Identity-based Threshold Signature from the Bilinear Pairings

In this paper, we formalize the concept of identity-based threshold signature and give the first provably secure scheme based on the bilinear pairings. An important feature of our scheme is that a private associated with an identity rather than a master key of the Public Key Generator is shared among signature generation servers, which, we claim, is more important in practice. From a theoretical point of view, an interesting aspect of our results is that the security of one of the verifiable secret sharing schemes used to construct the identity-based threshold signature scheme is relative to the modified Generalized Bilinear Inversion (mGBI) problem, which is a slight modification of the Generalized Tate Inversion (GTI) problem that Joux recently proposed and called for applying it to cryptographic protocols. Hence, our result gives a partial solution to Joux’s question.

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