TY - GEN
T1 - Faster PCA and linear regression through hypercubes in HElib
AU - Rathee, Deevashwer
AU - Mishra, Pradeep Kumar
AU - Yasuda, Masaya
N1 - Funding Information:
This work was supported by JST CREST Grant Number JPMJCR14D6, Japan. A part of this work was also supported by JSPS KAKENHI Grant Number 16H02830.
Publisher Copyright:
© 2018 Association for Computing Machinery.
PY - 2018/10/15
Y1 - 2018/10/15
N2 - 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.
AB - 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.
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U2 - 10.1145/3267323.3268952
DO - 10.1145/3267323.3268952
M3 - Conference contribution
AN - SCOPUS:85056855961
T3 - Proceedings of the ACM Conference on Computer and Communications Security
SP - 42
EP - 53
BT - WPES 2018 - Proceedings of the 2018 Workshop on Privacy in the Electronic Society, co-located with CCS 2018
PB - Association for Computing Machinery
T2 - 17th ACM Workshop on Privacy in the Electronic Society, WPES 2018, held in conjunction with the 25th ACM Conference on Computer and Communications Security, CCS 2018
Y2 - 15 October 2018
ER -