Research On Threshold Signature Scheme Based On National SM2 Signature Algorithm

Digital signature technology guarantees the security of transactions on the blockchain.The confidentiality of transaction information transmission,data integrity,non-repudiation of both parties to the transaction,and identity authentication of both parties are guaranteed through private key signatures.Once the private key in the blockchain wallet system is lost or leaked,irreparable losses will occur to users.In order to ensure the security of private keys,scholars worldwide have proposed the threshold signature algorithm.It realizes power distribution and prevents a single user from abusing the power.The SM2 digital signature algorithm is independently developed by Chinese researchers.After years of development,the SM2 digital signature algorithm has been widely used in cryptographic systems to authenticate user identities and ensure data integrity.This thesis proposes a threshold signature scheme.In addition,for the two-party signature system,a two-party threshold SM2 signature scheme with offline parties is further proposed.The main contributions of this thesis are as follows:(1)A threshold SM2 digital signature scheme is proposed,multi-party participants use CL homomorphic encryption in the scheme and they provide corresponding zero-knowledge proofs for CL ciphertexts;the zero-knowledge proof algorithm ZKPo Rep S for the discrete logarithm relationship is adopted,and the algorithm uses an additional round of challenges and reduces the number of proof rounds to one.Compared with the zero-knowledge proof algorithm used in similar schemes,the communication overhead and calculation speed are both improved.(2)A two-party threshold SM2 signature scheme with an offline party is proposed.In this scheme,the offline party only needs to generate a pair of public and private keys of an asymmetric encryption algorithm to go offline.If one of the participants is maliciously attacked,the offline party can go online instead to complete the signature task;the scheme adopts the CL homomorphic encryption scheme,which reduces the communication overhead and achieves low latency compared with the Paillier homomorphic encryption scheme;the scheme is based on the decision-type Diffie Hellman problem(DDH)and the HSM group.The security of the scheme is proved using a simulation-based proof method based on the hard problem assumption.