Research And Technology Development Of SM2 Digital Signature Co-generation Method Based On Homomorphic Encryption

As a kind of elliptic curve algorithm,SM2 algorithm naturally possesses the relevant characteristics of elliptic curve algorithm.So far,under continuous research and exploration of elliptic curve related algorithms,the SM2 algorithm as a national secret has slightly outperformed some other related elliptic curve cryptographic algorithms of international standards.Among the PKI-related algorithms,the SM2 algorithm has become a very high-security algorithm,which has been supported and promoted by relevant national departments.Based on this algorithm,related functions such as signature verification and data encryption and decryption can be realized.When performing digital signatures,it is important to ensure the security of the use of private keys.Compared with other asymmetric key encryption algorithms,the SM2 algorithm is quite special.For other asymmetric key encryption algorithms when performing digital signature operations,usually the usual secret sharing is sufficient.But for the digital signature of the SM2 algorithm,the situation is indeed different.The digital signature of the SM2 algorithm cannot be completed by the general secret sharing method and the corresponding cryptographic operation based on this method.To solve this problem,this paper proposes a SM2 digital signature collaborative generation method based on homomorphic encryption.This solution solves the problem of completing the SM2 digital signature without guaranteeing the security of the private key without using hardware,and realizes the collaborative generation system of SM2 digital signature based on homomorphic encryption.The SM2 digital signature is realized through secret sharing,which can effectively strengthen the security of the SM2 private key.In view of the problem that the general secret sharing method is not suitable for SM2 digital signatures,on the basis of in-depth study of the SM2 elliptic curve algorithm and the Paillier algorithm,two different SM2 digital signature collaborative generation schemes based on secret sharing are proposed.Cooperative generation system of SM2 digital signature based on homomorphic encryption of mobile terminal and SM2 password server.The SM2 digital signature collaborative generation system based on homomorphic encryption mainly includes the following two modules in the process of secret sharing: the Android mobile terminal password function module and the SM2 password server function module.The Android mobile terminal is mainly responsible for the SM2 private key segmentation and the division of the secret share storage based on the code that implements the SM2 mathematical operation and the Paillier algorithm,as well as the use of the secret share and the SM2 cryptographic server for digital signature collaborative operations.The main body of the SM2 password server adopts the SSM framework.The database uses the My SQL database,and the database stores the user’s username,password,and secret share corresponding to the user.The SM2 password server is mainly responsible for completing the logical part of user registration and login,the SM2 private key’s secret share storage and calling function,and can interact with the Android side to call the secret shares stored by themselves to complete the digital signature collaborative generation operation.