VeriFU：可验证的联邦遗忘学习

江泽豪; 熊金波; 黄佳毅; 张媛媛; 田有亮

doi:10.11959/j.issn.2096-109x.AQ26024

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VeriFU：可验证的联邦遗忘学习

学术论文 | 更新时间：2026-05-11

- VeriFU：可验证的联邦遗忘学习
- VeriFU: verifiable federated unlearning
- 网络与信息安全学报 2026年12卷第2期页码：104-117
- 作者机构：
  
  1.福建师范大学计算机与网络空间安全学院，福建福州 350117
  2.福建师范大学福建省网络安全与密码技术重点实验室，福建福州 350117
  3.贵州大学大数据与信息工程学院，贵州贵阳 550025
- 作者简介：
  
  [ "江泽豪（2000- ），男，福建师范大学硕士生，主要研究方向为数据安全与隐私保护、人工智能安全。" ]
  [ "熊金波（1981- ），男，博士，福建师范大学教授、博士生导师，主要研究方向为数据安全与隐私保护、人工智能安全等。" ]
  [ "黄佳毅（1997- ），男，福建师范大学博士生，主要研究方向为数据安全与隐私保护、人工智能安全。" ]
  [ "张媛媛（1992- ），女，博士，福建师范大学讲师、硕士生导师，主要研究方向为数据安全与隐私保护、人工智能安全等。" ]
  [ "田有亮（1982- ），男，博士，贵州大学教授、博士生导师，主要研究方向为算法博弈论、密码学与安全协议、大数据安全与隐私保护等。" ]
- 基金信息：
  
  国家自然科学基金资助项目(62272102;62272123);福建省自然科学基金资助项目(2023J02014;2024J08163)
- DOI：10.11959/j.issn.2096-109x.AQ26024
  中图分类号： TP181
- 收稿：2026-01-29，
  
  修回：2026-04-03，
  
  录用：2026-04-07，
  
  纸质出版：2026-04-25
- 稿件说明：
移动端阅览
江泽豪, 熊金波, 黄佳毅, 等. VeriFU：可验证的联邦遗忘学习[J]. 网络与信息安全学报, 2026, 12(2): 104-117.

Jiang Zehao, Xiong Jinbo, Huang Jiayi, et al. VeriFU: verifiable federated unlearning[J]. Chinese Journal of Network and Information Security, 2026, 12(2): 104-117.
江泽豪, 熊金波, 黄佳毅, 等. VeriFU：可验证的联邦遗忘学习[J]. 网络与信息安全学报, 2026, 12(2): 104-117. DOI： 10.11959/j.issn.2096-109x.AQ26024.

Jiang Zehao, Xiong Jinbo, Huang Jiayi, et al. VeriFU: verifiable federated unlearning[J]. Chinese Journal of Network and Information Security, 2026, 12(2): 104-117. DOI： 10.11959/j.issn.2096-109x.AQ26024.

摘要

联邦遗忘学习为客户端提供了遗忘贡献的支持，然而，客户端难以验证服务器是否诚实且有效地移除了其贡献。目前的大部分研究忽视了这一重要方面，通过所构建的基于零知识证明的验证模型，提出完整的可验证联邦遗忘学习框架，并结合动态更新的默克尔树结构，提出了一种可验证的联邦遗忘学习方案，方案具有零知识性，能够在保护其他客户端隐私数据不泄露的前提下高效生成服务器遗忘操作的密码学证明。通过实验评估了方案的有效性、计算开销，与基于RSA（Rivest-Shamir-Adleman）累加器和基于哈希链的方案相比，当模型参数量为

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4.23333359

2.53999996

数量级时，所提方案在证明生成速度上相较于RSA方案提升了约两个数量级，在验证速度上相较于RSA方案提升了13.2倍，且避免了哈希链方案验证开销随数据规模线性增长的瓶颈。

