Paper 2025/277

Tighter Control for Distributed Key Generation: Share Refreshing and Expressive Reconstruction Policies

Abstract

The secure management of private keys is a fundamental challenge, particularly for the general public, as losing these keys can result in irreversible asset loss. Traditional custodial approaches pose security risks, while decentralized secret sharing schemes offer a more resilient alternative by distributing trust among multiple parties. In this work, we extend an existing decentralized, verifiable, and extensible cryptographic key recovery scheme based on Shamir's secret sharing. We introduce a refresh phase that ensures proactive security, preventing long-term exposure of secret shares. Our approach explores three distinct methods for refreshing shares, analyzing and comparing their security guarantees and computational complexity. Additionally, we extend the protocol to support any monotone access structure, enabling the most general and fine-grained control over key reconstruction.

Note: The updated version does not introduce any substantial changes with respect to the previous one; we have corrected minor typos, rephrased some passages for clarity, slightly expanded certain sections to improve their exposition, reorganized the sections for better readability and flow, and added more comprehensive tables summarizing the complexity results.