Conditional Disclosure of Secrets and Storage over Graphs

Abstract

In the era of big data, it is essential to implement practical security and privacy measures to ensure the lawful use of data and provide users with trust and assurance. In the dissertation, I address this issue through several key steps. Firstly, I delve into the problem of conditional secret disclosure, representing it using graphs to determine the most efficient approach for storing and disclosing secrets. Secondly, I extend the conditional disclosure of secrets problem from a single secret to multiple secrets and from a bipartite graph to an arbitrary graph. Thirdly, I remove security constraints to observe how they affect the efficiency of storage and recovery. In our final paper, I explore the secure summation problem, aiming to determine the capacity of total noise. Throughout the dissertation, I leverage information-theoretic tools to address security and privacy concerns.