Logistic Regression on Homomorphic Encrypted Data at Scale

Abstract

Machine learning on (homomorphic) encrypted data is a cryptographic method for analyzing private and/or sensitive data while keeping privacy. In the training phase, it takes as input an encrypted training data and outputs an encrypted model without ever decrypting. In the prediction phase, it uses the encrypted model to predict results on new encrypted data. In each phase, no decryption key is needed, and thus the data privacy is ultimately guaranteed. It has many applications in various areas such as finance, education, genomics, and medical field that have sensitive private data. While several studies have been reported on the prediction phase, few studies have been conducted on the training phase.In this paper, we present an efficient algorithm for logistic regression on homomorphic encrypted data, and evaluate our algorithm on real financial data consisting of 422,108 samples over 200 features. Our experiment shows that an encrypted model with a sufficient Kolmogorov Smirnow statistic value can be obtained in ∼17 hours in a single machine. We also evaluate our algorithm on the public MNIST dataset, and it takes ∼2 hours to learn an encrypted model with 96.4% accuracy. Considering the inefficiency of homomorphic encryption, our result is encouraging and demonstrates the practical feasibility of the logistic regression training on large encrypted data, for the first time to the best of our knowledge.

Optimized homomorphic encryption solution for secure genome-wide association studies

“…We denote this as packed-matrix encoding . All matrix products in steps 2 through 8 of Algorithm 3 use the rotation-based SUMROWVEC and SUMCOLVEC procedures from [ 5 ]. Later in the algorithm (starting from step 9), the solution switches to single-integer ciphertexts for X and the vectors and matrices derived from X and y .…”

“…The first stage, the estimation of θ,θ , was widely addressed in the literature, in particular in the iDASH'17 secure genome analysis competition [4][5][6][7][8].…”

An Efficient Encrypted Floating-Point Representation Using HEAAN and TFHE

“…At the expense of this bit accuracy, HEAAN supports very fast arithmetic operations on word-sized encrypted data. is fast computation speed allows HEAAN to be used in many fields such as machine learning and machine control [17,18]. In addition, unlike TFHE, HEAAN has the advantage of providing a complete SIMD function.…”

Differentially Private Publication of Vertically Partitioned Data

“…Since IRs might leak training data information [1,9], they are mostly protected by additively homomorphic encryption (HE) [20,29] and secure multi-party computation (MPC) [27] in existing VFL, thanks to the sufficient computation power and network bandwidth of enterprise-level participants. In addition, given by the similar settings and assumptions, most existing VFL algorithms follow traditional privacypreserving multi-party machine learning methods [36,4,18,3,8], by applying Taylor approximation to the loss functions, so that HE can be adopted to protect the calculation of polynomial tasks in VFL's joint training.…”