基于同態(tài)加密和群簽名的可驗(yàn)證聯(lián)邦學(xué)習(xí)方案

李亞紅; 李一婧; 楊小東; 張?jiān)?/>
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doi:10.11999/JEIT240796

基于同態(tài)加密和群簽名的可驗(yàn)證聯(lián)邦學(xué)習(xí)方案

doi: 10.11999/JEIT240796

牛淑芬³

1.
蘭州交通大學(xué)電子與信息工程學(xué)院蘭州 730000
2.
電子科技大學(xué)計(jì)算機(jī)與工程學(xué)院成都 610054
3.
西北師范大學(xué)計(jì)算機(jī)工程學(xué)院蘭州 730000

基金項(xiàng)目: 國(guó)家自然科學(xué)基金(62461032)，甘肅省科技計(jì)劃(22JR5RA158,22JR5RA350)，甘肅省高校教師創(chuàng)新基金項(xiàng)目(2023A-041, 2023-ZD-234)，蘭州交通大學(xué)-天津大學(xué)聯(lián)合創(chuàng)新基金項(xiàng)目(LH2024003)

詳細(xì)信息

作者簡(jiǎn)介:
李亞紅：女，博士，副教授，研究方向?yàn)槊艽a學(xué)與信息安全

李一婧：女，碩士生，研究方向?yàn)槁?lián)邦學(xué)習(xí)與密碼學(xué)

楊小東：男，博士，教授，研究方向?yàn)閼?yīng)用密碼學(xué)與信息安全

張?jiān)矗耗校┦?，教授，研究方向?yàn)閼?yīng)用密碼學(xué)與信息安全

牛淑芬：女，博士，教授，研究方向?yàn)樵朴?jì)算和大數(shù)據(jù)網(wǎng)絡(luò)的隱私保護(hù)

通訊作者:
李亞紅　liyahong@lzjtu.edu.cn

中圖分類號(hào): TN918; TP309.7
計(jì)量
- 文章訪問數(shù): 131
- HTML全文瀏覽量: 41
- PDF下載量: 34
- 被引次數(shù): 0
出版歷程
- 收稿日期: 2024-09-14
- 修回日期: 2025-02-17
- 網(wǎng)絡(luò)出版日期: 2025-02-21

A Verifiable Federated Learning Scheme Based on Homomorphic Encryption and Group Signature

1.
School of Electronic and Information Engineering, Lanzhou Jiaotong University, Lanzhou 730000, China
2.
School of Computer Science and Engineering, University of Electronic Science and Technology of China, Chendu 610054, China
3.
School of Computer Science and Engineering, Northwestern Normal University, Lanzhou 730000, China

Funds: The National Natural Science Foundation of China (62461032), Gansu Science and Technology Plan (22JR5RA158,22JR5RA350), Gansu Province University Teachers Innovation Fund Project (2023A-041, 2023-ZD-234), Lanzhou Jiaotong University-Tianjin University Joint Innovation Fund Project (LH2024003)

