基于安全两方计算的隐私保护线性回归算法

doi:10.3778/j.issn.1002-8331.2007-0337

摘要/Abstract

摘要：

随着数据安全与隐私泄露事件频发，泄露规模连年加剧，如何保证机器学习中数据和模型参数的隐私引发科学界和工业界的广泛关注。针对本地存储计算资源的有限性及云平台的不可信性所带来的数据隐私问题，基于秘密共享技术提出了一种安全两方计算的隐私保护线性回归算法。利用加法同态加密和加法掩码实现了秘密共享值的乘法计算协议，结合小批量梯度下降算法，最终实现了在两个非共谋的云服务器上的安全线性回归算法。实验结果表明，该方案同时保护了线性回归算法训练及预测阶段中的数据及模型参数，且模型预测性能与在明文域中进行训练的模型相近。

关键词: 线性回归, 安全两方计算, 秘密共享, 加法同态加密, 隐私保护

Abstract:

With the frequent occurrence of data security and privacy leaks and the increasing scale of leaks year after year, how to ensure the privacy of data and model parameters in machine learning has aroused widespread concern in the scientific and industrial community. Aiming at the data privacy problem caused by the limitation of local storage and computing resources and the untrustworthiness of cloud platforms, this paper proposes a privacy protection linear regression algorithm for secure two-party computation based on secret sharing technology. This paper uses additive homomorphic encryption and additive masks to realize a multiplication calculation protocol of the secret shared values, and combines the mini-batch gradient descent algorithm to realize the secure linear regression algorithm on two non-collusive cloud servers. The experimental results show that the scheme protects the data and model parameters in the training and prediction phases of the linear regression algorithm at the same time, and the model prediction performance is similar to the model trained in the plaintext domain.

Key words: linear regression, secure two-party computation, secret sharing, addition homomorphic encryption, privacy protection

魏立斐，李梦思，张蕾，陈聪聪，陈玉娇，王勤. 基于安全两方计算的隐私保护线性回归算法[J]. 计算机工程与应用, 2021, 57(22): 139-146.

WEI Lifei, LI Mengsi, ZHANG Lei, CHEN Congcong, CHEN Yujiao, WANG Qin. Privacy-Preserving Linear Regression Algorithm Based on Secure Two-Party Computation[J]. Computer Engineering and Applications, 2021, 57(22): 139-146.

