Preprint Article Version 1 This version is not peer-reviewed

Matrix Manipulations and Tridiagonal Structures New Schemes in Secure Data Encryption

Version 1 : Received: 30 October 2024 / Approved: 31 October 2024 / Online: 31 October 2024 (07:59:33 CET)

How to cite: Kharal, A.; Bokhary, S. A. U. H.; Saeed, M. M. Matrix Manipulations and Tridiagonal Structures New Schemes in Secure Data Encryption. Preprints 2024, 2024102503. https://doi.org/10.20944/preprints202410.2503.v1 Kharal, A.; Bokhary, S. A. U. H.; Saeed, M. M. Matrix Manipulations and Tridiagonal Structures New Schemes in Secure Data Encryption. Preprints 2024, 2024102503. https://doi.org/10.20944/preprints202410.2503.v1

Abstract

This paper presents four novel schemes for secure data encryption utilizing mathematical transformations. The first scheme employs matrix manipulations and partitioning of numerical values derived from plain text characters, constructing a cipher through matrix additions. The second scheme introduces division operations and additional transformation layers for enhanced data obscurity. The third scheme incorporates tridiagonal matrices, creating a structured encryption process. The fourth scheme refines this approach with quotient-remainder operations and symmetric keys to construct a tridiagonal matrix cipher. Detailed algorithms for encryption and decryption are provided, with examples illustrating practical applications. This work contributes to mathematical cryptography by offering enhanced security methods for digital communication.

Keywords

tridiagonal matrices; matrix manipulations; data encryption; symmetric key cryptography 

Subject

Computer Science and Mathematics, Discrete Mathematics and Combinatorics

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