S-Boxes are important devices in the current cryptographic systems, which guarantee confusion and antagonism against attacks. This article extends a mathematical model of the building of resilient S-Boxes with the use of finite fields GF(2 n). The method takes advantage of multiplicative inverses, affine transformations, and permutation polynomials to provide high nonlinearity and low differential uniformity. Irreducible structures and polynomial representations are also used to come up with algebraic normal forms that increase the cryptographic strength. The experimental analysis shows an enhancement of performance, with a nonlinearity of above 112 and a differential uniformity of 4 surpassing traditional designs by a factor of about 12. The suggested technique guarantees a balanced output, great avalanche effect, as well as resistance to linear and differential cryptanalysis. It has the scalability that enables a flexible generation of S-Boxes, allowing lightweight and high-security applications, and adds a systematic and efficient design strategy. Future work examines the optimization of hardware and its resistance to side-channel attacks, and how to integrate both into more advanced encryption architecture that can be implemented in practice.