SM2-based Digital Signature Scheme Supporting Threshold Modification

doi:10.19678/j.issn.1000-3428.0070282

Abstract

Abstract:

Existing digital signature schemes are widely used in e-commerce, financial transactions, and medical systems. However, they cannot modify the content of signed messages while keeping the signature unchanged. Moreover, repeatedly performing signature operations increases complexity and latency. To address this issue, a digital signature scheme based on the SM2 algorithm and a supporting threshold modification, called SM2-TM, is proposed. This scheme supports the collaborative modification of signed message content in a threshold manner and achieves signature immutability through parameter control and the construction of hash collisions. Furthermore, it effectively solves complex certificate storage and management as well as key escrow issues. Privacy and security analyses results show that the SM2-TM scheme possesses unforgeability, immutability, and traceability. The performance analysis results indicate that the SM2-TM scheme has certain advantages in terms of computational overhead and significant advantages in terms of the storage overhead of public keys, private keys, and signatures, with storage overheads of only 64, 32, and 64 Byte, respectively.

Key words: SM2 algorithm, digital signature, threshold modification, certificateless, invariance

摘要：

现有的数字签名方案在电子商务、金融交易、医疗系统等场景中广泛应用, 但无法在保持签名不变时对已签名的消息内容进行修改, 而重复进行签名操作会提高复杂性和延迟。对此, 提出一种基于SM2算法并支持门限修改的数字签名方案SM2-TM。该方案支持以门限的方式协同修改已签名的消息内容, 并通过参数控制与构造哈希碰撞来实现签名的不变性。此外, 它有效解决了复杂的证书存储和管理以及密钥托管问题。隐私与安全性分析结果表明, SM2-TM方案具有不可伪造性、不变性、可追踪性等。性能分析结果表明, SM2-TM方案在计算开销上具有一定优势, 在公/私钥及签名的存储开销上也有显著优势, 存储开销分别仅为64、32和64 Byte。

关键词: SM2算法, 数字签名, 门限修改, 无证书, 不变性

ZHOU Quan, XIE Shuting, ZENG Zhikang, CHEN Lili, LU Zichong. SM2-based Digital Signature Scheme Supporting Threshold Modification[J]. Computer Engineering, 2026, 52(7): 255-264.

周权, 谢淑婷, 曾志康, 陈丽丽, 卢子冲. 一种基于SM2的支持门限修改的数字签名方案[J]. 计算机工程, 2026, 52(7): 255-264.

