Piecewise Function Approximation with Private Data

TL;DR

This paper introduces two secure computation protocols for private piecewise function approximation, combining garbled circuits and homomorphic encryption, with analysis of their efficiency based on data size and complexity.

Contribution

It proposes novel secure protocols for piecewise function approximation utilizing GC and HE, expanding privacy-preserving computation methods.

Findings

Full-GC is efficient for small data sizes.

Hybrid GC and HE is better for larger data.

Full-GC offers simpler implementation.

Abstract

We present two Secure Two Party Computation (STPC) protocols for piecewise function approximation on private data. The protocols rely on a piecewise approximation of the to-be-computed function easing the implementation in a STPC setting. The first protocol relies entirely on Garbled Circuit (GC) theory, while the second one exploits a hybrid construction where GC and Homomorphic Encryption (HE) are used together. In addition to piecewise constant and linear approximation, polynomial interpolation is also considered. From a communication complexity perspective, the full-GC implementation is preferable when the input and output variables can be represented with a small number of bits, while the hybrid solution is preferable otherwise. With regard to computational complexity, the full-GC solution is generally more convenient.