Key Generation in Cryptography Using Radio Path Coloring

Dhanyashree

doi:10.1109/ACCESS.2024.3392598

Key Generation in Cryptography Using Radio Path Coloring

2024-01-01

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DOI：10.1109/ACCESS.2024.3392598

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An L((p(1), p(2), p(3), ...,p(m)))- labeling of a graph G is an assignment of positive integers to the vertices of G such that the difference in the labels assigned to the vertices at distance i should be at least p(i ). The particular case of p(1) = d,p(2)= d-1,p(3) = d-2, ..., p(d )= 1 where d is the diameter of the graph, was known as the radio labeling of G . The minimum value of the maximum integer used in any feasible radio labeling of G was called as radio number of G denoted by rn(G) . The idea of radio path coloring was conceived to ensure secure communication in networks. If there exists a path between each pair of vertices, such that, the labeling in that path is an Lp(1), p(1)-1,p(1 )-2,..., 1)- labeling, then such a labeling was called an L(p(1),p(1 )-1,p(1 )-2, ..., 1)- path coloring or a radio path coloring of G . The minimum value of the largest label used in such a coloring was called as the radio path connection number. Earlier researchers have studied the case of p(1 )= 2 for different classes of graphs. We focus on the more general case of p(1) >= 3 and obtain an upper bound on the radio connection number k(p1c)(G) , of any semi-Hamiltonian graph G . An algorithm to obtain the radio path coloring of a Semi-Hamiltonian graph G is also discussed here and the same is used to generate keys for secure communication in cryptography.

Keyword:

Labeling

Cryptography

Encryption

Receivers

Interference

Entropy

Upper bound

radio labeling

path coloring

Key Generation in Cryptography Using Radio Path Coloring

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