摘要

摘要: 在車載網(wǎng)絡(luò)(VANETs)中，聯(lián)邦學(xué)習(xí)(FL)通過協(xié)同訓(xùn)練機(jī)器學(xué)習(xí)模型，實(shí)現(xiàn)了車輛間的數(shù)據(jù)隱私保護(hù)，并提高了整體模型的性能。然而，F(xiàn)L在VANETs中的應(yīng)用仍面臨諸多挑戰(zhàn)，如模型泄露風(fēng)險(xiǎn)、訓(xùn)練結(jié)果驗(yàn)證困難以及高計(jì)算和通信成本等問題。針對(duì)這些問題，該文提出一種面向聯(lián)邦學(xué)習(xí)的可驗(yàn)證隱私保護(hù)批量聚合方案。首先，該方案基于Boneh-Lynn-Shacham (BLS)動(dòng)態(tài)短群聚合簽名技術(shù)，保護(hù)了客戶端與路邊單元(RSU)交互過程中的數(shù)據(jù)完整性，確保全局梯度模型更新與共享過程的不可篡改性。當(dāng)出現(xiàn)異常結(jié)果時(shí)，方案利用群簽名的特性實(shí)現(xiàn)車輛的可追溯性。其次，結(jié)合改進(jìn)的Cheon-Kim-Kim-Song (CKKS)線性同態(tài)哈希算法，對(duì)梯度聚合結(jié)果進(jìn)行驗(yàn)證，確保在聯(lián)邦學(xué)習(xí)的聚合過程中保持客戶端梯度的機(jī)密性，并驗(yàn)證聚合結(jié)果的準(zhǔn)確性，防止服務(wù)器篡改數(shù)據(jù)導(dǎo)致模型訓(xùn)練無效的問題。此外，該方案還支持車輛在部分掉線的情況下繼續(xù)更新模型，保障系統(tǒng)的穩(wěn)定性。實(shí)驗(yàn)結(jié)果表明，與現(xiàn)有方案相比，該方案在提升數(shù)據(jù)隱私安全性和結(jié)果的可驗(yàn)證性的同時(shí)，保證了較高效率。
- 隱私保護(hù) /
- 聯(lián)邦學(xué)習(xí) /
- 車載自組網(wǎng) /
- 可驗(yàn)證聚合 /
- 群簽名
Abstract: Objective In Vehicular Ad-hoc NETworks (VANETs), network instability and frequent vehicle mobility complicate data aggregation and expose it to potential attacks. Traditional Federated Learning (FL) approaches face challenges such as high computational and communication overheads, insufficient privacy protection, and difficulties in verifying aggregation results, which impact model training efficiency and stability. To address these issues, this study proposes a scheme that integrates the Boneh-Lynn-Shacham (BLS) dynamic short group signature with an enhanced Cheon-Kim-Kim-Song (CKKS) homomorphic encryption technique. This approach reduces computational and communication costs, ensures data privacy under chosen-plaintext attacks, and maintains system stability by allowing vehicles to disconnect after submitting encrypted data. The proposed framework enhances privacy, verifiability, anonymity, traceability, and robustness, providing a secure and reliable FL solution for VANETs. Methods A batch aggregation scheme is proposed, integrating an improved CKKS linearly homomorphic encryption algorithm with a BLS-based dynamic short group signature technique to address key challenges in applying FL within VANETs. The improved CKKS linearly homomorphic encryption algorithm mitigates privacy leakage risks in vehicle data and training models. Data security and training privacy are ensured by maintaining ciphertext indistinguishability under chosen-plaintext attacks, preventing attackers from inferring original data from ciphertext and protecting vehicle users’ privacy. Linearly homomorphic hashing verifies aggregation result correctness while reducing computational load. This approach also allows vehicles to disconnect after submitting encrypted data, enhancing system robustness and stability. Consequently, model training continuity and reliability are maintained even in dynamic and unstable vehicular network conditions. The BLS-based dynamic short group signature technique simplifies group signature generation, improving aggregation efficiency and reducing computational costs. Combined with batch processing of gradient updates, this method significantly lowers computational and communication overhead on the aggregation server. These techniques collectively enhance system efficiency and ensure adaptability to resource-constrained vehicular environments, providing a practical and effective FL solution for VANETs. Results and Discussions The proposed scheme significantly enhances computational efficiency, reduces communication overhead, improves privacy protection, and ensures system stability in FL for vehicular networks. In terms of computational overhead, client-side computation is reduced by an average of 13.5% and 53.6%, while the aggregation server’s computational cost decreases by 42.4% and 33.8%, respectively (Fig. 2a, Fig. 2b), demonstrating the scheme’s ability to efficiently manage large-scale client environments with minimal computational burden. Communication overhead is also significantly minimized as the number of clients increases. By transmitting only masked gradients and hash values, the scheme achieves reductions of 70.7% and 66.8% compared to existing methods, streamlining the aggregation process and eliminating unnecessary data transmission (Fig. 3). This design ensures applicability in resource-constrained vehicular networks. The scheme maintains strong privacy protection, even under increasing noise accumulation. Experimental results confirm that data privacy is safeguarded during training, mitigating the risk of leakage (Table 4). Stability is further demonstrated as the aggregation server’s performance remains unaffected by client dropouts, regardless of dropout ratios or the scale of disconnections. Its non-interactive design allows vehicles to go offline after submitting encrypted gradients, enabling the system to function reliably and maintain stable performance in dynamic vehicular environments (Fig. 4). This feature is particularly critical in scenarios involving unstable network conditions or fluctuating client availability. Furthermore, the scheme achieves a convergence rate exceeding 95% within 15 training rounds (Fig. 5). This rapid convergence is facilitated by the improved CKKS homomorphic encryption algorithm, which supports floating-point operations and enhances the precision of gradient updates. By improving gradient accuracy, the scheme enables efficient and stable model training, even in dynamic network conditions. Collectively, these results demonstrate the scheme’s ability to address critical challenges in FL for VANETs. Conclusions The FL batch aggregation scheme proposed in this study addresses data privacy and security challenges in VANETs. By integrating the BLS dynamic short group signature technique with an improved CKKS linearly homomorphic hashing algorithm, data integrity is preserved during interactions between clients and Roadside Units (RSUs). The confidentiality and accuracy of gradient aggregation results are ensured, effectively preventing model training failures due to potential data tampering on the server side. The scheme also supports model updates despite vehicle disconnections, enhancing system stability. Experimental results demonstrate improvements in data privacy, security, and result verifiability while maintaining high efficiency. Additionally, it achieves low communication costs and reduced computation time as the number of clients increases, demonstrating strong scalability and practicality.
- Privacy preservation /
- Federated learning /
- Vehicular Ad-hoc NETworks (VANETs) /
- Verifiable aggregation /
- Group signature

