On sum graph-based access structure In a secret sharing scheme
Date of Publication
Bachelor of Science in Mathematics with specialization in Business Applications
Physical Sciences and Mathematics
College of Science
Mathematics and Statistics Department
This study is an exposition of the paper by Slamet et al.  on a new type of secrete sharing scheme based on an access structure. The authors of this study provided concrete examples where the new secret sharing scheme is applied.
Secret sharing scheme is a method to distribute secret information to a set P of participants so that only authorized subsets of P can reconstruct the secret. A set of subsets of P that can reconstruct the secret is called an access structure of the scheme. In the paper by Slamet et al. , they used Shamir's secret sharing scheme together with the concept of exclusive sum graph labeling to provide a new secret sharing scheme based on an access structure. A simple undirected graph G is called a sum graph if there exists a labeling L of the vertices of G into distinct positive integers such that any two distinct vertices u and v of G are adjacent if and only if there is a vertex w whose label is L(w) = L(u) + L(v). A variation of this concept called exclusive sum graph labeling was de ned by Slamet et al. . The survey paper by Gallian  provides an overview of the results about sum graphs and exclusive sum graphs. Shamir's secret sharing scheme is a type of secret sharing scheme to distribute the secret, give a share to each participant, and reconstruct the secret using a technique called Lagrange polynomial interpolation . Combining the concepts of Shamir's secret sharing scheme and sum graph labeling, a new secret sharing scheme with a size 2 access structure was formed. Some examples can be found in the paper on the application of this new scheme.
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De Chavez, D. R., & Sebastian, I. A. (2018). On sum graph-based access structure In a secret sharing scheme. Retrieved from https://animorepository.dlsu.edu.ph/etd_bachelors/18589