A Dominating Edge Block Partition Framework for Graph-Access Secret Sharing
Keywords:
Graph-access secret sharing, Dominating set, Dominating Edge Block Partition (DEBP), Edge partition, Access structure, Graph theory, Connected graphs, Share distribution, Cryptography.Abstract
Participant relationships can direct share distribution and secret reconstruction in graph-access secret sharing systems, where the access structure is determined by the structural characteristics of an underlying graph. The Dominating Edge Block Partition (DEBP), a graph-theoretic technique for creating graph-access secret sharing methodsin which the selected dominating vertices collectively constitute the authorized participant set, is introduced in this study. The suggested DEBP operator divides the edge set of a connected graph with one of its dominating sets into pairwise disjoint connected edge blocks, each of which is uniquely connected to a dominating vertex. The dealer distributes these block shares according to the graph access structure generated by the dominating set, represents the secret as the sum of edge labels, and calculates one block share for each dominating vertex by aggregating the labels of the corresponding edge block. The permitted dominating vertices' block shares are combined to accomplish secret reconstruction. The suggested framework introduces the use of graph-theoretic operations in cryptography by establishing a direct relationship between graph domination, edge splitting, and secret sharing. Formal mathematical proofs confirm the construction's correctness, and once the dominating set has been identified, its computational complexity is demonstrated to be linear in the number of graph edges. Detailed constructions on path graphs, cycle graphs, complete binary trees and grid graphs illustrate the applicability of the suggested framework. The suggested DEBP framework gives a platform for future studies on graph-theoretic techniques in safe information distribution as well as a methodical way for creating graph-access secret sharing schemes.
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