Practical Distributed Signatures in the Standard Model

A distributed signature scheme allows participants in a qualified set to jointly generate a signature which cannot be forged even when all the unqualified participants collude together. In this paper, we propose an efficient scheme for any monotone access structure and show its unforgeability and robustness under the computational Diffie-Hellman (CDH) assumption in the standard model. For 112-bit security, its secret key shares and signature fragments are as short as 255 bits and 510 bits, which are shorter than existing schemes assuming random oracle. We then propose two extensions. The first one allows new participants to dynamically join the system without any help from the dealer. The second one supports a type of multipartite access structures, where the participant set is divided into multiple disjoint groups, and each group is bounded so that a distributed signature cannot be generated unless a pre-defined number of participants from multiple groups work together.

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