Generalization of MacNeish’s Kronecker product theorem of mutually orthogonal Latin squares

El-Mesady, A.; Shaaban, Shaaban M.

doi:10.1080/09728600.2021.1966349

Cited by 5 publications

(1 citation statement)

References 12 publications

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“…MOGS for certain graphs were handled by [21]. El-Mesady et al [22] generalized the MacNeish's Kronecker product theorem of MOLS. MOGS were used to construct graph-transversal designs and graphauthentication codes in [3,23].…”

Section: Introductionmentioning

confidence: 99%

Construction of Mutually Orthogonal Graph Squares Using Novel Product Techniques

El-Mesady

Bazighifan

2022

Journal of Mathematics

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Sets of mutually orthogonal Latin squares prescribe the order in which to apply different treatments in designing an experiment to permit effective statistical analysis of results, they encode the incidence structure of finite geometries, they encapsulate the structure of finite groups and more general algebraic objects known as quasigroups, and they produce optimal density error-correcting codes. This paper gives some new results on mutually orthogonal graph squares. Mutually orthogonal graph squares generalize orthogonal Latin squares interestingly. Mutually orthogonal graph squares are an area of combinatorial design theory that has many applications in optical communications, wireless communications, cryptography, storage system design, algorithm design and analysis, and communication protocols, to mention just a few areas. In this paper, novel product techniques of mutually orthogonal graph squares are considered. Proposed product techniques are the half-starters’ vectors Cartesian product, half-starters’ function product, and tensor product of graphs. It is shown that by taking mutually orthogonal subgraphs of complete bipartite graphs, one can obtain enough mutually orthogonal subgraphs in some larger complete bipartite graphs. Also, we try to find the minimum number of mutually orthogonal subgraphs for certain graphs based on the proposed product techniques. As a direct application to the proposed different product techniques, mutually orthogonal graph squares for disjoint unions of stars are constructed. All the constructed results in this paper can be used to generate new graph-orthogonal arrays and new authentication codes.

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Section: Introductionmentioning

confidence: 99%

Construction of Mutually Orthogonal Graph Squares Using Novel Product Techniques

El-Mesady

Bazighifan

2022

Journal of Mathematics

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On Graph-Transversal Designs and Graph-Authentication Codes Based on Mutually Orthogonal Graph Squares

El-Mesady

Bazighifan

Shabana

2022

Journal of Mathematics

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Combinatorial designs have many interesting and genuine wide applications in areas including analysis and design of algorithms, cryptography, analysis and design of experiments, storage system design, tournament scheduling, optical communications, and computer networks to mention just a few areas. In this paper, we are concerned with the transversal designs and authentication codes as direct applications of combinatorial designs. The novelty of the current paper is demonstrated by the fact that it is the first to introduce the transversal designs and authentication codes by the mutually orthogonal graph squares (MOGS); we call them graph-transversal designs and graph-authentication codes, respectively. Here, the major contributions are the constructions of graph-transversal designs and graph-authentication codes based on several classes of graphs. Also, we present several results such as path-transversal designs, cycle-transversal designs, and disjoint unions of stars-transversal designs.

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A secure lightweight fuzzy embedder based user authentication scheme for internet of medical things applications

Praveen¹,

Pabitha²

2023

IFS

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The Internet of Medical Things (IoMT) is a network of medical devices, hardware infrastructure, and software that allows healthcare information technology to be communicated over the web. The IoMT sensors communicate medical data to server for the quick diagnosis. As, it handles private and confidential information of a user, security is the primary objective. The existing IoT authentication schemes either using two-factor(Username, password) or multi-factor (username, password, biometric) to authenticate a user. Typically the structural characteristics-based biometric trait like Face, Iris, Palm print or finger print is used as a additional factor. There are chances that these biometrics can be fabricated. Thus, these structural biometrics based authentication schemes are fail to provide privacy, security, authenticity, and integrity. The biodynamic-based bioacoustics signals are gained attention in the era of human-computer interactions to authenticate a user as it is a unique feature to each user. So, we use a frequency domain based bio-acoustics as a biometric input. Thus, this work propose a Secure Lightweight Bioacoustics based User Authentication Scheme using fuzzy embedder for the Internet of Medical Things applications. Also, the IoT sensors tends to join and leave the network dynamically, the proposed scheme adopts chinese remainder technique for generate a group secret key to protect the network from the attacks of former sensor nodes. The proposed scheme’s security is validated using the formal verification tool AVISPA(Automated Validation of Internet Security Protocols and Applications). The system’s performance is measured by comparing the proposed scheme to existing systems in terms of security features, computation and communication costs. It demonstrates that the proposed system outperforms existing systems.

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Generalization of MacNeish’s Kronecker product theorem of mutually orthogonal Latin squares

Cited by 5 publications

References 12 publications

Construction of Mutually Orthogonal Graph Squares Using Novel Product Techniques

Construction of Mutually Orthogonal Graph Squares Using Novel Product Techniques

On Graph-Transversal Designs and Graph-Authentication Codes Based on Mutually Orthogonal Graph Squares

A secure lightweight fuzzy embedder based user authentication scheme for internet of medical things applications

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