HTML全文

圖 1 系統(tǒng)模型

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圖 2 計(jì)算開銷對(duì)比

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圖 3 通信開銷對(duì)比

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圖 4 聚合服務(wù)器運(yùn)行時(shí)間

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圖 5 準(zhǔn)確率對(duì)比

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表 1 密碼學(xué)操作執(zhí)行時(shí)間

符號(hào)	描述	運(yùn)行時(shí)間(ms)
${T_{{\text{bp}}}}$	雙線性對(duì)操作	1.118 1
${T_{\text{h}}}$	映射到$G$的哈希操作	0.019 3
${T_{\text{m}}}$	$G$下的乘法操作	0.001 1
${T_{\text{a}}}$	$G$下的加法操作	0.000 4
${T_{\text{e}}}$	$Z_p^*$下的指數(shù)操作	0.065 0
${T_{{\text{o - enc}}}}$	一次性密碼本加密	0.394 0
${T_{{\text{o - dec}}}}$	一次性密碼本解密	0.442 0
${T_{{\text{dn - enc}}}}$	DH密鑰交換加密	2.761 1
${T_{{\text{dh - dec}}}}$	DH密鑰交換解密	0.008 7
${T_{{\text{c - enc}}}}$	CKKS加密	2.350 4
${T_{{\text{c - dec}}}}$	CKKS解密	0.055 8

