Blockchain Electronic Voting Scheme Based on Fully Homomorphic Encryption

doi:10.19678/j.issn.1000-3428.0069981

Abstract

Abstract:

In digital voting systems, the combination of Fully Homomorphic Encryption (FHE) and blockchain technology guarantees the security and privacy of E-voting. The overall performance of existing schemes is constrained owing to the complex computation process of FHE algorithm, especially in terms of vote-counting efficiency and fairness. To address these issues, this paper proposes a Blockchain E-voting Scheme based on Fully Homomorphic Encryption (BCEVS-FHE). This scheme optimizes the Brakerski—Fan—Vercauteren (BFV) FHE algorithm by mitigating the impact of noise factor to reduce the computational overhead during encryption and decryption, thereby improving the vote-counting efficiency. The SM2 digital signature algorithm is used to sign ballot information generated by voters, ensuring that the voters could not deny their voting behavior and preventing identity impersonation and fraud. Furthermore, smart contracts are introduced to improve the weighting method used for vote tallying. Consequently, the unforgeability and non-tampering of voter weights are ensured, thereby guaranteeing the fairness and impartiality of the voting process. Finally, all transaction information is stored in the chain using a private blockchain, ensuring that the entire voting process is tamperproof and fully traceable. Experimental results show that BCEVS-FHE not only guarantees security attributes such as privacy, confidentiality, security, uniqueness, and verifiability but also excels in functional attributes such as fairness and mobility. Overall, BCEVS-FHE meets the security requirements of E-voting protocols and has high potential for practical applications, which is of significant research for the widespread application of digital voting systems.

Key words: blockchain, E-voting, Fully Homomorphic Encryption (FHE), smart contract, signature algorithm

摘要：

在数字化投票系统中, 全同态加密(FHE)与区块链技术的结合保障了电子投票的安全性和隐私性, 但现有方案因FHE算法复杂的计算过程导致系统整体性能较差, 尤其是在计票效率和公平性方面, 因此提出一种基于FHE的区块链电子投票方案(BCEVS-FHE)。该方案首先通过优化BFV(Brakerski—Fan—Vercauteren) FHE算法中噪声因子的影响, 降低加解密过程中的计算开销, 从而提高计票效率; 然后利用SM2数字签名算法对投票者生成的选票信息进行签名, 确保投票者无法否认其投票行为, 防止身份信息假冒与欺诈; 接着引入智能合约对加权计票的加权方式进行改进, 确保投票者权重的不可伪造性和不可篡改性, 保障投票过程的公平公正; 最后通过私有区块链方式将所有交易信息都存储到链上, 确保整个投票过程不可篡改和可追溯。实验结果表明, 该方案不仅在隐私性、机密性、安全性、唯一性和可验证性等安全属性上得到了保障, 而且在公平性和可移动性等功能属性上表现出色。综合来看, BCEVS-FHE满足电子投票协议的安全需求, 还具有较高的实际应用潜力, 对于数字化投票系统的广泛应用具有重要的研究价值。

关键词: 区块链, 电子投票, 全同态加密, 智能合约, 签名算法

GAO Gaimei, DI Guoxia, LIU Chunxia, YANG Yuli, DANG Weichao, ZHANG Aizhen. Blockchain Electronic Voting Scheme Based on Fully Homomorphic Encryption[J]. Computer Engineering, 2026, 52(4): 313-326.

高改梅, 邸国霞, 刘春霞, 杨玉丽, 党伟超, 张爱贞. 基于全同态加密的区块链电子投票方案[J]. 计算机工程, 2026, 52(4): 313-326.

/ Recommend / Download Citations

URL: https://www.ecice06.com/EN/10.19678/j.issn.1000-3428.0069981

https://www.ecice06.com/EN/Y2026/V52/I4/313

Figures/Tables 15

Fig.1 BCEVS-FHE system model

Fig.2 Smart contract deployment model

Fig.3 Weighted calculation process

Fig.4 Comparison of homomorphic multiplication running times at different depths when explicit modulus t=2

Fig.5 Comparison of homomorphic multiplication running times at different depths when explicit modulus t=2¹⁶+1

