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

Mohammad Mazyad Hazzazi, Muhammad Nadeem, Muhammad Kamran, Nwazish Ali and Abdu Qaid Alameri

Journal of Mathematics, 2026, vol. 2026, 1-25

Abstract: 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.

Date: 2026
References: Add references at CitEc
Citations:

Downloads: (external link)
http://downloads.hindawi.com/journals/jmath/2026/3026642.pdf (application/pdf)
http://downloads.hindawi.com/journals/jmath/2026/3026642.xml (application/xml)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:hin:jjmath:3026642

DOI: 10.1155/jom/3026642

Access Statistics for this article

More articles in Journal of Mathematics from Hindawi
Bibliographic data for series maintained by Mohamed Abdelhakeem ().