计算机科学 ›› 2026, Vol. 53 ›› Issue (10): 447-454.doi: 10.11896/jsjkx.250800109

• 信息安全 • 上一篇    下一篇

在线友好的SM2两方门限签名方案

王少辉, 孙思源, 张平, 王化群   

  1. 南京邮电大学计算机学院、软件学院、网络空间安全学院 南京 210046
  • 收稿日期:2025-08-26 修回日期:2025-12-12 发布日期:2026-10-13
  • 通讯作者: 王少辉(wangshaohui@njupt.edu.cn)
  • 基金资助:
    国家自然科学基金联合基金(U23B2002)

Online-friendly Two-party Threshold Signature Scheme on SM2

WANG Shaohui, SUN Siyuan, ZHANG Ping, WANG Huaqun   

  1. College of Computer Science,Nanjing University of Posts and Telecommunications,Nanjing 210046, China
  • Received:2025-08-26 Revised:2025-12-12 Online:2026-10-13
  • About author:WANG Shaohui,born in 1977,Ph.D,professsor,masters’s supervisor.His main research interests include Internet of Things and cloud computing.
  • Supported by:
    Joint Funds of the National Natural Science Foundation of China(U23B2002).

摘要: 在数字签名算法中,如果签名私钥被泄露,敌手就可以随意伪造合法用户的签名,从而致使合法用户的权益受到侵害。两方门限签名将签名私钥拆分成两个部分,签名参与双方分别持有其中的一部分并协作生成数字签名,有效提高了方案的安全性。针对国产SM2签名算法,提出了一个新的两方门限签名算法。新算法将两方签名生成过程分为不需要用到待签名消息的线下阶段和需要用到待签名消息的线上阶段,并将现有的MtA协议应用于线下阶段一次,从而实现线上阶段的高效性。通过验证分析表明,相比其他的SM2两方签名方案,所提方案在协作签名的线上阶段只需完成简单的整数加法、乘法及取模运算,具有极高的效率和极低的计算开销,因而在全场景特别是低延迟场景下具有高协作签名运行效率和低带宽要求等显著优势。

关键词: SM2, 两方门限签名, 国产密码, 同态加密, MtA协议

Abstract: In digital signature algorithms,if the private signing key is leaked,an adversary can arbitrarily forge the signature of a legitimate user,thereby infringing upon the legitimate user’s rights and interests.Two-party threshold signature splits the private signing key into two parts,with each of the two signature participants holding one part and collaboratively generating the digital signature,which effectively enhances the security of the scheme.This paper proposes a new two-party threshold signature algorithm for the domestic SM2 signature algorithm.The new algorithm divides the two-party signature generation process into an offline phase thatdoes not require the message to be signed and an online phase that requires the message to be signed.It applies the existing MtA(Multiplicative-to-Additive) protocol once in the offline phase,thereby achieving high efficiency in the online phase.Analysis and verification show that,compared with other SM2 two-party signature schemes,the proposed scheme only needs to perform simple integer addition,multiplication,and modulo operations in the online phase of collaborative signature,it features extremely high efficiency and extremely low computational overhead,thus exhibiting significant advantages such as high collaborative signature operation efficiency and low bandwidth requirements in all scenarios,especially in low-latency scenarios.

Key words: SM2, Two-party threshold signature, Domestic cryptographic, Homomorphic encryption, Multiplicative-to-Additive protocol

中图分类号: 

  • TP309
[1] DIFFIE W,HELLMAN M.New directions in cryptography[J].IEEE Transactions on Information Theory,1976,22(6):644-654.
[2] KIARASH S,YAVUZ A A.A Comprehensive Survey ofThreshold Signatures:NIST Standards,Post-Quantum Cryptography,Exotic Techniques,and Real-World Applications[J]. arXiv:2311.05514,2023.
[3] SHAMIR A.How to share a secret[J].Communications of the ACM,1979,22(11):612-613.
[4] BLAKLE Y G R.Safeguarding cryptographic keys[C]//International Workshop on Managing Requirements Knowledge(MARK).1979:313-318.
[5] DESMEDTY,FRANKEL Y.Threshold cryptosystems[C]//CRYPTO 1989.Springer,1989:307-315.
[6] MACKENZIE P,REITER M K.Two-Party Generation of DSA Signatures[C]//CRYPTO 2001.Springer,2001:218-239.
[7] LINDELL Y.Fast Secure Two-Party ECDSA Signing[J].Journal of Cryptology,2021,34(4):1-38.
[8] LARA-NINO C A,DIAZ-PEREZ A,MORALES-SANDOVALM.Energy/Area-Efficient Scalar Multiplication with Binary Edwards Curves for the IoT[J].Sensors,2019,19(3):720-734.
[9] FANG W,CHEN W,ZHANG W,et al.Digital signature scheme for information non-repudiation in blockchain:a state of the art review[J].EURASIP Journal on Wireless Communications and Networking,2020,2020(1):56-71.
[10] JI Y,ZHANG R,TAO Y,et al.Designated confirmer threshold signature and its applications in block-chains[J].Cybersecurity,2024,7:67-82.
[11] RIVEST R L,ADLEMAN L,DERTOUZOSM L.On data banks and privacy homomorphisms[J].Foundations of Secure Computation,1978,4(11):169-180.
[12] PAILLIER P.Public-key cryptosystems based on composite degree residuosity classes[C]//EUROCRYPT ’99.Springer,1999:223-238.
[13] NISHIDE T,SAKURAI K.Distributed Paillier Cryptosystemwithout Trusted Dealer[C]//WISA 2010.Springer,2010:44-60.
[14] GENNARO R,GOLDFEDER S.Fast Multiparty ThresholdECDSA with Fast Trustless Setup[C]//CCS’18.New York,2018:1179-1194.
[15] XUE H,AU M H,XIE X,et al.Efficientonline-friendly two-party ECDSA signature[C]//CCS 2021.ACM,2021:558-573.
[16] KOCAMAN S,TALIBIALAOUI Y.Efficient Secure Two Party ECDSA[C]//IACR Cryptology.2023:1455.
[17] 国家密码管理局.SM2 椭圆曲线公钥密码算[EB/OL].http://www.oscca.gov.cn/UpFile/2010122214822692.pdf
[18] SHANG M,MA Y,LIN J Q,et al.A threshold scheme for SM2 elliptic curve cryptographic algorithm[J].Journal of Cryptologic Research,2014,1(2):155-166.
[19] HOU H X,YANG B,ZHANG L N,et al.Secure Two-PartySM2 Signature Algorithm[J].Acta Electronica Sinica,2020,48(1):1-8.
[20] FENG Q,HE D B,LUO M,et al.Efficient Two-Party SM2 Signing Protocol for Mobile Internet[J].Journal of Computer Research and Development,2020,57(10):2136-2146.
[21] ZHANG Y,HE D,ZHANG M,et al.A provable-secure andpractical two-party distributed signing protocol for SM2 signature algorithm[J].Frontiers of Computer Science,2020,14(3):1-14.
[22] LIU Z Y,LIN J Q.Framework of Two-party ThresholdSchemes for SM2 Digital Signatures[J].Ruan Jian Xue Bao/Journal of Software,2025,36(5):2188-2211.
[23] LINDELL Y,NOF A.Fast secure multiparty ECDSA with practical distributed key generation and applications to cryptocurrency custody[C]//CCS 2018.ACM,2018:1837-1854.
[24] CANETTI R.Universally composable security:A new paradigm for cryptographic protocols[C]//FOCS 2001.IEEE,2021:136-145.
Viewed
Full text


Abstract

Cited

  Shared   
  Discussed   
No Suggested Reading articles found!