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Figures/Tables 7

References 30

1	刘邦桂, 曾思财. 电子政务中身份认证技术的研究与实现. 软件工程, 2021, 24(11): 47- 50.
	LIU B G , ZENG S C . Research and implementation of identity authentication technology in e-government. Software Engineer, 2021, 24(11): 47- 50.
2	YANG Y, YI B X, ZHAN Y H, et al. Secure EHR sharing scheme based on limited sanitizable signature[EB/OL]. [2024-08-05]. https://link.springer.com/chapter/10.1007/978-981-19-8445-7_19.
3	ZHAN Y H , YI B X , YANG Y , et al. A privilege-constrained sanitizable signature scheme for e-health systems. Journal of Systems Architecture, 2023, 142, 102939. doi: 10.1016/j.sysarc.2023.102939
4	王浩, 胡艳珂, 郜勇. 医院移动电子签名的应用研究. 中国卫生信息管理杂志, 2023, 20(3): 471-474, 481.
	WANG H , HU Y K , GAO Y . Research on the application of hospital mobile electronic signature. Chinese Journal of Health Informatics and Management, 2023, 20(3): 471-474, 481.
5	LIU X X, ZHANG M H, ZHENG Y P, et al. A linkable ring signature electronic cash scheme based on blockchain[C]//Proceedings of the 3rd International Conference on Smart Block Chain (SmartBlock). Washington D.C., USA: IEEE Press, 2021: 1-4.
6	LIN I C , CHANG C C , CHIANG H C . A novel e-cash payment system with divisibility based on proxy blind signature in web of things. IEICE Transactions on Information and Systems, 2022(12): 2092- 2103.
7	WANG C H. An identity-based fair contract signing protocol constructed by the confirmation signature[C]//Proceedings of the IEEE Conference on Dependable and Secure Computing (DSC). Washington D.C., USA: IEEE Press, 2019: 1-6.
8	ZUO L M, ZHANG M L, ZHANG T T, et al. A blind signature scheme with disclaimer contract in the standard model[EB/OL]. [2024-08-05]. https://link.springer.com/chapter/10.1007/978-3-030-00009-7_37.
9	曹素珍, 王斐, 郎晓丽, 等. 基于无证书的多方合同签署协议. 电子与信息学报, 2019, 41(11): 2691- 2698.
	CAO S Z , WANG F , LANG X L , et al. Multi-party contract signing protocol based on certificateless. Journal of Electronics & Information Technology, 2019, 41(11): 2691- 2698.
10	国家密码管理局. SM2密码算法使用规范: GM/T0009-2012[S]. 北京: 国家密码管理局, 2012.
	State Cryptography Administration. SM2 cryptography algorithm application specification: GM/T0009-2012[S]. Beijing: State Cryptography Administration, 2012. (in Chinese)
11	GRIERSON S, BUCHANAN W J, THOMSON C, et al. Scalable multi-domain trust infrastructures for segmented networks[C]//Proceedings of the 28th IEEE International Workshop on Computer Aided Modeling and Design of Communication Links and Networks (CAMAD). Washington D.C., USA: IEEE Press, 2024: 182-187.
12	JEYASHEELA R M J, GEETHA K. Secure decentralized public key infrastructure with multi-signature in blockchains[EB/OL]. [2024-08-05]. https://link.springer.com/chapter/10.1007/978-981-15-7345-3_38.
13	杨小东, 李梅娟, 任宁宁, 等. 一种基于无证书的多方合同签署协议的安全性分析与改进. 电子与信息学报, 2022, 44(10): 3627- 3634.
	YANG X D , LI M J , REN N N , et al. Security analysis and improvement of a multi-party contract signing protocol based on certificateless. Journal of Electronics & Information Technology, 2022, 44(10): 3627- 3634.
14	YU H F , FU S F , LIU Y X , et al. Certificateless broadcast multisignature scheme based on MPKC. IEEE Access, 2020, 8, 12146- 12153. doi: 10.1109/ACCESS.2020.2965978
15	YU H F , WANG Z C . Certificateless blind signcryption with low complexity. IEEE Access, 2019, 7, 115181- 115191. doi: 10.1109/ACCESS.2019.2935788
16	FENG M Q , LIN C , WU W , et al. SM2-DualRing: efficient SM2-based ring signature schemes with logarithmic size. Computer Standards & Interfaces, 2024, 87, 103763.
17	DING F, LONG Y H, WU P L. Study on secret sharing for SM2 digital signature and its application[C]//Proceedings of the 14th International Conference on Computational Intelligence and Security (CIS). Washington D.C., USA: IEEE Press, 2018: 205-209.
18	XIAO Y C , ZHANG L , YANG Y F , et al. Provably secure multi-signature scheme based on the standard SM2 signature scheme. Computer Standards & Interfaces, 2024, 89, 103819.
19	ZHANG Y D, HE D B, ZHANG F G, et al. An efficient blind signature scheme based on SM2 signature algorithm[EB/OL]. [2024-08-05]. https://link.springer.com/chapter/10.1007/978-3-030-71852-7_25.
20	HE C, ZHANG B, ZHANG L, et al. Pairing-free certificateless signature scheme based on SM2 algorithm[EB/OL]. [2024-08-05]. https://link.springer.com/chapter/10.1007/978-981-97-4519-7_21.
21	HE C , ZHANG B , ZHANG L , et al. Improving throughput of mobile sensors via certificateless signature supporting batch verification. Electronics, 2023, 12(22): 1- 11.
22	LIU S G , LIU Z T , LIANG J Q , et al. A secure certificateless ring signcryption scheme based on SM2 algorithm in smart grid. Computer Communications, 2024, 218, 188- 197. doi: 10.1016/j.comcom.2024.02.015
23	DING Y J, ZHANG Y N, ZHOU T P. Continual leakage resilient SM2 signature scheme[C]//Proceedings of the 3rd International Conference on Unmanned Systems (ICUS). Washington D.C., USA: IEEE Press, 2020: 931-936.
24	范琳琳. 基于SM2门限密钥分散的电子签名系统研究与实现[D]. 绵阳: 西南科技大学, 2018.
	FAN L L. Research and implementation of electronic signature system based on SM2 threshold key dispersion[D]. Mianyang: Southwest University of Science and Technology, 2018. (in Chinese)
25	SHAMIR A . How to share a secret. Communications of the ACM, 1979, 22(11): 612- 613. doi: 10.1145/359168.359176
26	CHEN X F , ZHANG F G , TIAN H B , et al. Discrete logarithm based chameleon hashing and signatures without key exposure. Computers & Electrical Engineering, 2011, 37(4): 614- 623.
27	KOBLITZ N . Elliptic curve cryptosystems. Mathematics of Computation, 1987, 48(177): 203- 209. doi: 10.1090/S0025-5718-1987-0866109-5
28	POINTCHEVAL D , STERN J . Security arguments for digital signatures and blind signatures. Journal of Cryptology, 2000, 13(3): 361- 396. doi: 10.1007/s001450010003
29	HUANG K , ZHANG X S , MU Y , et al. Building redactable consortium blockchain for industrial Internet-of-Things. IEEE Transactions on Industrial Informatics, 2019, 15(6): 3670- 3679. doi: 10.1109/TII.2019.2901011
30	BONEH D , LYNN B , SHACHAM H . Short signatures from the Weil pairing. Journal of Cryptology, 2004, 17(4): 297- 319. doi: 10.1007/s00145-004-0314-9

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