参考文献

[1] MELL P，GRANCE T.The NIST definition of cloud computing：SP 800-145[S].National Institute of Standards and Technology，Information Technology Laboratory，2011.
[2] 吴吉义，沈千里，章剑林，等.云计算：从云安全到可信云[J].计算机研究与发展，2011，48（S1）：229-233.
WU J Y，SHEN Q L，ZHANG J L，et al.Cloud computing：cloud security to trusted cloud[J].Journal of Computer Research and Development，2011，48（S1）：229-233.
[3] 郑剑，邹鸿珍.差异化隐私预算分配的线性回归分析算法[J].计算机应用与软件，2016，33（3）：275-278.
ZHENG J，ZOU H Z.Linear regression anylysis algorithm of differential privacy budget allocation[J].Computer Applications and Software，2016，33（3）：275-278.
[4] DANDEKAR A，BASU D，BRESSAN S.Differential privacy for regularised linear regression[C]//LNCS 11030：29th International Conference on Database and Expert Systems Applications.Cham：Springer，2018：483-491.
[5] 葛宇航.基于差分隐私的线性回归分析[J].科技经济导刊，2019，27（14）：163-164.
GE Y H.Linear regression analysis based on differential privacy[J].Technology and Economic Guide，2019，27（14）：163-164.
[6] 李娟，马飞.基于同态加密的分布式隐私保护线性回归分析模型[J].微电子学与计算机，2016，33（1）：110-113.
LI J，MA F.A model on distributed privacy preserving linear regression anylysis based on homomorphic encryption[J].Microelectronics & Computer，2016，33（1）：110-113.
[7] KIKUCHI H，HAMANAGA C，YASUNAGA H，et al.Privacy-preserving multiple linear regression of vertically partitioned real medical datasets[J].Journal of Information Processing，2018，26：638-647.
[8] YANG H M，HE W C，ZHOU Q X，et al.Efficient and secure outsourced linear regression[C]//LNCS 11336：18th International Conference on Algorithms and Architectures for Parallel Processing.Cham：Springer，2018：89-102.
[9] YAO A C.Protocols for secure computation[C]//Annual Symposium on Foundations of Computer Science.Piscataway：IEEE，1982：160-164.
[10] 蒋瀚，徐秋亮.基于云计算服务的安全多方计算[J].计算机研究与发展，2016，53（10）：2152-2162.
JIANG H，XU Q L.Secure multiparty computation in cloud computing[J].Journal of Computer Research and Development，2016，53（10）：2152-2162.
[11] 蒋瀚，刘怡然，宋祥福，等.隐私保护机器学习的密码学方法[J].电子与信息学报，2020，42（5）：1068-1078.
JIANG H，LIU Y R，SONG X F，et al.Cryptographic approaches for privacy-preserving machine learning[J].Journal of Electronics and Information Technology，2020，42（5）：1068-1078.
[12] 谭作文，张连福.机器学习隐私保护研究综述[J].软件学报，2020，31（7）：2127-2156.
TAN Z W，ZHANG L F.Survey on privacy preserving techniques for machine learning[J].Journal of Software，2020，31（7）：2127-2156.
[13] DANKAR F，BRIEN R，ADAMS C，et al.Secure multi-party linear regression[C]//7th International Workshop on Privacy and Anonymity in the Information Society，Athens，Mar 28，2014：406-414.
[14] FU Z F.Linear regression protocol for privacy protect[C]//2017 9th International Conference on Intelligent Human-Machine Systems and Cybernetics，Hangzhou，Aug 26-27，2017.Piscataway：IEEE，2017：215-218.
[15] BLOOM J M.Secure multi-party linear regression at plaintext speed[J/OL].arXiv：1901.09531，2019.
[16] HALL R，FIENBERG S E，NARDI Y.Secure multiple linear regression based on homomorphic encryption[J].Journal of Official Statistics，2011，27（4）：669-691.
[17] MARTINE D C，RAFAEL D，ANDERSON N，et al.Fast，privacy preserving linear regression over distributed data-
sets based on pre-distributed data[C]//8th ACM Workshop on Artificial Intelligence and Security.New York：ACM，2015：3-14.
[18] DANKAR F K.Privacy preserving linear regression on distributed databases[J].Transactions on Data Privacy，2015，8（1）：3-28.
[19] ADRIà G，SCHOPPMANN P，BALLE B，et al.Privacy-preserving distributed linear regression on high-dimensional data[J].Nephron Clinical Practice，2017，4：345-364.
[20] MOHASSEL P，ZHANG Y.SecureML：a system for scalable privacy-preserving machine learning[C]//2017 IEEE Symposium on Security and Privacy.Piscataway：IEEE，2017：19-38.
[21] RABIN M.How to exchange secrets by oblivious transfer：TR-81[R].Aiken Computation Lab，Harvard University，1981.
[22] 唐春明，魏伟明.基于安全两方计算的具有隐私性的回归算法[J].信息网络安全，2018，18（10）：10-16.
TANG C M，WEI W M.Regression algorithm with privacy based on secure two-party computation[J].Netinfo Security，2018，18（10）：10-16.
[23] BEAVER D.Efficient multiparty protocols using circuit randomization[C]//LNVS 576：11th Annual International Cryptology Conference.Berlin：Springer，1991：420-432.
[24] AKAVIA A，SHAUL H，WEIS M，et al.Linear-regression on packed encrypted data in the two-server model[C]//7th ACM Workshop on Encrypted Computing & Applied Homomorphic Cryptography.New York：ACM，2019：21-32.
[25] DONG Y，CHEN X J，SHEN L Y，et al.Privacy-preserving distributed machine learning based on secret sharing[M]//Information and communications security.Berlin：Springer，2020：684-702.
[26] RIVEST R L，ADLEMAN L M，DERTOUZOS M L.On data banks and privacy homomorphisms[C]//Foundations of Secure Computation，New York，1978：169-179.
[27] PAILLIER P.Public-key cryptosystems based on composite degree residuosity classes[C]//LNCS 1592：18th International Conference on the Theory and Applications of Cryptographic Techniques.Berlin：Springer，1999：223-238.
[28] SHAMIR A.How to share a secret[J].Communications of the ACM，1979，22（11）：612-613.
[29] DU W L，ATALLAH M J.Privacy-preserving cooperative scientific computations[C]//14th IEEE Computer Security Foundations Workshop，Cape Breton，2001：273-282.
[30] 陈莉，林柏钢.基于分布式线性方程组求解的安全多方计算协议[J].信息网络安全，2013，13（9）：2-5.
CHEN L，LIN B G.Secure protocols for resolving distributed system of linear equations[J].Netinfo Security，2013，13（9）：2-5.