Polynomial multiplications based on the number theoretic transform (NTT) are critical in lattice-based post-quantum cryptography algorithms. Therefore, this paper presents a platform-agnostic unified hardware accelerator design (Unif-NTT) to compute the forward and inverse operations of the NTT for the CRYSTALS-Kyber algorithm. Moreover, a unified design (Unif-BU) of the Cooley-Tukey and Gentleman-Sande butterflies is presented using two adders, multipliers, subtractors, routing multiplexers and barret-based modular reduction units. Finally, a dedicated controller is implemented for efficient control functionalities. The implementation results are realized on field-programmable gate array (FPGA) and application-specific integrated circuit (ASIC) platforms. The Unif-NTT requires 1664 and 1792 clock cycles for one forward and inverse NTT computations, respectively. It can operate up to a maximum frequency of $212MHz$ and $2.5GHz$ over Virtex-7 FPGA and 28nm ASIC platforms, respectively. The Unif-NTT is 26% more efficient in Area-Time-Product compared to the most area-optimized NTT accelerator from the state-of-the-art. The Unif-NTT design is suited for applications that demand reasonable hardware resources with processing speed.

Researchers concentrate on data security using cryptography, using different approaches to protect confidential data, such as digital images holding private information. They use cryptography techniques, frequently using elliptic curves and chaotic structures for secure transmission. This paper introduces a novel technique for constructing S- boxes and their application in color image encryption. The utilization of discrete chaotic maps and elliptic curves results in low computational complexity, which is crucial for high-speed communication systems. The generation of S- boxes is based on elliptic curves over prime fields and discrete chaotic maps. The color image encryption scheme involves permutation, substitution, and bit-wise XOR operations of key with the color image’s corresponding substituted channels. The resistance of the newly constructed s-boxes against common attacks, such as linear, differential, and algebraic attacks, is analyzed by evaluating their non-linearity, linear approximation probability, differential approximation probability, bit avalanche criterion, and bit independence criterion. The encrypted images have strong resistance against statistical and differential attacks. Experimental results demonstrate that the newly constructed scheme can efficiently generate numerous distinct, uncorrelated, and secure S- boxes, outperforming some well-known existing techniques. The non-linearity of the proposed s-box is 107.5 and the entropy of the ciphered image of Baboon is 7.9989. The security analysis indicates that the color-encrypted image offers fast and higher protection against attacks, making it suitable for real-time applications with high security requirements.

Preference analysis is a significant component in decision-making (DM) when selecting an optimal alternative. By comparing any two alternatives pairwise, preference relations (PRs) effectively depict the preference degrees of decision-makers (DMrs). The rough set theory (RST) has been effectively applied to cope with preference analysis by swapping the equivalence relation (Er) with the dominance relation (DR). In this study, we propose new transfer functions to construct alternatives’ upward/downward fuzzy preference degree (FPD) for evaluating upward and downward fuzzy PRs (FPRs). Based on these newly proposed transfer functions, we present a novel method for fuzzifying RSs called the upward $\alpha $ -fuzzified preference rough sets ( $\alpha ^{\uparrow }$ -FPRSs). The basic properties of the proposed $\alpha ^{\uparrow }$ -FPRSs are thoroughly studied. Moreover, several uncertainty measures related to $\alpha ^{\uparrow }$ -FPRSs are presented. Meanwhile, we offered the notion of upward fuzzy $\beta $ -covering (UF $\beta $ C) and upward fuzzy $\beta $ -neighborhood (UF $\beta $ -nghd), upward $\beta $ -neighborhood (U $\beta $ -nghd), and several related properties are explored. Based on UF $\beta $ -nghd and U $\beta $ -nghd, we construct two new models of UF $\beta $ C rough sets (UF $\beta $ -CRSs) along with their properties. We formulate a novel technique of multi-attribute DM (MADM). To legitimise the practicality of our proposed model, we provide a real-life example of selecting an appropriate medication to treat a specific disease. Finally, we look into the efficacy of the launched scheme through a comparison study.

The notion of linear Diophantine fuzzy sets (LD-FSs) is a novel mechanism to combat uncertainties in decision analysis. Due to reference parameters associated with membership grade (MG) and non-membership grade (NMG), LD-FS is more efficient and reliable than ideas of the fuzzy set (FS), intuitionistic fuzzy set (IFS), Pythagorean fuzzy set (PyFS), and q-rung orthopair fuzzy set (q-ROFS). The main goal of this article is to present an innovative roughness strategy for LD-FSs using a fuzzy relation (FR) over dual universes, known as a linear Diophantine fuzzy rough set (LD-FRS). The lower and upper approximations of an LD-FS are formulated using fuzzy relation (FR) over dual universes, and several axiomatic systems are investigated. The suggested model of LD-FRS is more flexible to address fuzziness and roughness. Meanwhile, a relationship is made between LD-FRSs and linear Diophantine fuzzy topologies (LDF-topologies). It is shown that the collection of all lower approximations based on a reflexive FR leads to an LDF-topology. Moreover, several similarity relations among LD-FSs are also examined based on their lower and upper approximations. An application of multi-criteria group decision-making (MCGDM) is demonstrated by a supplier selection problem. Finally, a detailed comparative analysis with certain existing methods is given to verify the feasibility and superiority of the suggested model.

The current article focuses on studying the behavior of a ring $\Re /\Pi$ when ℜ admits generalized derivations $\Psi$ and $\Omega$ with associated derivations $\varphi$ and $\delta$, respectively. These derivations satisfy specific differential identities involving $\Pi$, where $\Pi$ is a prime ideal of an arbitrary ring ℜ, not necessarily prime or semiprime. Furthermore, we explore some consequences of our findings. To emphasize the necessity of the primeness of $\Pi$ in the hypotheses of our various theorems, we provide a list of examples.

This paper investigates the relationship between the commutativity of rings and the properties of their multiplicative generalized derivations. Let $\mathcal{F}$ be a ring with a semiprime ideal $\Pi$. A map $\varphi :\mathcal{F}\to \mathcal{F}$ is classified as a multiplicative generalized derivation if there exists a map $\sigma :\mathcal{F}\to \mathcal{F}$ such that $\varphi \left(xy\right)=\varphi \left(x\right)y+x\sigma \left(y\right)$ for all $x,y\in \mathcal{F}$. This study focuses on semiprime ideals $\Pi$ that admit multiplicative generalized derivations $\varphi$ and G that satisfy certain differential identities within $\mathcal{F}$. By examining these conditions, the paper aims to provide new insights into the structural aspects of rings, particularly their commutativity in relation to the behavior of such derivations.