Toward efficient privacy-preserving two-party training for RBF kernel SVMs

Abstract Privacy-preserving machine learning (PPML) techniques enable collaborative machine learning tasks without exposing raw data of the participating parties. However, the efficient evaluation of non-polynomial functions in PPML remains a key challenge. In this work, we propose NASE (Neat and Accurate Secure Exponentiation), an MPC protocol tailored to secure radial basis function (RBF) kernel evaluation. By exploiting the fact that the exponent in the RBF kernel is always non-positive, NASE admits a lightweight construction that reduces computation overhead by up to 1.65 $$\times $$ × and communication overhead by up to 3.97 $$\times $$ × in the RBF kernel evaluation task on our datasets compared to SIRNN (IEEE S& P 2021), the prior SOTA secure exponentiation framework that has been used in prior work for secure RBF kernel evaluation. Taking NASE as the building block, we propose a privacy-preserving two-party RBF kernel SVM training protocol. Using the BFV scheme and MPC techniques, we introduce group-batch sampling for efficient sampling in ciphertext with a provable convergence guarantee, and propose a partial rotation method tailored to our scenario to optimize dot product computation. Experiments on our real-world datasets show that our protocol achieves model accuracy comparable to plaintext training, and the reproduced comparison with previous work shows reduced training runtime under the evaluated LAN and WAN settings in the semi-honest model.