Secure Logistic Regression Based on Homomorphic Encryption: Design and Evaluation

Abstract

BackgroundLearning a model without accessing raw data has been an intriguing idea to security and machine learning researchers for years. In an ideal setting, we want to encrypt sensitive data to store them on a commercial cloud and run certain analyses without ever decrypting the data to preserve privacy. Homomorphic encryption technique is a promising candidate for secure data outsourcing, but it is a very challenging task to support real-world machine learning tasks. Existing frameworks can only handle simplified cases with low-degree polynomials such as linear means classifier and linear discriminative analysis.ObjectiveThe goal of this study is to provide a practical support to the mainstream learning models (eg, logistic regression).MethodsWe adapted a novel homomorphic encryption scheme optimized for real numbers computation. We devised (1) the least squares approximation of the logistic function for accuracy and efficiency (ie, reduce computation cost) and (2) new packing and parallelization techniques.ResultsUsing real-world datasets, we evaluated the performance of our model and demonstrated its feasibility in speed and memory consumption. For example, it took approximately 116 minutes to obtain the training model from the homomorphically encrypted Edinburgh dataset. In addition, it gives fairly accurate predictions on the testing dataset.ConclusionsWe present the first homomorphically encrypted logistic regression outsourcing model based on the critical observation that the precision loss of classification models is sufficiently small so that the decision plan stays still.

Drynx: Decentralized, Secure, Verifiable System for Statistical Queries and Machine Learning on Distributed Datasets

“…DPs [13] and Gazelle [32]. In Table 12a, we show that Drynx provides several functionalities in a strong threat model and achieves results that can rival with other secure and dedicated approaches, notably in the training of logistic regression models as depicted in Figure 12a.…”

“…In this context, decentralized data-sharing systems [10], [11], [12], [13], [14], [15] have raised considerable interest and are key enablers for privacy-conscious big-data analysis. By distributing the storage and the computation, thus avoiding single points of failure, these systems enable data sharing and minimize the risks incurred by centralized solutions.…”

A Bitwise Design and Implementation for Privacy-Preserving Data Mining: From Atomic Operations to Advanced Algorithms

“…For the multiple linear regression (d > 1), we set the initial values to (N, d, l, p) � (10, 2, 16, 1) for the experiment. e dataset consists of feature vectors x 1 � [2,4,5,6,8,10,13,16,17,19], x 2 � [3,5,6,7,8,11,14,15,18,20], and a target variable y � [5,9,12,14,15,18,24,26,30, 32] with 10 data created artificially, and it takes 1047 seconds with 0.01 running rate. e iteration proceeded 50 steps to converge θ � (− 0.952, 1.094, 3.331) with threshold value, ε � 0.1.…”

“…proposed a least square polynomial that broadens bounded domain of Taylor series expansion to (− 8, 8) [19,20]. e underlying principle is to derive a function g(x) that minimizes mean squared error (MSE) such that 1/|I|…”

Implementation of Supervised Learning towards Optimizing Queries in Database Systems

“…Miran Kim et al [12] in their work have discussed regarding homomorphic encryption, which can be used to protect user data privacy through the parameter exchange under the encryption mechanism during machine learning. They have also studied regarding the possibility of leakage at the raw data level.…”