The problem of listing factorizations of graph is a computationally expensive problem, and has not been successfully applied in the design of cryptographic systems up to date. This paper will solve this challenge by coming up with a systematic plan of listing graph factorizations and harnessing the combinatorics of graph factorizations to create secure cryptography systems. The main target of it is to create a powerful enumeration model and prove that it can be used in key generating, safe communication, and structural randomness. It is a mixture of algebraic graph theory, algorithms of combinatoric decomposition and enumeration model and tested on benchmark graph datasets, such as regular, complete and bipartite graphs. The experimental results indicate that the time of enumeration is reduced by 31.6 percent and structural uniqueness is also enhanced by 24.8 percent than the traditional brute-force computations and the diversity of cryptographic keys has been boosted by 27.3. The features that would be able to be differentiated in the comparative analysis are enhanced protection against structural attacks, and scalability. The solution introduces a new connection between the graph factorization theory and cryptographic primitives, which allow an effective, structure-based, security. This work establishes graph factorizations as a firm foundation for next-generation cryptographic systems.