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Efficient Privacy Preserving Logistic Regression Inference and Training

Recently, privacy-preserving logistic regression techniques on distributed data among several data owners drew attention in terms of their applicability in federated learning environment. Many of them have been built upon cryptographic primitives such as secure multiparty computations(MPC) and homomorphic encryptions(HE) to protect the privacy of data. The secure multiparty computation provides fast and secure unit operations for arithmetic and bit operations but they often does not scale with large data well enough due to large computation cost and communication overhead. From recent works, many HE primitives provide their operations in a batch sense so that the technique can be an appropriate choice in a big data environment. However computationally expensive operations such as ciphertext slot rotation or refreshment(so called bootstrapping) and large public key size are hurdles that hamper widespread of the technique in the industry-level environment. In this paper, we provide a new hybrid approach of a privacy-preserving logistic regression training and a inference, which utilizes both MPC and HE techniques to provide efficient and scalable solution while minimizing needs of key management and complexity of computation in encrypted state. Utilizing batch sense properties of HE, we present a method to securely compute multiplications of vectors and matrices using one HE multiplication, compared to the naive approach which requires linear number of multiplications regarding to the size of input data. We also show how we used a 2-party additive secret sharing scheme to control noises of expensive HE operations such as bootstrapping efficiently.