Abstract: The existing multi-signature scheme applied in the consensus mechanism scenario defaults that the signers are honest entities,so the security and validity of the signature could not be guaranteed when malicious nodes existed.In order to improve the robustness of multi-signature in the typical adversarial scenarios in consensus protocols,this paper proposes an ID-based multi-signature scheme based on the advantages of the ID-based cryptography system.In this signature scheme,non-fixed subgroup generates randomly cooperated to generate multi-signatures representing the entire group,and the validity of all subgroup signatures must be verified before signature aggregation.The bilinear pairings required by this scheme to generate multi-signatures are related to the number of subgroup members,which improve the security of the scheme at the cost of certain efficiency.This paper introduces a notion of robustness for robust subgroup ID-based multi-signatures,and the corresponding proof of the proposed scheme is given.Furthermore,under the random oracle model,relying on the hardness of the computational Diffie-Helman(CDH) problem,the scheme is proved is proved to be unforgeable under adaptive selection message attack.In addition,theoretical analysis and prototype implementation of the signature scheme are carried out,and the experimental results are compared with the performance of relevant signature schemes.

Key words: ID-based signature, Multi-signatures, Computational Diffie-Hellman(CDH) problem, Random oracle model, Forking lemma