中文摘要：

门限签名协议使得签名团体中任何t个参与者合作可以生成某个消息的有效签名;而少于t个参与者就无法得到该消息的合法签名。目前关于门限签名协议的安全性研究只是专注于单一协议执行时的安全性,针对这点,引入通用可组合框架。利用该框架的通用可组合性可以模块化地设计与分析门限签名协议。首先定义了门限签名协议在通用可组合框架下的安全模型,并证明其等价于门限签名协议标准概念下的安全模型,然后以前摄门限签名协议为例描述如何应用这个安全模型。提出的门限签名协议和前摄性门限签名协议不仅满足可证明安全性,还具有通用可组合安全性。

英文摘要：

Threshold signature allowed any subset of t parties generating a signature, but that disallowed the creation of a valid signature if fewer than t parties participate in the protocol. Since the security of threshold signature was only considered in a single instance before, the universal composability framework was introduced. The framework with its security preserving composition property allowed for modular design and analysis of the threshold signature. The defined ideal functionality of threshold signature is proved equals to the standard security notion of threshold signature. Furthermore, how to applying the ideal functionality is described. The proposed threshold signature protocol and proactive threshold signature protocol are not only provably secure, but also universally composable.