Coding for private and secure multiparty computing

We consider the problem of secure and private multiparty computation (MPC), in which the goal is to compute a general polynomial function distributedly over several workers, while keeping them oblivious to the content of the dataset, and preventing them from maliciously affecting the computation result. We demonstrate the role of Lagrange Coded Computing (LCC), a recently proposed coded computing technique that can be applied to general polynomial computations, on enabling secure and private MPC. We show that LCC offers both private and secure computation simultaneously, and is universal in the sense that all polynomials up to a certain degree can be computed on the same encoding. We also demonstrate that LCC achieves an optimal tradeoff between privacy and security, and requires a minimal amount of added randomness for privacy. Compared to prevalent algorithms in MPC (in particular the celebrated BGW scheme), we show that LCC significantly improves the storage, communication, and secret-sharing overhead needed for MPC.