Fig.6 Comparison of counting time with different number of voters

Fig.7 Comparison of running time for each stage of BCEVS-FHE

Fig.8 Comparison of counting time of similar E-voting schemes

References 26

1	CHAUM D L . Untraceable electronic mail, return addresses, and digital pseudonyms. Communications of the ACM, 1981, 24 (2): 84- 90. doi: 10.1145/358549.358563
2	IHM Y S , KIM S H . Development of a blockchain-based online secret electronic voting system. IEICE Transactions on Information and Systems, 2022, 105 (8): 1361- 1372.
3	ALAM K M R , TAMURA S , RAHMAN S M S , et al. An electronic voting scheme based on revised-SVRM and confirmation numbers. IEEE Transactions on Dependable and Secure Computing, 2021, 18 (1): 400- 410. doi: 10.1109/TDSC.2019.2892465
4	ARANHA D F, BAUM C, GJ∅STEEN K, et al. Lattice-based proof of shuffle and applications to electronic voting[C]//Proceedings of Cryptographers'Track at the RSA Conference. Berlin, Germany: Springer International Publishing, 2021: 227-251.
5	HAINES T, GORÉ R, SHARMA B. Did you mix me? Formally verifying verifiable mix nets in electronic voting[C]//Proceedings of the IEEE Symposium on Security and Privacy. Washington D.C., USA: IEEE Press, 2021: 1748-1765.
6	KUMAR M , CHAND S , KATTI C P . A secure end-to-end verifiable Internet-voting system using identity-based blind signature. IEEE Systems Journal, 2020, 14 (2): 2032- 2041. doi: 10.1109/JSYST.2019.2940474
7	KUMAR M, KATTI C P, SAXENA P C. A secure anonymous E-voting system using identity-based blind signature scheme[C]//Proceedings of the 13th International Conference on Information Systems Security. Berlin, Germany: Springer International Publishing, 2017: 29-49.
8	ZHANG X , ZHANG J Z , XIE S C . A secure quantum voting scheme based on quantum group blind signature. International Journal of Theoretical Physics, 2020, 59 (3): 719- 729. doi: 10.1007/s10773-019-04358-3
9	FAN X Y , WU T , ZHENG Q H , et al. HSE-voting: a secure high-efficiency electronic voting scheme based on homomorphic signcryption. Future Generation Computer Systems, 2020, 111, 754- 762. doi: 10.1016/j.future.2019.10.016
10	FAN X Y, WU T, ZHENG Q H, et al. DHS-voting: a distributed homomorphic signcryption E-voting[C]//Proceedings of the 5th International Conference on Dependability in Sensor, Cloud, and Big Data Systems and Applications. Singapore: Springer, 2019: 40-53.
11	熊世强, 何道敬, 王振东, 等. 联邦学习及其安全与隐私保护研究综述. 计算机工程, 2024, 50 (5): 1- 15. doi: 10.19678/j.issn.1000-3428.0067782
	XIONG S Q , HE D J , WANG Z D , et al. Review of federated learning and its security and privacy protection. Computer Engineering, 2024, 50 (5): 1- 15. doi: 10.19678/j.issn.1000-3428.0067782
12	FAN J F, VERCAUTEREN F. Somewhat practical fully homomorphic encryption[C]//Proceedings of International Conference on Codes, Cryptology, and Information Security. Berlin, Germany: Springer, 2017: 68-82.
13	BEHERA S, PRATHURI J R. FPGA-based design architecture for fast LWE fully homomorphic encryption[C]//Proceedings of ICCSDF'21. Singapore: Springer, 2021: 575-584.
14	KIM A, POLYAKOV Y, ZUCCA V. Revisiting homomorphic encryption schemes for finite fields[C]//Proceedings of the 27th International Conference on the Theory and Application of Cryptology and Information Security. Berlin, Germany: Springer International Publishing, 2021: 608-639.
15	YUAN K , SANG P , ZHANG S Y , et al. An electronic voting scheme based on homomorphic encryption and decentralization. PeerJ Computer Science, 2023, 9, e1649. doi: 10.7717/peerj-cs.1649
16	KHAN S , ARSHAD A , MUSHTAQ G , et al. Implementation of decentralized blockchain E-voting. EAI Endorsed Transactions on Smart Cities, 2020, 4 (10): 164859. doi: 10.4108/eai.13-7-2018.164859
17	DE MIRANDA L M B , GARCIA R D , RAMACHANDRAN G S , et al. Blockchain in inter-organizational collaboration: a privacy-preserving voting system for collective decision-making. Journal of Information Security and Applications, 2024, 85, 103837. doi: 10.1016/j.jisa.2024.103837
18	WANG L H , LI H L , LI Y N , et al. Self-tallying voting with blockchain in wireless network environment. IEEE Wireless Communications, 2024, 31 (5): 142- 147. doi: 10.1109/MWC.014.2300520
19	NAIDU P R, BOLLA D R, G P, et al. E-voting system using blockchain and homomorphic encryption[C]//Proceedings of the IEEE 2nd Mysore Sub Section International Conference (MysuruCon). Washington D.C., USA: IEEE Press, 2022: 1-5.
20	杨亚涛, 刘德莉, 刘培鹤, 等. BFV-Blockchainvoting: 支持BFV全同态加密的区块链电子投票系统. 通信学报, 2022, 43 (9): 100- 111.
	YANG Y T , LIU D L , LIU P H , et al. BFV-Blockchainvoting: blockchain-based electronic voting systems with BFV full homomorphic encryption. Journal on Communications, 2022, 43 (9): 100- 111.
21	FU J H , ZHOU W H , ZHANG S Z . Fabric blockchain design based on improved SM2 algorithm. International Journal on Semantic Web and Information Systems, 2023, 19 (1): 1- 13.
22	王超, 韩益亮, 段晓巍, 等. 基于RLWE困难假设的NTRU型代理重加密方案. 密码学报, 2021, 8 (5): 909- 920.
	WANG C , HAN Y L , DUAN X W , et al. NTRU-type proxy re-encryption scheme based on RLWE difficult assumption. Journal of Cryptologic Research, 2021, 8 (5): 909- 920.
23	BELOTTI M , BOŽIĆG N , PUJOLLE G , et al. A vademecum on blockchain technologies: when, which, and how. IEEE Communications Surveys & Tutorials, 2019, 21 (4): 3796- 3838.
24	DONG S , ABBAS K , LI M X , et al. Blockchain technology and application: an overview. PeerJ Computer Science, 2023, 9, e1705.. doi: 10.7717/peerj-cs.1705
25	ALBRECHT M, CHASE M, CHEN H, et al. Homomorphic encryption standard[EB/OL]. [2024-05-17]. https://homomorphicencryption.github.io/.
26	吴淇毓, 杨帆, 周福才, 等. 基于区块链和简短可链接环签名的安全电子投票方案. 东北大学学报(自然科学版), 2024, 45 (5): 619- 627.
	WU Q Y , YANG F , ZHOU F C , et al. A secure electronic voting scheme based on blockchain and short linkable ring signatures. Journal of Northeastern University (Natural Science), 2024, 45 (5): 619- 627.

