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.

中文翻译：

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具有离线恢复方的阈值 ECDSA

$(t,n)-$ 阈值签名方案允许在 $n$ 个玩家之间进行分布式签名，这样任何大小为 $t$ 的子组都可以签名，而任何玩家较少的组则不能。我们的目标是产生与现有集中式签名方案兼容的签名：密钥生成和签名算法被双方之间的通信协议所取代，但验证算法与使用集中式算法发布的签名保持一致。从 R. Gennaro 和 S. Goldfeder 提出的 ECDSA 签名的阈值方案开始，我们提出了第一个支持在密钥生成阶段与离线参与者进行多方签名的协议，而不依赖于受信任的第三方。遵循公认的方法，