Abstract

Federated unlearning enables clients to withdraw their contributions from a global model.However

enabling clients to verify whether the server has honestly and effectively removed their contributions remains a critical challenge. To address this aspect

which has been largely overlooked in existing literature

a verification model based on zero-knowledge proofs was constructed

and a comprehensive framework for verifiable federated unlearning was proposed. Combined with a dynamically updated Merkle tree structure

a novel verifiable federated unlearning scheme was presented characterized by its zero-knowledge property. This allows for the efficient generation of cryptographic proofs for server unlearning operations while rigorously protecting the data privacy of other clients. We evaluate the effectiveness and computational overhead of the proposed scheme. Comparative experiments with Rivest-Shamir-Adleman (RSA) accumulator-based and Hash chain-based schemes demonstrate that

when the model parameter size reaches the order of

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https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=107601851&type=

4.23333359

2.53999996

the proposed scheme improves proof generation speed by approximately two orders of magnitude and verification speed by 13.2 times compared to the RSA-based scheme. Furthermore

it effectively avoids the scalability bottleneck of data linear growth in verification overhead inherent in Hash chain-based schemes.

关键词

Keywords

references

周传鑫 , 孙奕 , 汪德刚 , 等 . 联邦学习研究综述 [J ] . 网络与信息安全学报 , 2021 , 7 ( 5 ): 77 - 92 .

Zhou C X , Sun Y , Wang D G , et al . Survey of federated learning research [J ] . Chinese Journal of Network and Information Security , 2021 , 7 ( 5 ): 77 - 92 .

Intersoft Consulting . General data protection regulation (GDPR) [R ] . 2016 .

Purtova N . The law of everything. Broad concept of personal data and future of EU data protection law [J ] . Law, Innovation and Technology , 2018 , 10 ( 1 ): 40 - 81 .

Wu C , Zhu S C , Mitra P . Federated unlearning with knowledge distillation [PP ] . aeXiv ( 2022-01-24 )[ 2026-01-29 ] . arXiv: arXiv. 2201 . 09441 .

王鹏飞 , 魏宗正 , 周东生 , 等 . 联邦忘却学习研究综述 [J ] . 计算机学报 , 2024 , 47 ( 2 ): 396 - 422 .

Wang P F , Wei Z Z , Zhou D S , et al . A survey on federated unlearning [J ] . Chinese Journal of Computers , 2024 , 47 ( 2 ): 396 - 422 .

Ginart A , Guan M , Valiant G , et al . Making AI forget you: data deletion in machine learning [C ] // Proceedings of the 33rd Intemational Conference on Neural Information Processing Systems , 2019 : 3518 - 3531 .

Sun X Q , Yu F R , Zhang P , et al . A survey on zero-knowledge proof in blockchain [J ] . IEEE Network , 2021 , 35 ( 4 ): 198 - 205 .

Merkle R C . A digital signature based on a conventional encryption function [C ] // Conference on the Theory and Applications of Cryptographic Techniques on Advances in Cryptology . Berlin : Springer , 1988 : 369 - 378 .

Kreutzer M , Niederhagen R , Shrishak K , et al . Quotable signatures using merkle trees [C ] // GI-Jahrestagung 2019 . Bonn : GI , 2019 : 473 - 477 .

刘芳 , 蔡永泉 , 王朝翔 , 等 . Merkle树遍历机制的改进及应用研究 [J ] . 计算机工程与应用 , 2012 , 48 ( 14 ): 98 - 101, 167 .

Liu F , Cai Y Q , Wang C X , et al . Research of traverse and application of Merkle authentication tree [J ] . Computer Engineering and Applications , 2012 , 48 ( 14 ): 98 - 101, 167 .

Kuznetsov O , Rusnak A , Yezhov A , et al . Efficient and universal Merkle tree inclusion proofs via OR aggregation [J ] . Cryptography , 2024 , 8 ( 3 ): 28 .

