A Robust Algorithm for Asymmetric Cryptography Using Rainbow Vertex Antimagic Coloring

Abstract

Cryptography plays a crucial role in securing information and communications in the face of advancing technologies. Asymmetric encryption, also known as public-key cryptography, plays a crucial role in cryptography. Unlike symmetric encryption, which uses a single key for both encryption and decryption, asymmetric encryption involves a pair of keys, namely a public key and a private key. Asymmetric cryptography is closely associated with the secure management of keys, addresses, and transactions within the blockchain ecosystem, especially in cryptocurrency platform. In this study,we present a novel concept known as rainbow vertex antimagic coloring. This concept extends the idea of rainbow vertex coloring by incorporating antimagic labeling. Let f : E(G) → {1, 2, . . . , |E(G)|} be a function, where the weight of a vertex v ∈ V (G) with respect to f is defined as wf (v) = Σe∈E(v) f(e). Here, E(v) denotes the set of edges incident to v. Thefunction f is termed a vertex antimagic edge labeling if it assigns distinct weights to each vertex. A path is termed a rainbow path if, for any vertices u and v, all internal vertices on the u − v path have distinct weights. The rainbow vertexantimagic connection number of a graph G, denoted by rvac(G), is defined as the minimum number of colors requiredin any rainbow coloring derived from rainbow vertex antimagic labelings of G. In this paper, we will obtain some newlemmas or theorems concerning rvac(G), and we will implement the obtained lemmas or theorems of RVAC on asymmetric cryptography technique.