Non-interactive SM2 threshold signature scheme with identifiable abort

Abstract

A threshold signature is a special digital signature in which the $N$-signer share the private key $x$ and can construct a valid signature for any subset of the included $t$-signer, but less than $t$-signer cannot obtain any information. Considering the breakthrough achievements of threshold ECDSA signature and threshold Schnorr signature, the existing threshold SM2 signature is still limited to two parties or based on the honest majority setting, there is no more effective solution for the multiparty case. To make the SM2 signature have more flexible application scenarios, promote the application of the SM2 signature scheme in the blockchain system and secure cryptocurrency wallets. This paper designs a non-interactive threshold SM2 signature scheme based on partially homomorphic encryption and zero-knowledge proof. Only the last round requires the message input, so make our scheme non-interactive, and the pre-signing process takes 2 rounds of communication to complete after the key generation. We allow arbitrary threshold $t\le n$ and design a key update strategy. It can achieve security with identifiable abort under the malicious majority, which means that if the signature process fails, we can find the failed party. Performance analysis shows that the computation and communication costs of the pre-signing process grows linearly with the parties, and it is only $1/3$ of the Canetti’s threshold ECDSA (CCS'20).

Graphical abstract

Keywords

SM2 signature / secure multi-party computation / threshold signature / UC-secure / dishonest majority

Huiqiang Liang is currently pursing his MS degree at School of Mathematics and Statistics, Wuhan University, China. His main research interests include cryptography and information security and SMPC

Jianhua Chen received the MS and PhD degrees from School of Mathematics and Statistics, Wuhan University, China in 1989 and 1994, respectively. He is currently a professor of the Applied Mathematics Department, Wuhan University, China. His current research interests include number theory, information security, and network security

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Acknowledgements

Thanks to my supervisor and our team for helpful discussions, thanks to the reviewers and editors for making this paper better.

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