Matrix Manipulations and Tridiagonal Structures New Schemes in Secure Data Encryption

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.