research-article

Public Access

Faster PCA and Linear Regression through Hypercubes in HElib

Authors:

Deevashwer Rathee,

Pradeep Kumar Mishra,

Masaya YasudaAuthors Info & Claims

WPES'18: Proceedings of the 2018 Workshop on Privacy in the Electronic Society

Pages 42 - 53

https://doi.org/10.1145/3267323.3268952

Published: 15 January 2018 Publication History

Abstract

The significant advancements in the field of homomorphic encryption have led to a grown interest in securely outsourcing data and computation for privacy critical applications. In this paper, we focus on the problem of performing secure predictive analysis, such as principal component analysis (PCA) and linear regression, through exact arithmetic over encrypted data. We improve the plaintext structure of Lu et al.'s protocols (from NDSS 2017), by switching over from linear array arrangement to a two-dimensional hypercube. This enables us to utilize the SIMD (Single Instruction Multiple Data) operations to a larger extent, which results in improving the space and time complexity by a factor of matrix dimension. We implement both Lu et al.'s method and ours for PCA and linear regression over HElib, a software library that implements the Brakerski-Gentry-Vaikuntanathan (BGV) homomorphic encryption scheme. In particular, we show how to choose optimal parameters of the BGV scheme for both methods. For example, our experiments show that our method takes 45 seconds to train a linear regression model over a dataset with 32k records and 6 numerical attributes, while Lu et al.'s method takes 206 seconds.

Supplementary Material

ZIP File (wpes06.zip)

Download
21.44 KB

References

[1]

Dan Boneh, Eu-Jin Goh, and Kobbi Nissim. 2005. Evaluating 2-DNF Formulas on Ciphertexts. In Proceedings of the Second International Conference on Theory of Cryptography (TCC'05). Springer-Verlag, Berlin, Heidelberg, 325--341.

Digital Library

[2]

Raphael Bost, Raluca Ada Popa, Stephen Tu, and Shafi Goldwasser. 2015. Machine Learning Classification over Encrypted Data. In 22nd Annual Network and Distributed System Security Symposium, NDSS 2015, San Diego, California, USA, February 8--11, 2015. https://www.ndss-symposium.org/ndss2015/ machine-learning-classification-over-encrypted-data

[3]

Zvika Brakerski, Craig Gentry, and Vinod Vaikuntanathan. 2012. (Leveled) Fully Homomorphic Encryption Without Bootstrapping. In Proceedings of the 3rd Innovations in Theoretical Computer Science Conference (ITCS '12). ACM, New York, NY, USA, 309--325.

Digital Library

[4]

Zvika Brakerski and Vinod Vaikuntanathan. 2011. Fully Homomorphic Encryption from Ring-LWE and Security for Key Dependent Messages. In Advances in Cryptology -- CRYPTO 2011, Phillip Rogaway (Ed.). Springer Berlin Heidelberg, Berlin, Heidelberg, 505--524.

Digital Library

[5]

Jung Hee Cheon, Andrey Kim, Miran Kim, and Yongsoo Song. 2017. Homomorphic Encryption for Arithmetic of Approximate Numbers. In Advances in Cryptology -- ASIACRYPT 2017, Tsuyoshi Takagi and Thomas Peyrin (Eds.). Springer International Publishing, Cham, 409--437.

[6]

J. H. Cheon, M. Kim, and M. Kim. 2016. Optimized Search-and-Compute Circuits and Their Application to Query Evaluation on Encrypted Data. IEEE Transactions on Information Forensics and Security 11, 1 (Jan 2016), 188--199.

[7]

E. Dekel, D. Nassimi, and S. Sahni. 1981. Parallel Matrix and Graph Algorithms. SIAM J. Comput. 10, 4 (1981), 657--675. arXiv:https://doi.org/10.1137/0210049

Digital Library

[8]

Dua Dheeru and Efi Karra Taniskidou. 2017. UCI Machine Learning Repository. http://archive.ics.uci.edu/ml

[9]

G.C Fox, S.W Otto, and A.J.G Hey. 1987. Matrix algorithms on a hypercube I: Matrix multiplication. Parallel Comput. 4, 1 (1987), 17 -- 31.

[10]

Craig Gentry. 2009. Fully Homomorphic Encryption Using Ideal Lattices. In Proceedings of the Forty-first Annual ACM Symposium on Theory of Computing (STOC '09). ACM, New York, NY, USA, 169--178.

Digital Library

[11]

Craig Gentry, Shai Halevi, and Nigel P. Smart. 2012. Homomorphic Evaluation of the AES Circuit. In Advances in Cryptology -- CRYPTO 2012, Reihaneh Safavi-Naini and Ran Canetti (Eds.). Springer Berlin Heidelberg, Berlin, Heidelberg, 850--867.

