoTs, embedded systems, and smart cards limit the use of these techniques in constrained environments. These concerns always arise there. To address this issue, this study conducts a broad comparative analysis of Kyber and NTRU, with special focus on their security, performance, and implementation efficiency in such environments (IOT/constrained environments). In addition, a case study was conducted by applying KEMs to a low-power embedded device to analyze their performance in real-world scenarios. These results offer an important comparison for cyber security engineers and cryptographers who are involved in integrating post-quantum cryptography into resource-constrained devices.

The efficiency of mixed convection peristaltic flow can be investigated through pressure rise per wavelength $$(\Delta P_{{{\uplambda }}} )$$( Δ P λ ) and frictional forces ( $${F}_{\uplambda }$$F λ ). The main aim of the present study is to discover the sensitivity analysis of non-Newtonian fluids using the Bingham plastic fluid model. In order to achieve this objective, we have empirically modeled the pressure rise per wavelength $$(\Delta {P}_{\uplambda })$$( Δ P λ ) and frictional forces ( $${F}_{\uplambda }$$F λ ) as a function varying with leading parameters of problem. The flow problem is governed by three coupled nonlinear partial differential equations. They are reduced to nonlinear coupled ordinary differential equations by using the long wavelength and low Reynolds number approximations. They are solved numerically using MATLAB built-in routine bvp4c to analyze the sensitivity of pressure rise per wavelength ( $$\Delta {P}_{\uplambda }$$Δ P λ ) and frictional forces ( $${F}_{\uplambda }$$F λ ). We first derive the empirical model among each of responses $$\Delta {P}_{\uplambda }$$Δ P λ and $${F}_{\uplambda }$$F λ and physical parameters which govern the flow using response surface methodology. The goodness of fit of empirical model is decided on the basis of coefficient of determination ( $${R}^{2}$$R 2 ) obtained from the analysis of variance (ANOVA). The coefficients of determination ( $${R}^{2}$$R 2 ) are 99.78% both for $$\Delta {P}_{\uplambda }$$Δ P λ and $${F}_{\uplambda }$$F λ . The higher values of $${R}^{2}$$R 2 determine the goodness of fit of empirical model. No correlation has been developed to optimize $$\Delta {P}_{\uplambda }$$Δ P λ and $${F}_{\uplambda }$$F λ in peristaltic flow for Bingham plastic fluids using RSM. The results of sensitivity analysis revealed that $$\Delta {P}_{\uplambda }$$Δ P λ and $${F}_{\uplambda }$$F λ are most sensitive to flow rate (q) at all levels such as low (− 1), medium (0) and high (+ 1). The sensitivity of $$\Delta {P}_{\uplambda }$$Δ P λ to Bingham number (Bn) shows a distinct behavior with varying levels of flow rate (q). At low level (− 1) of flow rate (q), the sensitivity is positive, and at high level (+ 1) of flow rate (q), the sensitivity becomes negative. Conversely, the sensitivity of $${F}_{\uplambda }$$F λ to Bingham number (Bn) at low to high level of flow rate (q).

In this study the authors aim to investigate sensitivity analysis of pressure rise per wavelength and frictional forces in magnetohydrodynamics peristaltic flow of viscoplastic nanofluid with the effect of electro-osmotic and chemical reaction in tapered channel. To achieve this aim, we have adopted an empirical modeling methodology that establishing pressure rise per wavelength and frictional forces on upper and lower wall relationships as functions that vary according to the governing parameters essential to the problem. To analyze the sensitivity of transport parameters, including pressure rise per wavelengthand frictional forces on upper and lower wall, we initially develop an empirical model for key responses, (pressure rise per wavelengthand frictional forces on upper and lower wall). To my best knowledge, no empirical correlations for pressure rise per wavelength and frictional forces associated with viscoplastic nanofluid peristaltic flow in tapered channels have addressed in the literature. To develop this empirical model, we used the approach of Response Surface Methodology and Artificial Neural Networks. The appropriateness of empirical model is evaluated by determining the coefficient of determination and conducting an analysis of variance to ensure accuracy and reliability. The empirical model display good fit, with the coefficient of determination of 97.65% for all resulting responses, (pressure rise per wavelengthand frictional forces on upper and lower wall). Residuals are plotted to verify accuracy and reliability of empirical correlation. A sensitivity analysis was performed to identify the most influential input parameters. The results, presented graphically, show that the values of resulting responses (pressure rise per wavelengthand frictional forces on upper and lower wall) are highly sensitive to variation in Brownian motion parameter in most situations. This innovative approach contributes valuable insights for optimizing flow performance in biomedical and engineering applications, filling a critical gap in the existing body of knowledge.

This study investigates the effects of magnetohydrodynamics (MHD) and bioconvection on Casson-Williamson nanofluid flow along a stretched sheet. Such a fluid dynamics analysis considers the impact of MHD, chemical reactions, and gyrotactic microorganisms. For velocity and magnetic field behavior exploration, the concept of buoyancy ratio has also been proposed in the study. The Casson and Williamson rheological models characterize the fluid properties to understand the effects of these parameters by the motion of motile gyrotactic microorganisms. Similarity variable is used to reduce nonlinear partial differential equations including boundary conditions to strong coupled ordinary differential equations, which are easier to analyze. The solutions can be obtained by the use of `bvp4c', a popular numerical method for nonlinear boundary value problems, which enables sensitivity about fluid dynamics of different physical parameters on profiles of ????′(????),????(????),????(????), ????(????), ????′′(????) and ????′(????). Numerous physical characteristics, such as the buoyancy ratio, thermophoresis variable, Brownian motion variable, bioconvection number, Eckert number, and thermal radiation, determine the behavior of non-Newtonian fluids. The result shows that the skin friction decreases by increasing the value of the magnetic field the Nusselt number decreases by raising the value of heat generation parameters and the Sherwood number increases by increasing the value of Lewis number. The study aims to notice the impact of buoyancy ratio and Rayleigh number on fluid behavior. The velocity profile declines by increasing the value of and and the temperature profile increases for thermophoresis and Brownian motion parameter value rise.