Privacy preserving cloud computing through piecewise approximation of multivariate functions

In cloud computing, computation is demanded to several cloud computing servers and each of them can have access to different data sets. Such data and also the derived computation results could not be publicly shared among the clouds involved for privacy reasons. Secure Multi-Party Computation (SMPC) protocols could be used to protect private data during computation. The search for efficient universal computing architectures is an active research topic in SMPC. By extending a previous protocol for the piece-wise linear approximation of a generic one-dimensional function, a new SMPC protocol for the approximation of n-dimensional functions f(x1,..., xn) can be developed. In the case of two inputs, a quad-tree decomposition is used to decompose the function domain into subsets wherein a constant or a bilinear approximation is used. This solution can be easily extended to the approximation of n-variate functions. Two different implementations are considered: the first one relies completely on Garbled Circuits (GC), while the second one exploits a hybrid construction where GC and Homomorphic Encryption (HE) are used together. As it is shown in the present paper, the best choice between the two approaches depends on the specific settings with the hybrid solution being preferable for inputs characterized by a large bit-length.