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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 subsetwith fewer players cannot. The goal is to produce threshold digital signaturesthat are compatible with an existing centralized signature scheme. Startingfrom the threshold scheme for the ECDSA signature due to Battagliola et al., wepresent the first protocol that supports EdDSA multi-party signatures with anoffline participant during the key-generation phase, without relying on atrusted third party. Under standard assumptions we prove our scheme secureagainst adaptive malicious adversaries. Furthermore we show how our securitynotion can be strengthen when considering a rushing adversary. We discuss theresiliency of the recovery in the presence of a malicious party. Using aclassical game-based argument, we prove that if there is an adversary capableof forging the scheme with non-negligible probability, then we can build aforger for the centralized EdDSA scheme with non-negligible probability.

A Provably-Unforgeable Threshold EdDSA with an Offline Recovery Party