[1]	ZHAO Kai, YAN Junqiao, HU Yuhuan, BI Xuehua, ZHANG Linlin. Data Supervision Scheme of Medical Centralized Purchase Based on Multi-Chain Collaboration [J]. Computer Engineering, 2026, 52(4): 409-423.
[2]	ZHU Bingcheng, ZHOU Feng, TIAN Youliang, XIANG Axin, XIONG Wei, PENG Changgen. Certificateless Multi-Signature Based on SM2 Algorithm and Its Application in Blockchain Transaction [J]. Computer Engineering, 2026, 52(4): 290-301.
[3]	ZHOU Yuelin, ZHONG Bocheng, WANG Rui. Lightweight Vehicular Ad-Hoc Network Conditional Privacy-Preserving Authentication Based on Blockchain [J]. Computer Engineering, 2026, 52(3): 201-210.
[4]	LIN Dan, LU Shunfeng, LIU Ziyan, ZHANG Bozhao, HE Long, JIANG Zigui, WU Jiajing, ZHENG Zibin. Large Language Models Empowering Blockchain Service Security: A Comprehensive Survey of Status, Challenges, and Opportunities (Invited) [J]. Computer Engineering, 2026, 52(1): 1-21.
[5]	SHEN Zhenlong, TONG Yanxiang, WANG Xiao, WANG Ben, ZHANG Pengcheng. Cross-chain Anomalous Transaction Detection Based on BERT Model [J]. Computer Engineering, 2026, 52(1): 254-265.
[6]	ZHANG Qianhui, YUAN Lingyun, XIE Tianyu, WU Jiaying. Fair Verifiable Secret Sharing Driven by Smart Contracts [J]. Computer Engineering, 2025, 51(9): 177-191.
[7]	XU Ying, FU Ziwei, ZHANG Wei, CHEN Yunfang. Smart Contract Vulnerability Detection Technology Based on Abstract Syntax Tree Embedding [J]. Computer Engineering, 2025, 51(9): 149-157.
[8]	FANG Yonghao, YAO Zhongyuan, LI Min, SI Xueming. A Secure and Efficient Blockchain Consensus Algorithm for Distributed Power Trading [J]. Computer Engineering, 2025, 51(8): 250-261.
[9]	WANG Qun, LI Fujuan, MA Zhuo. Research on Application of Blockchain in BGP Route Leakage Prevention [J]. Computer Engineering, 2025, 51(8): 39-52.
[10]	ZHAO Kai, HU Yuhuan, YAN Junqiao, BI Xuehua, ZHANG Linlin. Overview of Copyright Protection Research Based on Blockchain [J]. Computer Engineering, 2025, 51(8): 1-15.
[11]	XIAO Ke, LIU Ying, HE Yunhua, XU Gang, WANG Chao. On-Chain and Off-Chain Secure Retrieval Scheme for Energy Data Based on Multi-Chain [J]. Computer Engineering, 2025, 51(8): 238-249.
[12]	WANG Guilan, ZHANG Cheng, ZHOU Guoliang. Multi-objective Economic Scheduling of Distribution Networks with FISCO BCOS and Topology Optimization Consistency Algorithm [J]. Computer Engineering, 2025, 51(7): 348-361.
[13]	LI Junji, ZHANG Jiaqi, GAO Gaimei, YANG Li. Consensus Algorithm for Internet of Vehicles Based on Reputation Mechanism [J]. Computer Engineering, 2025, 51(4): 217-226.
[14]	YANG Linfeng, HUANG Zheng, XU Yan, DING Zhijun. Modeling and Detection of Blockchain Smart Contract Attackers Based on Petri Nets [J]. Computer Engineering, 2025, 51(4): 15-26.
[15]	JIANG Qiqi, ZHANG Liang, PENG Lingqi, KAN Haibin. Accountable and Verifiable Outsourced Hierarchical Attribute Encryption Scheme Based on Blockchain [J]. Computer Engineering, 2025, 51(3): 24-33.

Please choose a citation manager

Content to export