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arXiv 2305.13699cs.CR
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在基于Schnorr的多签名中实现最大效率及其在区块链中的应用

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

Peng Zhang, Fa Ge, Yuhong Liu

AI总结:

通过引入公共第三方(PTP)解决$k$-sum攻击,提出基于离散对数假设的两轮多签名方案MEMS,实现Schnorr多签名的最大通信与计算效率,并应用于Fabric区块链提升交易效率。

摘要:

多签名将多个用户对同一消息的签名聚合成一个联合签名,广泛应用于区块链中以减少区块中签名的比例并提高交易吞吐量。$k$-sum攻击是设计安全多签名方案的主要挑战之一。在本研究中,我们通过定义公共第三方(PTP)从新角度解决$k$-sum攻击,PTP是一个可由公众验证的自动过程,限制签名阶段在收到所有签名者的承诺前继续进行。进一步,提出了一种带PTP的两轮多签名方案MEMS,在随机预言机模型中基于离散对数假设证明安全。由于每个签名者直接与PTP通信而非其他共同签名者,通信总量显著减少。此外,因PTP参与聚合和签名算法的计算,每个签名者和验证者的计算成本与基础Schnorr签名保持相同。据我们所知,这是基于Schnorr的多签名方案能实现的最大效率。MEMS进一步应用于区块链平台(如Fabric)以提高交易效率。

英文摘要:

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.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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