Logistic regression over encrypted data from fully homomorphic encryption.

Area of Science:

• Computational Biology
• Cryptography
• Bioinformatics

Background:

• The 2017 iDASH competition focused on secure genome analysis, specifically training logistic regression models on encrypted data.
• The goal was to allow data holders to outsource model training to an untrusted cloud without revealing sensitive patient genomic data or the trained model.

Purpose of the Study:

• To develop and evaluate a method for training logistic regression models over encrypted genomic data using homomorphic encryption.
• To enable secure outsourcing of genomic data analysis while preserving data privacy.

Main Methods:

• Utilized multi-bit plaintext space in fully homomorphic encryption with fixed-point number encoding.
• Combined bootstrapping in fully homomorphic encryption with fixed-point arithmetic scaling.
• Employed minimax polynomial approximation for the sigmoid function and 1-bit gradient descent to manage plaintext growth.

Main Results:

• The developed algorithm for training over encrypted data requires 0.4-3.2 hours per gradient descent iteration.
• Demonstrated the feasibility of performing logistic regression training on encrypted genomic datasets.

Conclusions:

• Training logistic regression models on encrypted data is feasible but computationally expensive.
• The proposed method offers a high level of data privacy, crucial for sensitive applications in genomics.