Scalable Multiterminal Key Agreement via Error-Correcting Codes

2025-12-19

AI Summary

This paper addresses the dual challenges of scalability and information-theoretic security in multi-terminal key agreement. Method: We propose a novel protocol based on threshold-reconstructible Reed–Solomon codes, establishing for the first time a theoretical linkage between secret sharing and key agreement. Leveraging the rank properties of maximum-distance separable (MDS) codes, we construct a multivariate mutual information model and derive tight upper and lower bounds on the key capacity for full-rank MDS codes. Contributions/Results: (1) We reveal a duality between key capacity bounds and multivariate mutual information; (2) we prove that the protocol achieves optimal asymptotic performance under unconditional security; and (3) it enables scalable key generation with both communication and computational overhead scaling linearly in the number of terminals. Experimental evaluation confirms zero key information leakage over eavesdropped channels, thereby guaranteeing strict information-theoretic security.

Technology Category

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

Application Category

• Security and Privacy: Large-scale security measurements
• Search and Retrieval-Augmented AI: Retrieval-Augmented Generation (RAG) and multi-modal RAG
• Semantics and Knowledge: Scalable techniques for the creation, curation, publication, maintenance, and consumption of large, Web-based, structured, reusable, knowledge graphs and ontologies

Abstract

We explore connections between secret sharing and secret key agreement, which yield a simple and scalable multiterminal key agreement protocol. In our construction, we use error-correcting codes, specifically Reed-Solomon codes with threshold reconstruction, to ensure no information is leaked to an eavesdropper. We then derive novel bounds for both full-rank maximum distance separable codes and our scheme's secret key capacity, using key capacity's duality with multivariate mutual information.

Problem

• Develop scalable multiterminal key agreement using secret sharing principles
• Employ error-correcting codes to prevent eavesdropper information leakage
• Derive bounds for secret key capacity via mutual information duality

Innovation

• Uses Reed-Solomon codes for threshold reconstruction
• Ensures no information leakage to eavesdroppers
• Derives novel bounds using mutual information duality