A SM2 Elliptic Curve Threshold Signature Scheme without a Trusted Center

Threshold signature is very important in identity authentication and some other applications. In December 2010, Chinese Encryption Administration released the SM2 elliptic curve digital signature algorithm as the first standard of the digital signature algorithm in China. At present, the papers on the threshold signature scheme based on this algorithm are few. A SM2 elliptic curve threshold signature scheme without a trusted center is proposed according to the Joint-Shamir-RSS algorithm, the Joint-Shamir-ZSS algorithm, the sum or diff-SS algorithm, the Mul-SS algorithm, the Inv-SS algorithm and the PM-SS algorithm. The proposed scheme is analyzed from correctness, security and efficiency. The correctness analysis shows that the proposed scheme can realize the effective threshold signature. The security analysis shows that the proposed scheme can resist some kinds of common attacks. The efficiency analysis shows that if the same secret sharing algorithms are used to design the threshold signature schemes, the SM2 elliptic curve threshold signature scheme will be more efficient than the threshold signature scheme based on ECDSA.