Privacy Preserving Ridge Regression on Hundreds of Millions of Records

Ridge regression is an algorithm that takes as input a large number of data points and finds the best-fit linear curve through these points. The algorithm is a building block for many machine-learning operations. We present a system for privacy-preserving ridge regression. The system outputs the best-fit curve in the clear, but exposes no other information about the input data. Our approach combines both homomorphic encryption and Yao garbled circuits, where each is used in a different part of the algorithm to obtain the best performance. We implement the complete system and experiment with it on real data-sets, and show that it significantly outperforms pure implementations based only on homomorphic encryption or Yao circuits.