Combinatorial designs are a mathematical basis to build secure and effective cryptographic systems. They allow randomness to be well structured, uniformly distributed, and highly diffused, which is critical to the security primitives in the modern world. In this paper, the interaction between orthogonal arrays, Latin squares and quasigroup constructions in fortifying substitution permutation networks and S-box design is discussed. It provides a single analytical framework between combinatorial properties and algebraic hardness assumptions, which allow strong resistance to linear, differential and algebraic attacks. Also, hybridization with the current cryptography methods, and, in particular, post-quantum methods, is considered to improve scalability and resilience. The theoretical and experimental analyses show that it has better security measures, structural efficiency, and fault tolerances than the traditional constructions. The findings underscore the importance of the combinatorial design theory as an effective instrument to the next-generation cryptographic architecture. This book offers information on safe, scalable, and ground-based system design.