A $(t,n)-$ threshold signature scheme enables distributed signing among $n$
players such that any subgroup of size $t$ can sign, whereas any group with
fewer players cannot. Our goal is to produce signatures that are compatible
with an existing centralized signature scheme: the key generation and signature
algorithm are replaced by a communication protocol between the parties, but the
verification algorithm remains identical to that of a signature issued using
the centralized algorithm. Starting from the threshold schemes for the ECDSA
signature due to R. Gennaro and S. Goldfeder, we present the first protocol
that supports multiparty signatures with an offline participant during the Key
Generation Phase, without relying on a trusted third party. Following
well-established approaches, we prove our scheme secure against adaptive
malicious adversaries.

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