A NOVEL ENCRYPTION FRAMEWORK USING SELF- INVERTIBLE MATRICES AND COMPLETE GRAPH ADJACENCY MATRIX STRUCTURES

Encryption techniques form the foundation for securing communication
and protecting information in the modern digital era. With the rapid growth
of internet usage and network-based interactions, the need for robust
encryption methods has become increasingly critical. Transmitting
sensitive information over unsecured or vulnerable networks exposes it to
risks such as cyberattacks, data breaches, and unauthorized access. To
address these challenges, cryptographic techniques have been widely
developed and applied. Classical methods such as the Caesar Cipher,
Atbash Cipher, Hill Cipher, along with various symmetric encryption
schemes, have significantly contributed to secure communication. In this
paper, we propose an encryption approach that integrates a self-invertible
matrix, the adjacency matrix, and the structure of a complete graph with a
Hamiltonian circuit to generate complex ciphertext from given message
units. A key feature of this method is the use of a self-invertible matrix as
the encryption key, which inherently guarantees the existence of its inverse
without requiring explicit computation. This property simplifies the
decryption process and considerably reduces computational complexity
while maintaining the strength of the encryption scheme.