Research On Secure And Efficient Multi-signature And Its Application To Blockchain

With the process of society and the improvement of science technology,digital signature has been studied and developed rapidly,and a series of different types of digital signature have appeared.Among them,multi-signature,as an important deformation of digital signature,can merge the signatures of different signers on the same message into one signature,which only needs to be verified once in the verification algorithm.Due to the simple and efficient characteristics of multi-signature,multi-signature has attracted the attention of many scholars.How to improve the efficiency of multi-signature under the condition of ensuring the security of multi-signature has become the key to research.From the perspective of multi-signature,this paper studies and improves the security and efficiency of multi-signature,and applies it to the blockchain transaction protocol.Its main contents and research results include:(1)We studied the current multi-signature scheme CoSi.Combined with the characteristics of Gamma signature,we constructed a new multi-signature scheme GMS.This scheme can avoid rogue-key attack and k-sum problem attack that both exist in CoSi.It can avoid the problem of excessive power of root node happened in CoSi and achieve almost the same scalability as CoSi as well.Therefore,our proposed multi-signature scheme GMS has a wide range of applications.Then,considering the online/offline characteristics of signature,we constructed a new multi-signature scheme AGMS by combing the signature algorithm and key aggregation algorithm and modifying the procedure order of signature algorithm,based on our proposed scheme GMS.This scheme can precompute some complicated calculations before the message comes,which makes it better in online/offline performance,and solve the problem of real-time network congestion.(2)We analyzed and studied the security of Gayathri et al.certificateless aggregate signature scheme.Based on it,we designed new certificateless aggregate signature,multisignature schemes ACLAS and CLMS.Compared with the Gayathri et al.scheme,the computation complexity of our scheme is not significant improved.However,in partial private key generation algorithm of our scheme,Key Generation Center(KGC)can transfer the partial private key to the destinated user in a public channel.It also avoids the security problem of adversary type II in signing algorithm of Gayathri et al.scheme.At the same time,we applied the characteristics of online/offline signature reasonably,so that our proposed scheme also has fast online signature.(3)We studied the transaction process of Alliance chain,Hyperledger Fabric.We firstly introduced the transaction process of Hyperledger Fabric v1.0.Then,combined with AGMS multi-signature scheme and certificateless signature scheme CLMS,based on elliptic curve discrete logarithm problem,we replaced ECDSA scheme with AGMS.We also improved the original access mechanism of a node by choosing the certificateless signature and did the experiments to test the results.According to the experiment results,our schemes has better signature efficiency online and decrease the storage place in blocks to achieve the goal of efficiency and security.To sum up,this paper proposed two different multi-signature schemes AGMS and CLMS based on CoSi and Gayathri et al.scheme,and applied them to Alliance chain to solve the existing problems of efficiency and security.