Secret sharing with additive access structures from correlated random variables

2026-01-14

AI Summary

This work investigates efficient secret sharing under dynamically growing additive access structures, leveraging correlated randomness and public communication. Specifically, it addresses scenarios where the access structure expands monotonically over time, any subset of participants may join at any moment, and the dealer learns of structural changes only when they occur. The paper presents the first extension of the correlated-randomness-based secret sharing model to such a dynamic setting. The proposed scheme achieves, at every step, the optimal secret rate attainable in the static model and meets the information-theoretic capacity for threshold access structures. This significantly broadens the applicability of existing theoretical frameworks in secret sharing.

Technology Category

• Machine Learning: Structured Learning
• Reasoning under Uncertainty: Stochastic Optimization
• Multiagent Systems: Mechanism Design

Application Category

• Security and Privacy: Large-scale security measurements
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems

Abstract

We generalize secret-sharing models that rely on correlated randomness and public communication, originally designed for a fixed access structure, to support a sequence of dynamic access structures, which we term an Additive Access Structure. Specifically, the access structure is allowed to monotonically grow by having any subset of participants added to it at a given time step, and the dealer only learns of these changes to the access structure on the time step that they occur. For this model, we prove the existence of a secret sharing strategy that achieves the same secret rate at each time step as the best known strategy for the fixed access structure version of this model. We also prove that there exists a strategy that is capacity-achieving at any time step where the access structure is a threshold access structure.

Problem

• secret sharing
• additive access structure
• correlated random variables
• dynamic access structure
• threshold access structure

Innovation

• secret sharing
• additive access structure
• correlated random variables
• dynamic access structure
• capacity-achieving