Enhancing key distribution via discrete mathematical structures in cryptosystems

In the rapidly evolving field of cryptography, ensuring the efficiency and security of key distribution mechanisms is critical for protecting sensitive information in digital systems. Traditional key management methods often face challenges related to scalability, security vulnerabilities, and computational overhead. This paper presents a comprehensive study on optimizing key distribution protocols by harnessing the power of discrete mathematical structures. In our proposed work we have introduced a set of novel algorithms that exploit the unique properties of these discrete mathematical frameworks to enhance the overall performance of key distribution by using the set of finite fields, graph theory, and combinatorial designs to address the inherent limitations of conventional approaches. By integrating the symmetry and structure of finite fields, the connectivity and efficiency of graph theory, and the organization of combinatorial designs, we have developed a key management solution that offers improved scalability, reduced computational complexity, and heightened security.