Super-encryption technique of graphs via matricial approach

Domada, Triveni; Ashok, Gudela; Kumar, S. Ashok; Kumari, D. Chaya

doi:10.47974/JDMSC-1976

Open Access Research Article

Super-encryption technique of graphs via matricial approach

^*Triveni DomadaCorresponding authortrivenidomada@gmail.comDepartment of MathematicsAndhra University TDR-HUBVisakhapatnam, Andhra Pradesh, 531081, IndiaView full profile → , Gudela Ashokashokavf@gmail.comDepartment of MathematicsAndhra University TDR-HUBVisakhapatnam, Andhra Pradesh, 531081, IndiaView full profile → , S. Ashok Kumarsaiashok.84@gmail.comDepartment of MathematicsGayatri Vidya Parishad College for UG & PG Courses (A)Visakhapatnam, Andhra Pradesh, 530017, IndiaView full profile → , D. Chaya Kumarichayakumari.divakarla@gmail.comDepartment of MathematicsGayatri Vidya Parishad College for UG & PG Courses (A)Visakhapatnam, Andhra Pradesh, 530017, IndiaView full profile →

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pp. 1215–1222Vol. 27Issue 4June 2024DOI: 10.47974/JDMSC-1976 Crossmark XML

Published Online:: 26 Jun 2024
Article type:: Research Article
Language:: EN
Article no.:: JDMSC-1976
Pages:: 1215–1222

Abstract

Graph theory is quickly becoming an important area of research due to its numerous applications in areas like cryptography, coding theory, communication networks and their security. In this paper a super-encryption method of graphs is proposed via matricial approach for maintaining confidentiality in communicating the messages with two layers of encryption by taking the first level of encryption as the incidence matrix. The message is further encrypted using Fibonacci numbers (taken in matrix form) by adding to the corresponding elements of the product of the incidence matrix of the graph and message (taken as diagonal matrix). Here the graph can be taken as private key. The matrix so formed can be treated as an adjacency matrix which in turn can be represented as a graph and will be sent to the receiver as super encrypted message. The receiver writes the adjacency matrix corresponding to the graph, then subtracts the Fibonacci matrix from adjacency matrix and then multiplies it with the inverse of incidence matrix. Finally, receiver decrypts the message using the private key shared.

Keywords

Primary 11B39 94A60 Secondary 05C07

Subject Classifications

Fibonacci matrixMatricesGraph Fibonacci NumbersCryptography

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