Chromatic Polynomials and Cryptographic Hashing on WIP-Quasigroup Structures

Cryptographic hash functions are indispensable for today’s information security because they secure data integrity, authentication and encrypted storage. Recently, graph-theoretic constructions have acquired interest in the design of hash functions because of their noteworthy sensitivity to structural alterations and rich combinatorial structure. Chromatic polynomials of graphs, in particular, are intriguing possibilities for cryptographic hashing processes because they exhibit strong combinatorial invariants whose values alter substantially under minor changes to the underlying graph. In this paper, we give a hashing framework based on chromatic polynomials generated by graphs related to weak inverse property quasigroups. Graph models can be utilized naturally represent the algebraic subloops of weak inverse property quasigroups, an important type of nonassociative algebraic structures. The chromatic polynomials PtΘVCΞ1×Ξ2,⊙, PtΘVAΞ1×Ξ2,⊙ and PtΘVℵΞ1×Ξ2,⊙ have been calculated and investigated along with the polynomial PtΘPΞ1×Ξ2,⊙ of the complete bipartite graph K3n,3n. These polynomials are the fundamental components of the recommended hashing algorithm and encompass significant combinatorial characteristics found in the underlying algebraic structures.