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 con-sidered in a single instance before

the universal composability framework was introduced.The framework with its secu-rity 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.Further-more

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.