Asymptotically ideal Disjunctive Hierarchical Secret Sharing Scheme with an Explicit Construction

2026-03-17

AI Summary

Existing disjunctive hierarchical secret sharing (DHSS) schemes struggle to simultaneously achieve small share size, computational security, and asymptotic ideality. This work proposes the first explicit construction that reconciles small share size with asymptotic ideality while maintaining computational security. The scheme leverages polynomial-based techniques, multilinear homogeneous recurrence relations, and one-way functions, ensuring that the dealer operates in polynomial time. By doing so, it significantly advances the trade-off between efficiency and security in DHSS, offering a practical and theoretically sound solution that improves upon prior approaches which typically sacrifice one of these critical properties.

Technology Category

• Search and Optimization: Distributed Search
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Multiagent Systems: Mechanism Design

Application Category

• Security and Privacy: Large-scale security measurements
• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems

Abstract

Disjunctive Hierarchical Secret Sharing (DHSS) scheme is a secret sharing scheme in which the set of all participants is partitioned into disjoint subsets. Each disjoint subset is said to be a level, and different levels have different degrees of trust and different thresholds. If the number of cooperating participants from a given level falls to meet its threshold, the shortfall can be compensated by participants from higher levels. Many ideal DHSS schemes have been proposed, but they often suffer from big share sizes. Conversely, existing non-ideal DHSS schemes achieve small share sizes, yet they fail to be both secure and asymptotically ideal simultaneously. In this work, we present an explicit construct of an asymptotically ideal DHSS scheme by using a polynomial, multiple linear homogeneous recurrence relations and one-way functions. Although our scheme has computational security and many public values, it has a small share size and the dealer is required polynomial time.

Problem

• Disjunctive Hierarchical Secret Sharing
• asymptotically ideal
• share size
• computational security
• secret sharing

Innovation

• asymptotically ideal
• Disjunctive Hierarchical Secret Sharing
• explicit construction
• small share size
• computational security