Jia H R , Yaghini M , Choquette-Choo C A , et al . Proof-of-learning: definitions and practice [C ] // Proceedings of the 2021 IEEE Symposium on Security and Privacy (SP) . Piscataway : IEEE Press , 2021 : 1039 - 1056 .

Qu X D , Wang S L , Hu Q , et al . Proof of federated learning: a novel energy-recycling consensus algorithm [J ] . IEEE Transactions on Parallel and Distributed Systems , 2021 , 32 ( 8 ): 2074 - 2085 .

Wang J X , Guo S , Xie X , et al . Federated unlearning via class-discriminative pruning [C ] // Proceedings of the ACM Web Conference 2022 . New York : ACM Press , 2022 : 622 - 632 .

Liu Z Y , Ye H Y , Jiang Y , et al . Privacy-preserving federated unlearning with certified client removal [J ] . IEEE Transactions on Information Forensics and Security , 2025 , 20 : 3966 - 3978 .

Baumhauer T , Schöttle P , Zeppelzauer M . Machine unlearning: linear filtration for logit-based classifiers [J ] . Machine Learning , 2022 , 111 ( 9 ): 3203 - 3226 .

Sekhari A , Acharya J , Kamath G , et al . Remember what you want to forget: Algorithms for machine unlearning [J ] . Advances in Neural Information Processing Systems , 2021 , 34 : 18075 - 18086 .

Liu Y , Xu L , Yuan X L , et al . The right to be forgotten in federated learning: an efficient realization with rapid retraining [C ] // Proceedings of the IEEE INFOCOM 2022 - IEEE Conference on Computer Communications . Piscataway : IEEE Press , 2022 : 1749 - 1758 .

Su N X , Li B C . Asynchronous federated unlearning [C ] // Proceedings of the IEEE INFOCOM 2023 - IEEE Conference on Computer Communications . Piscataway : IEEE Press , 2023 : 1 - 10 .

Gao X S , Ma X J , Wang J Y , et al . VeriFi: towards verifiable federated unlearning [J ] . IEEE Transactions on Dependable and Secure Computing , 2024 , 21 ( 6 ): 5720 - 5736 .

Guo C , Goldstein T , Hannun A , et al . Certified data removal from machine learning models [PP ] . arXiv ( 2023-11-08 )[ 2026-01-29 ] .arXiv: arXiv. 1911 . 03030 .

Thudi A , Deza G , Chandrasekaran V , et al . Unrolling SGD: understanding factors influencing machine unlearning [C ] // Proceedings of the 2022 IEEE 7th European Symposium on Security and Privacy (EuroS&P) . Piscataway : IEEE Press , 2022 : 303 - 319 .

Sommer D M , Song L W , Wagh S , et al . Athena: probabilistic verification of machine unlearning [J ] . Proceedings on Privacy Enhancing Technologies , 2022 , 2022( 3 ): 268 - 290 .

Uchida Y , Nagai Y , Sakazawa S , et al . Embedding watermarks into deep neural networks [C ] // Proceedings of the 2017 ACM on International Conference on Multimedia Retrieval . New York : ACM Press , 2017 : 269 - 277 .

李璇 , 邓天鹏 , 熊金波 , 等 . 基于模型后门的联邦学习水印 [J ] . 软件学报 , 2024 , 35 ( 7 ): 3454 - 3468 .

Li X , Deng T P , Xiong J B , et al . Federated learning watermark based on model backdoor [J ] . Journal of Software , 2024 , 35 ( 7 ): 3454 - 3468 .

Eisenhofer T , Riepel D , Chandrasekaran V , et al . Verifiable and provably secure machine unlearning [PP ] . arXiv ( 2025-03-05 )[ 2026-01-29 ] . arXiv: arXiv. 2210.09126.

翁嘉思 , 辜燕云 , 刘家男 , 等 . 公开可验证的模型遗忘方案 [J ] . 计算机学报 , 2025 , 48 ( 2 ): 477 - 496 .

