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

Multi-signature aggregates signatures from multiple users on the same message into a joint signature, which is widely applied in blockchain to reduce the percentage of signatures in blocks and improve the throughput of transactions. The $k$-sum attacks are one of the major challenges to design secure multi-signature schemes. In this work, we address $k$-sum attacks from a novel angle by defining a Public Third Party (PTP), which is an automatic process that can be verifiable by the public and restricts the signing phase from continuing until receiving commitments from all signers. Further, a two-round multi-signature scheme MEMS with PTP is proposed, which is secure based on discrete logarithm assumption in the random oracle model. As each signer communicates directly with the PTP instead of other co-signers, the total amount of communications is significantly reduced. In addition, as PTP participates in the computation of the aggregation and signing algorithms, the computation cost left for each signer and verifier remains the same as the basis Schnorr signature. To the best of our knowledge, this is the maximum efficiency that a Schnorr-based multi-signature scheme can achieve. Further, MEMS is applied in blockchain platform, e.g., Fabric, to improve the transaction efficiency.