arXiv subjects

Abhishek Kesarwani

Publications and source records attributed to Abhishek Kesarwani.

4 recordsLinked to original sources

arXiv2026

MDS matrices from skew polynomials with automorphisms and derivations

Maximum Distance Separable (MDS) matrices play a central role in coding theory and symmetric-key cryptography due to their optimal diffusion properties. In this paper, we present a construction of MDS matrices using skew polynomial rings $ \mathbb{F}_q[X;θ,δ] $, where $ θ$ is an automorphism and $ δ$ is a $ θ$-derivation on $ \mathbb{F}_q $. We introduce the notion of $ δ_θ $-circulant matrices and study their structural properties. Necessary and sufficient conditions are derived under which these matrices are involutory and satisfy the MDS property. The resulting $δ_θ$-circulant matrix can be viewed as a generalization of classical constructions obtained in the absence of $θ$-derivations. One of the main contribution of this work is the construction of quasi recursive MDS matrices. In the setting of the skew polynomial ring $\mathbb{F}_q[X;θ]$, we construct quasi recursive MDS matrices associated with companion matrices. These matrices are shown to be involutory, yielding a strict improvement over the quasi-involutory constructions previously reported in the literature. Several illustrative results and examples are also provided.

cs.IT↗

arXiv2025

On the construction of Cauchy MDS matrices over Galois rings via nilpotent elements and Frobenius maps

Let $s,m$ be the positive integers and $p$ be any prime number. Next, let $GR(p^s,p^{sm})$ be a Galois ring of characteristic $p^s$ and cardinality $p^{sm}$. In the present paper, we explore the construction of Cauchy MDS matrices over Galois rings. Moreover, we introduce a new approach that considers nilpotent elements and Teichmüller set of Galois ring $GR(p^s,p^{sm})$ to reduce the number of entries in these matrices. Furthermore, we construct $p^{(s-1)m}(p^m-1)$ distinct functions with the help of Frobenius automorphisms. These functions preserve MDS property of matrices. Finally, we prove some results using automorphisms and isomorphisms of the Galois rings that can be used to generate new Cauchy MDS matrices.

cs.IT↗

arXiv2025

Quasi-recursive MDS Matrices over Galois Rings

Let $p$ be a prime and $s,m,n$ be positive integers. This paper studies quasi-recursive MDS matrices over Galois rings $GR(p^{s}, p^{sm})$ and proposes various direct construction methods for such matrices. The construction is based on skew polynomial rings $GR(p^{s}, p^{sm})[X;σ]$, whose rich factorization properties and enlarged class of polynomials are used to define companion matrices generating quasi-recursive MDS matrices. First, two criteria are established for characterizing polynomials that yield recursive MDS matrices, generalizing existing results, and then an additional criterion is derived in terms of the right roots of the associated Wedderburn polynomial. Using these criteria, methods are developed to construct skew polynomials that give rise to quasi-recursive MDS matrices over Galois rings. This framework extends known constructions to the non-commutative setting and significantly enlarges the family of available matrices, with potential applications to efficient diffusion layers in cryptographic primitives. The results are particularly relevant for practical implementations when $s = 1$ and $p = 2$, i.e., over the finite field $\mathbb{F}_{2^m}$, which is of central interest in real-world cryptographic applications.

cs.IT↗

arXiv2019

Development of trust based access control models using fuzzy logic in cloud computing

Cloud computing is the technology that provides different types of services as a useful resource on the Internet. Resource trust value will help the cloud users to select the services of a cloud provider for processing and storing their essential information. Also, service providers can give access to users based on trust value to secure cloud resources from malicious users. In this paper, trust models are proposed, which comes under the subjective trust model based on the behavior of user and service provider to calculate the trust values. The trust is fuzzy, which motivated us to apply fuzzy logic for calculating the trust values of the cloud users and service providers in the cloud environment. We use a Mamdani fuzzy method with gauss membership function for fuzzification and triangular membership function for defuzzification. Parameters such as performance and elasticity are taken for trust evaluation of the resource. The attributes for calculating performance are workload and response time. And for calculating elasticity, we have taken scalability, availability, security, and usability. The fuzzy C-means clustering is applied to parameters for evaluating the trust value of users such as bad requests, bogus requests, unauthorized requests, and total requests.

cs.CR↗