Abstract

Performing computations while maintaining privacy is an important problem in today's distributed device ecosystem. Consider the following set up where the client would like to perform an operation of computing the inverse of a large matrix that it hosts, but would like to use the superior computing ability of the server to do so while ensuring differential privacy of any communications from the client to the server. We present a scheme for splitting the client data into privatized shares called splinters that are transmitted to the server in such a setting. Splinters are noisy linear combinations of the original sensitive matrix with several random matrices. The server performs the requested operations on these shares instead of on the raw client data at the server. The obtained intermediate results are sent back to the client where they are assembled by the client using private coefficients that it holds in order to obtain the final result. Our mechanism ensures that any communication made from the client in terms of the shares is private with respect to it's matrix that needs to be inverted and the client's sensitive coefficients that it holds.