A secured communications system is a structure or infrastructure that is intended to ensure the confidentiality, integrity, and authenticity of data being exchanged between entities. Such systems use various security technologies to guarantee that communications are not tampered with, read, or accessed by unauthorized parties. The intractability of factoring huge composite numbers is a prerequisite for RSA's security. With big enough key sizes, it is still computationally infeasible for attackers to defeat RSA encryption with today's technology. Efficient domination is an idea based on graph theory, specifically in the investigation of domination in graphs. Although it has many applications in problems in computation, it is only for cryptography in contexts involving efficient algorithms, combinatorial structures, and optimization for security that it finds uses. This idea provides minimal redundancy in domination, similar to the optimization of resources in a cryptographic scenario. In this work, we concentrate on enhancing the complexity of secure systems using a mathematical model that is based on fuzzy graph networks. The suggested model combines efficient domination, the RSA algorithm, and triangular fuzzy membership functions. By integrating these optimized parameters, we construct a very secure mathematical fuzzy graph network that can efficiently protect secret information. [ABSTRACT FROM AUTHOR]

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