Weng J S , Gu Y Y , Liu J N , et al . A publicly accountable machine unlearning method [J ] . Chinese Journal of Computers , 2025 , 48 ( 2 ): 477 - 496 .

Fraboni Y , Van Waerebeke M , Scaman K , et al . Sifu: Sequential informed federated unlearning for efficient and provable client un-learning in federated optimization [C ] // International Conference on Artificial Intelligence and Statistics . PMLR , 2024 : 3457 - 3465 .

Zhu X R , Li G Y , Hu W . Heterogeneous federated knowledge graph embedding learning and unlearning [C ] // Proceedings of the ACM Web Conference 2023 . New York : ACM Press , 2023 : 2444 - 2454 .

Halimi A , Kadhe S , Rawat A , et al . Federated unlearning: how to efficiently erase a client in FL? [PP ] . arXiv ( 2023-10-20 )[ 2026-01-29 ] . arXiv: arXiv. 2207 . 05521 .

Gong J N , Kang J , Simeone O , et al . Forget-SVGD: particle-based Bayesian federated unlearning [C ] // Proceedings of the 2022 IEEE Data Science and Learning Workshop (DSLW) . Piscataway : IEEE Press , 2022 : 1 - 6 .

Wang H Z , Zhu X J , Chen C , et al . Goldfish: an efficient federated unlearning framework [C ] // Proceedings of the 2024 54th Annual IEEE/IFIP International Conference on Dependable Systems and Networks (DSN) . Piscataway : IEEE Press , 2024 : 252 - 264 .

Liu G Y , Ma X Q , Yang Y , et al . FedEraser: enabling efficient client-level data removal from federated learning models [C ] // Proceedings of the 2021 IEEE/ACM 29th International Symposium on Quality of Service (IWQOS) . Piscataway : IEEE Press , 2021 : 1 - 10 .

Goldwasser S , Micali S , Rackoff C . The knowledge complexity of interactive proof-systems [C ] // Proceedings of the Seventeenth Annual ACM Symposium on Theory of Computing . New York : ACM Press , 1985 : 291 - 304 .

Blum M , Blum M , Feldman P , et al . Non-interactive zero-knowledge and its applications [C ] // Proceedings of the Twentieth Annual ACM Symposium on Theory of Computing . New York : ACM Press , 1988 : 103 - 112 .

李威翰 , 张宗洋 , 周子博 , 等 . 简洁非交互零知识证明综述 [J ] . 密码学报 , 2022 , 9 ( 3 ): 379 - 447 .

Li W H , Zhang Z Y , Zhou Z B , et al . An overview on succinct non-interactive zero-knowledge proofs [J ] . Journal of Cryptologic Research , 2022 , 9 ( 3 ): 379 - 447 .

Naor M , Nissim K . Certificate revocation and certificate update [J ] . IEEE Journal on Selected Areas in Communications , 2000 , 18 ( 4 ): 561 - 570 .

Groth J . On the size of pairing-based non-interactive arguments [C ] // Annual International Conference on the Theory and Applications of Cryptographic Techniques . Berlin : Springer , 2016 : 305 - 326 .

Baghery K , Kohlweiss M , Siim J , et al . Another look at extraction and randomization of Groth’s zk-SNARK [C ] // International Conference on Financial Cryptography and Data Security . Berlin : Springer , 2021 : 457 - 475 .

LeCun Y , Bottou L , Bengio Y , et al . Gradient-based learning applied to document recognition [J ] . Proceedings of the IEEE , 1998 , 86 ( 11 ): 2278 - 2324 .

He K M , Zhang X Y , Ren S Q , et al . Deep residual learning for image recognition [C ] // Proceedings of the 2016 IEEE Conference on Computer Vision and Pattern Recognition (CVPR) . Piscataway : IEEE Press , 2016 : 770 - 778 .

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