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Logistic regression over encrypted data from fully homomorphic encryption

Cited 1 time in webofscience Cited 4 time in scopus
Authors
Chen, Hao; Gilad-Bachrach, Ran; Han, Kyoohyung; Huang, Zhicong; Jalali, Amir; Laine, Kim; Lauter, Kristin
Issue Date
2018-10-11
Publisher
BioMed Central
Citation
BMC Medical Genomics, 11(Suppl 4):81
Keywords
CryptographyHomomorphic encryptionLogistic regression
Abstract
Background
One of the tasks in the 2017 iDASH secure genome analysis competition was to enable training of logistic regression models over encrypted genomic data. More precisely, given a list of approximately 1500 patient records, each with 18 binary features containing information on specific mutations, the idea was for the data holder to encrypt the records using homomorphic encryption, and send them to an untrusted cloud for storage. The cloud could then homomorphically apply a training algorithm on the encrypted data to obtain an encrypted logistic regression model, which can be sent to the data holder for decryption. In this way, the data holder could successfully outsource the training process without revealing either her sensitive data, or the trained model, to the cloud.

Methods
Our solution to this problem has several novelties: we use a multi-bit plaintext space in fully homomorphic encryption together with fixed point number encoding; we combine bootstrapping in fully homomorphic encryption with a scaling operation in fixed point arithmetic; we use a minimax polynomial approximation to the sigmoid function and the 1-bit gradient descent method to reduce the plaintext growth in the training process.

Results
Our algorithm for training over encrypted data takes 0.4–3.2 hours per iteration of gradient descent.

Conclusions
We demonstrate the feasibility but high computational cost of training over encrypted data. On the other hand, our method can guarantee the highest level of data privacy in critical applications.
ISSN
1755-8794
Language
English
URI
http://hdl.handle.net/10371/145165
DOI
https://doi.org/10.1186/s12920-018-0397-z
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College of Natural Sciences (자연과학대학)Dept. of Mathematical Sciences (수리과학부)Journal Papers (저널논문_수리과학부)
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