摘要

We present a secure backpropagation neural network training model (SecureBP), which allows a neural network to be trained while retaining the confidentiality of the training data, based on the homomorphic encryption scheme. We make two contributions. The first one is to introduce a method to find a more accurate and numerically stable polynomial approximation of functions in a certain interval. The second one is to find a strategy of refreshing ciphertext during training, which keeps the order of magnitude of noise at O˜e33.

授权许可

Copyright © 2020 Qinju Liu et al. 2020
This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

通讯作者

Qinju Liu.State Key Laboratory of Information Security, Institute of Information Engineering, CAS, Beijing 100093, China, cas.cn;School of Cyber Security, University of Chinese Academy of Sciences, Beijing 100049, China, ucas.ac.cn.liuqinju@iie.ac.cn

推荐引用方式

Qinju Liu,Xianhui Lu,Fucai Luo,Shuai Zhou,Jingnan He,Kunpeng Wang. SecureBP from Homomorphic Encryption. Security and Communication Networks ,Vol.2020(2020)

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参考文献

[1]	T. Chen, S. Zhong. (2009). Privacy-preserving backpropagation neural network learning. IEEE Transactions on Neural Networks.20(10):1554-1564. DOI: 10.1038/nature21056.
[2]	L. Ducas, D. Micciancio. (2015). FHEW: bootstrapping homomorphic encryption in less than a second. Advances in Cryptology—EUROCRYPT 2015, Part I, Lecture Notes in Computer Science.9056:617-640. DOI: 10.1038/nature21056.
[3]	A. Kim, Y. Song, M. Kim, K. Lee. et al.(2018). Logistic regression model training based on the approximate homomorphic encryption. BMC Medical Genomics.11(S4). DOI: 10.1038/nature21056.
[4]	C. L. Blake. (1998). UCI Repository of Machine Learning Databases. DOI: 10.1038/nature21056.
[5]	J. W. Bos, K. Lauter, M. Naehrig. (2014). Private predictive analysis on encrypted medical data. Journal of Biomedical Informatics.50:234-243. DOI: 10.1038/nature21056.
[6]	C. Orlandi, A. Piva, M. Barni. (2007). Oblivious neural network computing via homomorphic encryption. EURASIP Journal on Information Security.2007(1). DOI: 10.1038/nature21056.
[7]	I. Chillotti, N. Gama, M. Georgieva, M. Izabach`ene. et al.(2016). Faster fully homomorphic encryption: bootstrapping in less than 0.1 seconds. Advances in Cryptology—ASIACRYPT 2016, Part I:3-33. DOI: 10.1038/nature21056.
[8]	D. E. Rumelhart, G. E. Hinton, R. J. Williams. (1985). Learning internal representations by error propagation. . DOI: 10.1038/nature21056.
[9]	A. Piva, C. Orlandi, M. Caini, T. Bianchi. et al.(2008). Enhancing privacy in remote data classification. IFIP International Information Security Conference:33-46. DOI: 10.1038/nature21056.
[10]	M. Barni, C. Orlandi, A. Piva. A privacy-preserving protocol for neural-network based computation. :146-151. DOI: 10.1038/nature21056.
[11]	S. Halevi, V. Shoup. Algorithms in HElib. Advances in Cryptology—CRYPTO:554-571. DOI: 10.1038/nature21056.
[12]	H. Chen, K. Laine, R. Player. Simple encrypted arithmetic library—SEAL v2.1. Financial Cryptography and Data Security.10323:3-18. DOI: 10.1038/nature21056.
[13]	P. Mohassel, Y. Zhang. SecureML: a system for scalable privacypreserving machine learning. :19-38. DOI: 10.1038/nature21056.
[14]	C. Juvekar, V. Vaikuntanathan, A. Chandrakasan. GAZELLE: a low latency framework for secure neural network inference. :1651-1669. DOI: 10.1038/nature21056.
[15]	C. Gentry, A. Sahai, B. Waters. (2013). Homomorphic encryption from learning with errors: conceptually-simpler, asymptotically-faster, attribute-based. Advances in Cryptology—CRYPTO 2013.8042:75-92. DOI: 10.1038/nature21056.
