The invention discloses a method for jointly generating SM2
digital signature by multiple parties. The method comprises following steps that all parties P1, P2, ... , P<Tau> joining digital signaturerandomly select partial private keys x1, x2, ... , x<x>(belonging to Zn), and two partial random numbers k1, k2, ... , k<x>(belonging to Zn) and Rho1, Rho2, ... , Rho<x>(belonging to Zn); then all parties calculate through an interactive ideal function F<MULT> to obtain a public key P<pub>=(Q-G)=(Sigma<lota=1><Tau>x<lota>G-G) of SM2, and two intermediate variables R=Sigma<lota=1><Tau>k<lota>G=(r<x>,r<y>) and alpha =xRhomode n; for a message m, all parties separately calculate a hash value e=h(m) and a first signature r=r<x>+e mod n, and calculates through the interactive ideal function F<MULT>to obtain a third
intermediate variable beta=Rho(k+r)mod n; and finally, all parties separately calculate a second signature s=min{alpha<-1>beta-r, n-alpha<-1>beta+r}, and outputs complete SM2
digital signature (r,s) after signature
verification succeeds. Through adoption of the method, an SM2
digital signature is generated by multiple parties jointly, it is ensured that all parties do not disclose partial private keys in signing, and digital signature involves all parties, so that multi-party signature is safe and fair.