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表 2 計(jì)算開銷對(duì)比

方案	客戶端計(jì)算開銷(ms)	聚合服務(wù)器計(jì)算開銷(ms)
文獻(xiàn)[12]	$n(19{T_{\text{m}}} + 13{T_a} + {T_{\text{h}}} + 2{T_{{\text{bp}}}} + {T_{\text{e}}} + {T_{{\text{o-enc}}}})$	$(9n + 8){T_{\text{m}}} + (5n + 2){T_{{\text{bp}}}} + (9n + 6){T_{\text{a}}} + {T_{\text{h}}} + 2{T_{\text{e}}} + {T_{{\text{o-dec}}}}$
文獻(xiàn)[13]	$n{T_{{\text{o-enc}}}} + n(19{T_{\text{m}}} + 13{T_{\text{a}}} + {T_{\text{h}}} + 2{T_{{\text{bp}}}} + {T_{\text{e}}})$	$24n{T_{\text{m}}} + (4n + 2){T_{{\text{bp}}}} + 11n{T_{\text{e}}} + 26n{T_{\text{a}}} + (n + 1){T_{\text{h}}}$
所提方案	$n({T_{{\text{c-enc}}}} + {T_{\text{m}}} + {T_{\text{h}}})$	$(7n - 1){T_{\text{m}}} + (3n + 1){T_{{\text{bp}}}} + 10n{T_{\text{a}}} + (3n + 2){T_{\text{h}}} + n{T_{{\text{c-dec}}}}$

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表 3 通信開銷對(duì)比

方案	客戶端與聚合服務(wù)器間通信	聚合服務(wù)器間通信
文獻(xiàn)[12]	$7\|G\| + 3\|Z_p^*\| + \|T\|$	$7\|G\| + 2\|Z_p^*\| + \|{\text{ID}}\| + \|T\|$
文獻(xiàn)[13]	$7\|G\| + 2\|Z_p^*\| + \|T\|$	$6\|G\| + 2\|Z_p^*\| + \|T\|$
所提方案	$7\|G\| + \|Z_p^*\|$	$7\|G\| + \|Z_p^*\| + \|T\|$

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表 4 隱私保護(hù)強(qiáng)度數(shù)據(jù)表

操作次數(shù)$k$	累積噪聲$N(k)$	隱私保護(hù)強(qiáng)度$S$
10	$1.1 \times {10^{ - 5}}$	0.998 9
50	$5.1 \times {10^{ - 5}}$	0.994 9
100	$1.01 \times {10^{ - 4}}$	0.989 9
500	$5.001 \times {10^{ - 4}}$	0.949 9

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參考文獻(xiàn)(17)

