Fuzzy identity-based threshold signature scheme based on bilinear maps

Threshold signature is a useful tool for sharing the power to sign, which has been extensively studied in the certificate-based public key setting and identity-based setting. Inspired by the work of Sahai and Waters´s fuzzy identity-based encryption, we introduce the concept of fuzzy identity-based threshold signature. In this notion, the trusted dealer´s identity-based private key is shared among n participating parties who are identified by their attribute sets, any subset of t participating parties out of n can generate a signature on behalf the dealer, but fewer than t participating parties can not create a valid signature on behalf of the dealer. The definition and security model of fuzzy identity-based threshold signature scheme are formalized, and a provably secure fuzzy identity-based threshold signature based on the bilinear maps is presented in this paper.