Digital Library

[12]

Thore Graepel, Kristin Lauter, and Michael Naehrig. 2013. ML Confidential: Machine Learning on Encrypted Data. In Proceedings of the 15th International Conference on Information Security and Cryptology (ICISC'12). Springer-Verlag, Berlin, Heidelberg, 1--21.

Digital Library

[13]

C. Guo and N. Higham. 2006. A Schur-Newton Method for the Matrix pth Root and its Inverse. SIAM J. Matrix Anal. Appl. 28, 3 (2006), 788--804. arXiv:https://doi.org/10.1137/050643374

Digital Library

[14]

Shai Halevi and Victor Shoup. 2013. Design and implementation of a homomorphicencryption library. http://people.csail.mit.edu/shaih/pubs/he-library.pdf

[15]

Shai Halevi and Victor Shoup. 2014. Algorithms in HElib. In Advances in Cryptology -- CRYPTO 2014, Juan A. Garay and Rosario Gennaro (Eds.). Springer Berlin Heidelberg, Berlin, Heidelberg, 554--571.

[16]

Wenjie Lu, Shohei Kawasaki, and Jun Sakuma. 2016. Using Fully Homomorphic Encryption for Statistical Analysis of Categorical, Ordinal and Numerical Data (This is the full version of the conference paper presented at NDSS 2017). IACR Cryptology ePrint Archive, Report 2016/1163 (2016). https://eprint.iacr.org/2016/ 1163

[17]

Michael Naehrig, Kristin Lauter, and Vinod Vaikuntanathan. 2011. Can Homomorphic Encryption Be Practical?. In Proceedings of the 3rd ACM Workshop on Cloud Computing Security Workshop (CCSW '11). ACM, New York, NY, USA, 113--124.

Digital Library

[18]

Pascal Paillier. 1999. Public-Key Cryptosystems Based on Composite Degree Residuosity Classes. In Advances in Cryptology - EUROCRYPT '99, Jacques Stern (Ed.). Springer Berlin Heidelberg, Berlin, Heidelberg, 223--238.

Digital Library

[19]

R. L. Rivest, A. Shamir, and L. Adleman. 1978. A Method for Obtaining Digital Signatures and Public-key Cryptosystems. Commun. ACM 21, 2 (Feb. 1978), 120--126.

Digital Library

[20]

N. P. Smart and F. Vercauteren. 2010. Fully Homomorphic Encryption with Relatively Small Key and Ciphertext Sizes. In Proceedings of the 13th International Conference on Practice and Theory in Public Key Cryptography (PKC'10). Springer- Verlag, Berlin, Heidelberg, 420--443.

Digital Library

[21]

N. P. Smart and F. Vercauteren. 2014. Fully Homomorphic SIMD Operations. Des. Codes Cryptography 71, 1 (April 2014), 57--81.

Digital Library

[22]

David Wu and Jacob Haven. 2012. Using Homomorphic Encryption for Large Scale Statistical Analysis. https://crypto.stanford.edu/~dwu4/FHE-SI_Report.pdf

[23]

Masaya Yasuda, Takeshi Shimoyama, Jun Kogure, Kazuhiro Yokoyama, and Takeshi Koshiba. 2013. Secure Pattern Matching Using Somewhat Homomorphic Encryption. In Proceedings of the 2013 ACM Workshop on Cloud Computing Security Workshop (CCSW '13). ACM, New York, NY, USA, 65--76.

Digital Library

[24]

Masaya Yasuda, Takeshi Shimoyama, Jun Kogure, Kazuhiro Yokoyama, and Takeshi Koshiba. 2015. Secure Statistical Analysis Using RLWE-Based Homomorphic Encryption. In Information Security and Privacy, Ernest Foo and Douglas Stebila (Eds.). Springer International Publishing, Cham, 471--487.

Cited By

Zhu LHua QChen YJin H(2024)Secure Outsourced Matrix Multiplication with Fully Homomorphic EncryptionComputer Security – ESORICS 202310.1007/978-3-031-50594-2_13(249-269)Online publication date: 12-Jan-2024
https://doi.org/10.1007/978-3-031-50594-2_13
Ma XMa CJiang YGe C(2023)Improved privacy-preserving PCA using optimized homomorphic matrix multiplicationComputers & Security10.1016/j.cose.2023.103658(103658)Online publication date: Dec-2023
https://doi.org/10.1016/j.cose.2023.103658
Qu HXu G(2023)Improvements of Homomorphic Secure Evaluation of Inverse Square RootInformation and Communications Security10.1007/978-981-99-7356-9_7(110-127)Online publication date: 20-Oct-2023
https://doi.org/10.1007/978-981-99-7356-9_7
Show More Cited By

Index Terms

Faster PCA and Linear Regression through Hypercubes in HElib
1. Security and privacy
  1. Security services
    1. Privacy-preserving protocols