[1]	WEN Jie, ZHANG Zhixia, LAN Yang, et al. A survey on federated learning: challenges and applications[J]. International Journal of Machine Learning and Cybernetics, 2023, 14(2): 513–535. doi: 10.1007/s13042-022-01647-y.
[2]	LI Li, FAN Yuxi, TSE M, et al. A review of applications in federated learning[J]. Computers & Industrial Engineering, 2020, 149: 106854. doi: 10.1117/12.2675351.
[3]	魏立斐, 張無忌, 張蕾, 等. 基于本地差分隱私的異步橫向聯(lián)邦安全梯度聚合方案[J]. 電子與信息學(xué)報(bào), 2024, 46(7): 3010–3018. doi: 10.11999/JEIT230923. WEI Lifei, ZHANG Wuji, ZHANG Lei, et al. A Secure Gradient Aggregation Scheme Based on Local Differential Privacy in Asynchronous Horizontal Federated Learning[J]. Journal of Electronics & Information Technology, 2024, 46(7): 3010–3018. doi: 10.11999/JEIT230923.
[4]	QU Zhiguo, TANG Yang, MUHAMMAD G, et al. Privacy protection in intelligent vehicle networking: A novel federated learning algorithm based on information fusion[J]. Information Fusion, 2023, 98: 101824. doi: 10.1016/j.inffus.2023.101824.
[5]	LI Zhang, XU Jianbo, VIJAYAKUMAR P, et al. Homomorphic encryption-based privacy-preserving federated learning in IoT-enabled healthcare system[J]. IEEE Transactions on Network Science and Engineering, 2022, 10(5): 2864–2880. doi: 10.1109/TNSE.2022.3185327.
[6]	TAMILARASI G, GANDHI K R, and PALANISAMY V. Improved Homomorphic Encryption with Optimal Key Generation Technique for VANETs[J]. Intelligent Automation & Soft Computing, 2022, 33(2). doi: 10.32604/iasc.2022.024687.
[7]	WIBAWA F, CATAK F O, KUZLU M, et al. Homomorphic encryption and federated learning based privacy-preserving CNN training: Covid-19 detection use-case[C]. Proceedings of the 2022 European Interdisciplinary Cybersecurity Conference. Barcelona, Spain, 2022: 85-90. doi: 10.1145/3528580.3532845.
[8]	ZHANG Jiale, LIU Yue, WU Di, et al. VPFL: A verifiable privacy-preserving federated learning scheme for edge computing systems[J]. Digital Communications and Networks, 2023, 9(4): 981–989. doi: 10.1016/j.dcan.2022.05.010.
[9]	WANG Peng, and LIU Yining. SEMA: Secure and efficient message authentication protocol for VANETs[J]. IEEE systems journal, 2021, 15.(1): 846–855. doi: 10.1109/JSYST.2021.3051435.
[10]	AN Haoyang, HE Debiao, BAO Zijian, et al. An identity-based dynamic group signature scheme for reputation evaluation systems[J]. Journal of Systems Architecture, 2023, 139: 102875. doi:org/ 10.1016/j.sysarc.2023.102875. doi: 10.1016/j.sysarc.2023.102875.
[11]	張海波, 陳舟, 黃宏武, 等. VANET 系統(tǒng)中基于中國(guó)剩余定理的群內(nèi)相互認(rèn)證密鑰協(xié)商協(xié)議[J]. 通信學(xué)報(bào), 2022, 43(1): 182–193. doi: 10.11959/j.issn.1000-436x.2022002. ZHANG Haibo, CHEN Zhou, HUANG Hongwu, et al. Intra-group mutual authentication key agreement protocol based on Chinese remainder theorem in VANET system[J]. Journal on Communications, 2022, 43(1): 182–193. doi: 10.11959/j.issn.1000-436x.2022002.
[12]	XIA Feng, LIU Haiyang, YANG Haowei, et al. Batch-Aggregate: Efficient Aggregation for Private Federated Learning in VANETs[J]. IEEE Transactions on Dependable and Secure Computing, 2024.1-15. doi: 10.1109/TDSC.2024.3364371.
[13]	XIA Feng, WANG Xiaofeng, LIU Haiyang, et al. A Privacy-preserving Aggregation Scheme with Continuous Authentication for Federated Learning in VANETs[J]. IEEE Transactions on Vehicular Technology, 2024, 73(7): 9465–9477. doi: 10.1109/TVT.2024.3369942.
[14]	WANG Ruyan, YUAN Xingmin, YANG Zhigang, et al. RFLPV: A robust federated learning scheme with privacy preservation and verifiable aggregation in IoMT[J]. Information Fusion, 2024, 102: 102029. doi: 10.1016/j.inffus.2023.102029.
[15]	CHEON J H, KIM A, KIM M, et al. Homomorphic encryption for arithmetic of approximate numbers[C]. Advances in Cryptology–ASIACRYPT 2017: 23rd International Conference on the Theory and Applications of Cryptology and Information Security, Hong Kong, China, December 3-7, 2017, Proceedings, Part I 23. Springer International Publishing, 2017. doi: 10.1007/978-3-319-70694-8_15.
[16]	LEE Y, LEE J W, and KIM Y S. Near-Optimal Polynomial for Modulus Reduction Using L2-Norm for Approximate Homomorphic Encryption[J]. IEEE Access, vol. 8, pp. 144321-144330, 2020. doi: 10.1109/ACCESS.2020.3014369.
[17]	王勇. 聯(lián)邦學(xué)習(xí)模型安全聚合關(guān)鍵技術(shù)研究[D]. [博士論文]. 安徽師范大學(xué), 2024. doi: 10.26920/d.cnki.gansu.2024.000005. WANG Yong, Research on key technologies of secure model aggregation for federated learning[D]. [Ph. D. dissertation], Anhui Normal University, 2024. doi: 10.26920/d.cnki.gansu.2024.000005.