Paper 2022/866

Communication-Efficient Secure Logistic Regression

Abstract

We present a novel construction that enables two parties to securely train a logistic regression model on private secret-shared data. Our goal is to minimize online communication and round complexity, while still allowing for an efficient offline phase. As part of our construction, we develop many building blocks of independent interest. These include a new approximation technique for the sigmoid function that results in a secure protocol with better communication, protocols for secure powers evaluation and secure spline computation on fixed-point values, and a new comparison protocol that optimizes online communication. We also present a new two-party protocol for generating keys for distributed point functions (DPFs) over arithmetic sharing, where previous constructions do this only for Boolean outputs. We implement our protocol in an end-to-end system and benchmark its efficiency. We can securely evaluate a batch of $10^3$ sigmoids with $\approx 0.5$ MB of online communication, $4$ online rounds, and $\approx 1.6$ seconds of online time over WAN. This is $\approx 30 \times$ less in online communication, $\approx 31\times$ fewer online rounds, and $\approx 5.5\times$ less online time than the well-known MP-SPDZ's protocol. Our system can train a logistic regression model over $6$ epochs and a database containing $70,000$ samples and $15$ features with $208.09$ MB of online communication and $9.68$ minutes of online time. We compare our logistic regression training against MP-SPDZ over a synthetic dataset of $1000$ samples and $10$ features and show an improvement of $\approx 130\times$ in online communication and $\approx 4.75\times$ in online time over WAN. We converge to virtually the same model as plaintext in all cases. We open-source our system and include extensive tests.