  Digital signature is a major component of transactions on Blockchain
platforms, especially in enterprise Blockchain platforms, where multiple
signatures from a set of peers need to be produced to endorse a transaction.
However, such process is often complex and time-consuming. Multi-signature,
which can improve transaction efficiency by having a set of signers cooperate
to produce a joint signature, has attracted extensive attentions. In this work,
we propose two multi-signature schemes, GMS and AGMS, which are proved to be
more secure and efficient than state-of-the-art multi-signature schemes.
Besides, we implement the proposed schemes in a real Enterprise Blockchain
platform, Fabric. Experiment results show that the proposed AGMS scheme helps
achieve the goal of high transaction efficiency, low storage complexity, as
well as high robustness against rogue-key attacks and k-sum problem attacks.
