A Comprehensive Review of Graph Theory Applications in Secret Sharing Schemes

Mohamed Akdim1, Ahmed Drissi1
1National School for Applied Sciences (ENSA of Tangier), AbdelMalek Essaadi University, Tangier, Morocco

Abstract

In secret sharing, the relationships between participants and the information they hold can be modeled effectively using graph structures. Graphs allow us to visualize and analyze these relationships, making it easier to define access structures, optimize share distributions, and ensure security. This paper provides the first comprehensive review of existing research on the application of graph theory to secret sharing comparing different classic and modern approaches and analyzing the current litterature. Through this study we highlight the key advances and methodologies that have been developed, underscoring the pivotal role of graph theoretic approaches in enhancing the security and efficiency of secret sharing schemes. Furthermore, the review identifies open challenges and future research directions, providing insights into potential innovations that could further strengthen cryptographic practices. This work serves as a foundational resource for researchers and practitioners seeking to deepen their understanding of the intersection between graph theory and secret sharing, fostering the development of more robust and sophisticated cryptographic solutions.

Keywords: Secret sharing, Graph access structure, Graph decompositions, Bipartite graph