Robust Schnorr-based subgroup multi-signature scheme

Abstract

The consensus mechanism has been considered as the core technology of blockchain systems. However, current consensus mechanisms have encountered three issues: low consensus efficiency, low reliability and security, and high computational complexity. To address these issues, a new Schnorr-based subgroup multi-signature scheme was proposed. This scheme retained the advantage of low computational complexity inherent in the Schnorr digital signature cryptosystem while incorporating the benefits of subgroup multi-signature. It allowed an indeterminate number of members from the entire set to form subgroups to generate multi-signatures, which replaced the group signature. The unpredictability of the subgroups effectively avoided the occurrence of Byzantine traitors, thus enhancing security and solving the problems of low reliability, security, and high computational complexity in consensus mechanisms. Additionally, a public third party was introduced, implemented by automatically and publicly executed smart contracts. It was completely open and transparent, capable of resisting the rogue public-key attack, and reduced the total number of communication rounds and time overhead in the signing process, addressing the issue of low consensus efficiency. The robustness of this scheme was proven in detail, demonstrating an improvement in the security of consensus mechanisms. Based on the discrete logarithm assumption, the scheme was shown to be unforgeable in the random oracle model. Theoretical analysis and experimental results show that the scheme possesses smaller public key length, private key length, single signature length, and multi-signature length, with fewer communication rounds and reduced time overhead in the signature generation and verification algorithms, providing superior performance when applied to consensus mechanisms.

Keywords

• schnorr signature
• multi-signature
• robustness
• discrete logarithmic assumption
• random oracle model