Abstract
BackgroundSecurity concerns have been raised since big data became a prominent tool in data analysis. For instance, many machine learning algorithms aim to generate prediction models using training data which contain sensitive information about individuals. Cryptography community is considering secure computation as a solution for privacy protection. In particular, practical requirements have triggered research on the efficiency of cryptographic primitives.MethodsThis paper presents a method to train a logistic regression model without information leakage. We apply the homomorphic encryption scheme of Cheon et al. (ASIACRYPT 2017) for an efficient arithmetic over real numbers, and devise a new encoding method to reduce storage of encrypted database. In addition, we adapt Nesterov’s accelerated gradient method to reduce the number of iterations as well as the computational cost while maintaining the quality of an output classifier.ResultsOur method shows a state-of-the-art performance of homomorphic encryption system in a real-world application. The submission based on this work was selected as the best solution of Track 3 at iDASH privacy and security competition 2017. For example, it took about six minutes to obtain a logistic regression model given the dataset consisting of 1579 samples, each of which has 18 features with a binary outcome variable.ConclusionsWe present a practical solution for outsourcing analysis tools such as logistic regression analysis while preserving the data confidentiality.
Highlights
Security concerns have been raised since big data became a prominent tool in data analysis
Machine learning (ML) is a class of methods in artificial intelligence, the characteristic feature of which is that they do not give the solution of a particular problem but they learn the process of finding solutions to a set of similar problems
We provide a solution to the third track of iDASH 2017 competition, which aims to develop Homomorphic encryption (HE) based secure solutions for building a ML model on encrypted data
Summary
Logistic regression or logit model is a ML model used to predict the probability of occurrence of an event by fitting data to a logistic curve [17]. For the rotation keys rk, output a ciphertext ct encrypting the rotated plaintext vector of ct by r positions. Step 2: To obtain the inner product zTi β(t), the public cloud aggregates the values of zijβj(t) in the same row This step can be done by adapting the incomplete column shifting operation. The output ciphertext encrypts the values of g zTi β(t) in its plaintext slots: ct. Step 7: This step aggregates the vectors g zTi β(t) to compute the gradient of the loss function It is obtained by recursively adding ct to its row shifting: ct6 ← Add ct, Rotate ct6; 2j for j = log(f + 1), . For the homomorphic evaluation of Nesterov’s accelerated gradient, a clients sends one more ciphertext ct(v0) encrypting the initial vector v(0) to the public cloud.
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