Piecewise Function Approximation with Private Data
This work addresses privacy-preserving computation for data analysis, but it is incremental as it builds on existing secure computation techniques.
The paper tackles the problem of approximating piecewise functions on private data using secure two-party computation, presenting both a garbled circuit protocol and a hybrid garbled circuit/homomorphic encryption protocol, with the full-garbled circuit solution being more efficient in computational complexity and preferable for small bit representations.
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.