A Provably-Unforgeable Threshold EdDSA with an Offline Recovery Party

TL;DR

This paper introduces a new threshold EdDSA signature scheme that allows distributed signing with an offline participant, providing provable security without trusted third parties, and ensuring unforgeability under standard cryptographic assumptions.

Contribution

It presents the first protocol for threshold EdDSA signatures with an offline recovery party, extending existing schemes to enhance security and practicality.

Findings

Scheme is secure against adaptive malicious adversaries

Security can be strengthened against rushing adversaries

Resiliency of recovery process is analyzed

Abstract

A $(t,n)$-threshold signature scheme enables distributed signing among $n$ players such that any subset of size at least $t$ can sign, whereas any subset with fewer players cannot. The goal is to produce threshold digital signatures that are compatible with an existing centralized signature scheme. Starting from the threshold scheme for the ECDSA signature due to Battagliola et al., we present the first protocol that supports EdDSA multi-party signatures with an offline participant during the key-generation phase, without relying on a trusted third party. Under standard assumptions we prove our scheme secure against adaptive malicious adversaries. Furthermore we show how our security notion can be strengthen when considering a rushing adversary. We discuss the resiliency of the recovery in the presence of a malicious party. Using a classical game-based argument, we prove that if there is an adversary capable of forging the scheme with non-negligible probability, then we can build a forger for the centralized EdDSA scheme with non-negligible probability.