Polynomial Representations of Weak Inverse Property Quasigroups and Their Role in Cryptographic Primitives

A connection between cryptography and polynomial functions is extremely significant. Mathematical performance of polynomials helps to enhance the cryptographic primitives, which are trustworthy as well as straightforward representation tools, in everyday use. In this research, explicit topological sequences Qf which correspond to degree-based, distance-based, and degree-distance-based indices f have been developed for 2αp1k1p2k2-order relatively prime graphs Γ of finite commutative weak inverse property quasigroups, C2×Z2γ,⋄. Through the utilization of Lagrange interpolation and polynomial approximation for introducing quasigroup curves PQf, it additionally gives polynomial formulations that encode the structural complexity of graphs interconnected with commutative weak inverse property quasigroups. Compared to previous investigations, the current research highlights a systematic polynomial-sequence connection. Quasigroup curves, cryptographic primitives, and graph invariants are all integrated together in a single framework. For lightweight cryptographic parameterization, the utilization of commutative weak inverse property quasigroups, relatively prime graphs, and polynomial modeling is an entirely new mathematical and technical advancement not previously seen in the literature.