Applications of Rainbow Antimagic Coloring of Flower Snark Graphs in secure Cryptographic Protocol Design

Abstract

Graph theory and cryptography maintain a profound theoretical relationship, especially concerning structural complexity and computational diculty. This paper investigates a new intersection by utilizing Rainbow Antimagic Edge Coloring on Flower Snark graphs, which are a type of non-Hamiltonian,non-3-edge-colorable cubic graphs for creating secure Cryptographic protocols. Rainbow Antimagic Coloring assigns distinct edge weights such that each vertex sums are unique, resulting in a one-way encoding system well-suited for encryption and hashing purposes. We illustrate how the challenge of computing valid Rainbow Antimagic Colorings for Flower Snark graphs can be leveraged to develop secure public key systems by encryption algorithm. The fundamental structural complexity of the Flower Snark graph allows for the establishment of Cryptographic primitives that are provably secure and resilient to both classical and quantum attacks.