[16]	F. Bourse, M. Minelli, M. Minihold, P. Paillier. et al.(2018). Fast homomorphic evaluation of deep discretized neural networks. Advances in Cryptology—CRYPTO 2018, Proceedings, Part III, Lecture Notes in Computer Science.10993:483-512. DOI: 10.1038/nature21056.
[17]	Z. Brakerski, C. Gentry, V. Vaikuntanathan. (Leveled) fully homomorphic encryption without bootstrapping. :309-325. DOI: 10.1038/nature21056.
[18]	M. Van Dijk, C. Gentry, S. Halevi, V. Vaikuntanathan. et al.Fully homomorphic encryption over the integers. :24-43. DOI: 10.1038/nature21056.
[19]	M. R. Albrecht, R. Player, S. Scott. (2015). On the concrete hardness of learning with errors. Journal of Mathematical Cryptology.9(3):169-203. DOI: 10.1038/nature21056.
[20]	B. D. Rouhani, M. S. Riazi, F. Koushanfar. DeepSecure: scalable provably-secure deep learning. . DOI: 10.1038/nature21056.
[21]	C. Gentry. Fully homomorphic encryption using ideal lattices. .9. DOI: 10.1038/nature21056.
[22]	F. Schroff, D. Kalenichenko, J. Philbin. Facenet: a unified embedding for face recognition and clustering. :815-823. DOI: 10.1038/nature21056.
[23]	J. H. Cheon, K. Han, A. Kim, M. Kim. et al.(2018). Bootstrapping for approximate homomorphic encryption. Advances in Cryptology—EUROCRYPT 2018, Proceedings, Part I:360-384. DOI: 10.1038/nature21056.
[24]	J. H. Cheon, A. Kim, M. Kim, Y. S. Song. et al.(2017). Homomorphic encryption for arithmetic of approximate numbers. Advances in Cryptology—ASIACRYPT 2017, Part I.10624:409-437. DOI: 10.1038/nature21056.
[25]	J. Yuan, S. Yu. (2014). Privacy preserving back-propagation neural network learning made practical with cloud computing. IEEE Transactions on Parallel and Distributed Systems.25(1):212-221. DOI: 10.1038/nature21056.
[26]	M. S. Riazi, C. Weinert, O. Tkachenko, E. M. Songhori. et al.Chameleon: a hybrid secure computation framework for machine learning applications. :707-721. DOI: 10.1038/nature21056.
[27]	J. H. Cheon, K. Han, A. Kim, M. Kim. et al.(2018). A full RNS variant of approximate homomorphic encryption. Selected Areas in Cryptography—SAC.11349:347-368. DOI: 10.1038/nature21056.
[28]	V. Gulshan, L. Peng, M. Coram. (2016). Development and validation of a deep learning algorithm for detection of diabetic retinopathy in retinal fundus photographs. JAMA.316(22):2402-2410. DOI: 10.1038/nature21056.
[29]	A. Esteva, B. Kuprel, R. A. Novoa. (2017). Dermatologist-level classification of skin cancer with deep neural networks. Nature.542(7639):115-118. DOI: 10.1038/nature21056.
[30]	Z. Brakerski, C. Gentry, V. Vaikuntanathan. (2014). (Leveled) fully homomorphic encryption without bootstrapping. ACM Transactions on Computation Theory.6(3):1-36. DOI: 10.1038/nature21056.
[31]	R. L. Rivest, L. Adleman, M. L. Dertouzos. (1978). On data banks and privacy homomorphisms. Foundations of Secure Computation:169-180. DOI: 10.1038/nature21056.
[32]	C. Gentry, S. Halevi, N. P. Smart. (2012). Homomorphic evaluation of the AES circuit. Advances in Cryptology—Crypto 2012, Lecture Notes in Computer Science.7417:850-867. DOI: 10.1038/nature21056.
[33]	J. H. Cheon, D. Stehl´e. Fully homomophic encryption over the integers revisited. :513-536. DOI: 10.1038/nature21056.
[34]	R. Gilad-Bachrach, N. Dowlin, K. Laine, K. Lauter. et al.Cryptonets: applying neural networks to encrypted data with high throughput and accuracy. :201-210. DOI: 10.1038/nature21056.
[35]	I. Chillotti, N. Gama, M. Georgieva, M. Izabach`ene. et al.(2017). Faster packed homomorphic operations and efficient circuit bootstrapping for TFHE. Advances in Cryptology—ASIACRYPT 2017, Part I.10624:377-408. DOI: 10.1038/nature21056.
[36]	Z. Brakerski, V. Vaikuntanathan. (2014). Efficient fully homomorphic encryption from (standard) $\mathsf{LWE}$. SIAM Journal on Computing.43(2):831-871. DOI: 10.1038/nature21056.