Optimizing Threshold Secret Sharing with Hierarchical Access Structures in ECDSA

Secret sharing schemes divide sensitive information into multiple parts for secure distribution. The (t, n) threshold multi-secret sharing scheme based on Verifiable Secret Sharing (VSS) is a well-known method, but it typically uses a uniform access structure, which limits its application in organizations with hierarchical access needs. While hierarchical schemes often rely on a tree structure, this research explores a model where share values at each level directly relate to the secret.In this study, we employed three (t, n) threshold secret sharing schemes on the Elliptic Curve Digital Signature Algorithm (ECDSA): one without a hierarchical access structure and two with hierarchical access structure. Performance analysis based on computation time and time complexity shows that hierarchical schemes outperform non-hierarchical one, as they reduce the polynomial degree into smaller hierarchical levels. Additionally, all three schemes were evaluated against the five core characteristics of digital signatures—authenticity, unforgeability, non-reusability, inalterability, and non-repudiation—and were found to satisfy these criteria.