The complexity of the connected graph access structure on seven participants

Abstract

In this paper, we study an important problem in secret sharing that determines the exact value or bound for the complexity. First, we use the induced subgraph complexity of the graph G with access structure Γ to obtain a lower bound on the complexity of the graph G. Then, applying decomposition techniques, we obtain an upper bound on the complexity of the graph G. We determine the exact values of the complexity for each of the ten graph access structures on seven participants. Also, we improve the value bound of the complexity for the six graph access structures with seven participants.

Keywords

• access structure
• complexity
• secret sharing scheme
• connected graph
• induced subgraph
• 68r10
• 94a62