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

El-Mesady, A.; Bazighifan, Omar; Shabana, H.

doi:10.1155/2022/8992934

Cited by 8 publications

(4 citation statements)

References 13 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…All the constructed results in this paper can be used to generate new graph-orthogonal arrays, new graph-authentication codes, and new graph-transversal designs [3,23]. +ey can also be used in the design of experiments [24].…”

Section: Discussionmentioning

confidence: 99%

See 1 more Smart Citation

Construction of Mutually Orthogonal Graph Squares Using Novel Product Techniques

El-Mesady

Bazighifan

2022

Journal of Mathematics

Self Cite

View full text Add to dashboard Cite

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.

show abstract

Section: Discussionmentioning

confidence: 99%

“…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]. MOGS are used to construct orthogonal arrays that have many applications [24].…”

Section: Introductionmentioning

confidence: 99%

Construction of Mutually Orthogonal Graph Squares Using Novel Product Techniques

El-Mesady

Bazighifan

2022

Journal of Mathematics

Self Cite

View full text Add to dashboard Cite

show abstract

“…Step 4: Encrypted Message Block Cipher 2: {4, 8, 24,32,48,56,72,80,96,104,120,128,77,157,221,30,118,182,15,111,55,136,16,144,152,160,168,176,184,192,200,208,216,93,157,221,38,126,190,52,119,175,224,232,7,240,248,256,264,272,280,288,296,304,101,165,229,54,134,198,23,91,183,10,9,…”

Section: Illustration For a Block Cipher Consider The Plaintext "I Fl...mentioning

confidence: 99%

“…Ustimenko [8] used the graphs with the largest girths in constructing a cryptosystem. A few more applications of graph theory in coding theory can be referred to in [9][10][11][12].…”

Section: Introductionmentioning

confidence: 99%

Block Encryption and Decryption of a Sentence Using Decomposition of the Turan Graph

Beaula¹,

Venugopal

Praba³

2023

Journal of Mathematics

View full text Add to dashboard Cite

Encryption and decryption are the two processes in cryptography to conceal and convey important information to an authorized person without third-party interruption in a network. Cryptography is a branch of computer science in which the system has to be updated every second. It mainly depends on mathematical concepts like number theory and algebra. Recently, graph theory concepts are employed in cryptography to make it stronger. The usage of complex graphs in cryptosystems makes it difficult to hack. In this paper, we proposed a cryptosystem using the Turan graph which has a complex graph structure. The advantage of using a Turan graph is that it is a unique multipartite complete graph with more edges than other multipartite complete graphs. This adds robustness to the cryptosystem. The novelty of this paper is the decomposition of the Turan graph into paths and stars and applying edge labeling to them to encrypt and decrypt a sentence of k words. The algorithms for encryption and decryption are also proposed in this paper.

show abstract

Complete Multipartite Graphs Decompositions Using Mutually Orthogonal Graph Squares

El-Mesady,

Al-Mdallal,

Abdeljawad

2023

Int. J. Appl. Comput. Math

View full text Add to dashboard Cite

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

Cited by 8 publications

References 13 publications

Construction of Mutually Orthogonal Graph Squares Using Novel Product Techniques

Construction of Mutually Orthogonal Graph Squares Using Novel Product Techniques

Block Encryption and Decryption of a Sentence Using Decomposition of the Turan Graph

Complete Multipartite Graphs Decompositions Using Mutually Orthogonal Graph Squares

Contact Info

Product

Resources

About