Democratic Ramp Secret Sharing

2024-12-23

AI Summary

Traditional threshold secret sharing schemes provide security guarantees only in worst-case or best-case scenarios, failing to ensure uniform protection across all maximal unauthorized subsets—i.e., they lack balanced security over the access structure. Method: We propose a “democratized” threshold secret sharing scheme, introducing for the first time the notion of *democratic security*, a second-layer security requirement ensuring that every maximal unauthorized set obtains identical (and strictly bounded) information about the secret. Our construction leverages monomial-Cartesian codes, integrating linear coding theory, information-theoretic analysis, and the ramp secret sharing framework. Contributions: (1) We break the conventional single-layer security paradigm by rigorously guaranteeing uniform secret non-recoverability across all maximal unauthorized sets; (2) We prove that several classical high-quality schemes inherently satisfy this democratic security property; (3) We present a constructive and efficiently verifiable scheme that tightly controls unauthorized information leakage without compromising authorized reconstruction capability.

Technology Category

• Game Theory and Economic Paradigms: Mechanism Design
• Multiagent Systems: Mechanism Design
• Machine Learning: Privacy

Application Category

• Security and Privacy: Large-scale security measurements
• Responsible Web: Web for democratic and emancipatory futures
• Economics, Online Markets and Human Computation: Fairness, privacy, and diversity in economic environments

Abstract

In this work we revisit the fundamental findings by Chen et al. in [5] on general information transfer in linear ramp secret sharing schemes to conclude that their method not only gives a way to establish worst case leakage [5, 25] and best case recovery [5, 19], but can also lead to additional insight on non-qualifying sets for any prescribed amount of information. We then apply this insight to schemes defined from monomial-Cartesian codes and by doing so we demonstrate that the good schemes from Sec. IV in [14] have a second layer of security. Elaborating further, when given a designed recovery number, in a new construction the focus is entirely on ensuring that the access structure possesses desirable second layer security, rather on what is the worst case information leakage in terms of number of participants. The particular structure of largest possible sets being not able to determine given amount of information suggests that we call such schemes democratic

Problem

• Secure Secret Sharing
• Worst-case Information Protection
• Optimal Information Recovery

Innovation

• Dual-Layer Security
• Univariate-Cartesian Code
• Democratic Schemes