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Multi-signature aggregates signatures from multiple users on the same messageinto a joint signature, which is widely applied in blockchain to reduce thepercentage of signatures in blocks and improve the throughput of transactions.The $k$-sum attacks are one of the major challenges to design securemulti-signature schemes. In this work, we address $k$-sum attacks from a novelangle by defining a Public Third Party (PTP), which is an automatic processthat can be verifiable by the public and restricts the signing phase fromcontinuing until receiving commitments from all signers. Further, a two-roundmulti-signature scheme MEMS with PTP is proposed, which is secure based ondiscrete logarithm assumption in the random oracle model. As each signercommunicates directly with the PTP instead of other co-signers, the totalamount of communications is significantly reduced. In addition, as PTPparticipates in the computation of the aggregation and signing algorithms, thecomputation cost left for each signer and verifier remains the same as thebasis Schnorr signature. To the best of our knowledge, this is the maximumefficiency that a Schnorr-based multi-signature scheme can achieve. Further,MEMS is applied in blockchain platform, e.g., Fabric, to improve thetransaction efficiency.

Achieving Maximum Efficiency in Schnorr-based Multi-signature and Applications in Blockchain