Computer Science ›› 2026, Vol. 53 ›› Issue (10): 447-454.doi: 10.11896/jsjkx.250800109

• Information Security • Previous Articles     Next Articles

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 Published: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).

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

CLC Number: 

  • 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.
[1] LI Ruirui, GUO Rui, ZHANG Yinghui, LI Xuelei, LIU Guangjun. Edge Federated Learning Privacy Protection Scheme Based on Multi-key Homomorphic Encryption [J]. Computer Science, 2026, 53(6): 446-459.
[2] HAN Yingmei, LI Bin, LI Kun, ZHOU Qinglei, YU Shiliang. Efficient Hardware Implementation of Pipelined NTT for Dynamic Rotation Factor Generation [J]. Computer Science, 2025, 52(9): 160-169.
[3] XIE Zhenjie, LIU Yiming, CAI Ruijie, LUO Youqiang. Performance Optimization Method for Domestic Cryptographic Algorithm SM9 [J]. Computer Science, 2025, 52(6): 390-396.
[4] XIE Zhenjie, ZHANG Yao, YANG Qichao, SONG Enzhou. Ring Signature Scheme Based on Domestic Cryptographic Algorithm SM9 [J]. Computer Science, 2025, 52(12): 384-390.
[5] XIE Zhenjie, LUO Youqiang, ZHAO Fangfang, REN Shuai. Signcryption Scheme Based on SM9 Domestic Cryptographic Algorithm [J]. Computer Science, 2025, 52(11A): 241200049-8.
[6] LI Jincheng, LI Yingna, FU Guoqing. Design and Application of Decision Tree Algorithms for Privacy-preserving [J]. Computer Science, 2025, 52(11A): 241200115-9.
[7] XIE Zhenjie, LIU Yiming, YIN Xiaokang, LIU Shengli, ZHANG Yongguang. Additively Homomorphic Encryption Scheme Based on Domestic Cryptographic Algorithm SM9 [J]. Computer Science, 2025, 52(11): 408-414.
[8] ZHANG Jindou, CHEN Jingwei, WU Wenyuan, FENG Yong. Privacy-preserving Principal Component Analysis Based on Homomorphic Encryption [J]. Computer Science, 2024, 51(8): 387-395.
[9] XIANG Yanjie, HUANG Xiaofang, XIANG Kefeng, ZHENG Ji’nan. Blockchain Certificateless Encryption Mechanism Based on National Secret Algorithm [J]. Computer Science, 2024, 51(8): 440-446.
[10] ZANG Hongrui, YANG Tingting, LIU Hongbo, MA Kai. Study on Cryptographic Verification of Distributed Federated Learning for Internet of Things [J]. Computer Science, 2024, 51(6A): 230700217-5.
[11] DING Hongfa, YU Yingying, JIANG Heling. Correctness Verifiable Outsourcing Computation Scheme of Shortest Path Querying over Encrypted Graph Data [J]. Computer Science, 2024, 51(5): 400-413.
[12] LIU Zechao, LIANG Tao, SUN Ruochen, HAO Zhiqiang, LI Jun. Research and Implementation of MQTT Security Mechanism Based on Domestic CryptographicAlgorithms [J]. Computer Science, 2024, 51(2): 333-342.
[13] LU Xingyuan, CHEN Jingwei, FENG Yong, WU Wenyuan. Privacy-preserving Data Classification Protocol Based on Homomorphic Encryption [J]. Computer Science, 2023, 50(8): 321-332.
[14] GAO Guangyong, HAN Tingting, XIA Zhihua. Recoverable Data Aggregation Protocol for Wireless Sensor Networks Based on Reversible DigitalWatermarking [J]. Computer Science, 2023, 50(8): 333-341.
[15] ZHAO Min, TIAN Youliang, XIONG Jinbo, BI Renwan, XIE Hongtao. Neural Network Model Training Method Based on Homomorphic Encryption [J]. Computer Science, 2023, 50(5): 372-381.
Viewed
Full text


Abstract

Cited

  Shared   
  Discussed   
No Suggested Reading articles found!