Empowering Secure Communication With Specific Triangular Matrices: Practical Examples Unveiled Using Different Approximations

Abstract

In the fast-evolving realm of digital interaction and information sharing, cryptographic security serves as a fundamental pillar, safeguarding sensitive data and ensuring privacy. Cryptographic protocols, the fundamental elements of secure communication, rely on mathematical principles and computational strategies to foil attempts at breaching confidentiality and integrity. Within this domain, the upper triangular matrix has emerged as a significant mathematical concept. In this paper, an upper triangular matrix is used with Hill Chipher, logic map, and encryption/ decryption algorithms written in python programming language for cryptography. The mapping is done in a dictionary consisting of only writable characters of ASCII values and Turkish characters. Thus, both the Turkish character sensitivity and the character limit are extended with the string data type. Additionally, to these cryptographic methods, another different crypto approximation named as Hash function is considered; phyton codes prepared for the example, too.