Recommendations

Toward practical privacy-preserving linear regression
Abstract
Linear regression is an ordinary machine learning algorithm that models the relation between the input values and the output ones with underlying linear functions. Giacomelli et al. (ACNS 2018) proposed the first system training the ...
Faster Homomorphic Linear Transformations in HElib
Advances in Cryptology – CRYPTO 2018
Abstract
HElib is a software library that implements homomorphic encryption (HE), with a focus on effective use of “packed” ciphertexts. An important operation is applying a known linear map to a vector of encrypted data. In this paper, we describe several ...
On Implementing Linear Regression on Homomorphically Encrypted Data: A Case-Study
ARES '24: Proceedings of the 19th International Conference on Availability, Reliability and Security

Fully Homomorphic Encryption (FHE) is a key technological enabler for secure computations as it allows a third-party to perform arbitrary computations on encrypted data learning neither the input nor the results of a computation. Notwithstanding the ...

Comments

Information & Contributors

Information

Published In

cover image ACM Conferences

WPES'18: Proceedings of the 2018 Workshop on Privacy in the Electronic Society

October 2018

190 pages

ISBN:9781450359894

DOI:10.1145/3267323

General Chairs:
David Lie
University of Toronto, Canada
,
Mohammad Mannan
Concordia University, Canada
,
Program Chair:
Aaron Johnson
U.S. Naval Research Laboratory, USA

Copyright © 2018 ACM.

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

Sponsors

SIGSAC: ACM Special Interest Group on Security, Audit, and Control

Publisher

Association for Computing Machinery

New York, NY, United States

Publication History

Published: 15 January 2018

Permissions

Request permissions for this article.

Request Permissions

Check for updates

Author Tags

Qualifiers

Research-article

Funding Sources

Conference

CCS '18

Sponsor:

SIGSAC

CCS '18: 2018 ACM SIGSAC Conference on Computer and Communications Security

October 15, 2018

Toronto, Canada

Acceptance Rates

WPES'18 Paper Acceptance Rate 11 of 25 submissions, 44%;

Overall Acceptance Rate 106 of 355 submissions, 30%

Upcoming Conference

CCS '24

Sponsor:
sigsac

ACM SIGSAC Conference on Computer and Communications Security

October 14 - 18, 2024

Salt Lake City , UT , USA

Contributors

Other Metrics

View Article Metrics

Bibliometrics & Citations

Bibliometrics

Article Metrics

8
Total Citations
View Citations
383
Total Downloads

Downloads (Last 12 months)104
Downloads (Last 6 weeks)20

Reflects downloads up to 27 Jul 2024

Other Metrics

View Author Metrics

Citations

Cited By

Zhu LHua QChen YJin H(2024)Secure Outsourced Matrix Multiplication with Fully Homomorphic EncryptionComputer Security – ESORICS 202310.1007/978-3-031-50594-2_13(249-269)Online publication date: 12-Jan-2024
https://doi.org/10.1007/978-3-031-50594-2_13
Ma XMa CJiang YGe C(2023)Improved privacy-preserving PCA using optimized homomorphic matrix multiplicationComputers & Security10.1016/j.cose.2023.103658(103658)Online publication date: Dec-2023
https://doi.org/10.1016/j.cose.2023.103658
Qu HXu G(2023)Improvements of Homomorphic Secure Evaluation of Inverse Square RootInformation and Communications Security10.1007/978-981-99-7356-9_7(110-127)Online publication date: 20-Oct-2023
https://doi.org/10.1007/978-981-99-7356-9_7
Huang HZong H(2022)Secure matrix multiplication based on fully homomorphic encryptionThe Journal of Supercomputing10.1007/s11227-022-04850-479:5(5064-5085)Online publication date: 10-Oct-2022
https://doi.org/10.1007/s11227-022-04850-4
Zong HHuang HWang S(2021)Secure Outsourced Computation of Matrix Determinant Based on Fully Homomorphic EncryptionIEEE Access10.1109/ACCESS.2021.30564769(22651-22661)Online publication date: 2021
https://doi.org/10.1109/ACCESS.2021.3056476
Panda S(2021)Principal Component Analysis Using CKKS Homomorphic SchemeCyber Security Cryptography and Machine Learning10.1007/978-3-030-78086-9_4(52-70)Online publication date: 1-Jul-2021
https://doi.org/10.1007/978-3-030-78086-9_4
Mishra PRathee DDuong DYasuda M(2020)Fast secure matrix multiplications over ring-based homomorphic encryptionInformation Security Journal: A Global Perspective10.1080/19393555.2020.1836288(1-16)Online publication date: 28-Oct-2020
https://doi.org/10.1080/19393555.2020.1836288

View Options

View options

PDF

View or Download as a PDF file.

eReader

View online with eReader.

Get Access

Login options

Check if you have access through your login credentials or your institution to get full access on this article.

Full Access

Get this Publication

Media

Figures

Other

Tables

View Table of Contents