Private Polynomial Computation from Lagrange Encoding
This work extends private computation to high-degree polynomials and data privacy, addressing secure distributed computing for applications like cloud-based data processing.
The paper tackles the problem of enabling private computation of polynomials on distributed datasets without revealing the function identity or data to servers, achieving robustness against Byzantine and straggling servers and collusion.
Private computation is a generalization of private information retrieval, in which a user is able to compute a function on a distributed dataset without revealing the identity of that function to the servers. In this paper it is shown that Lagrange encoding, a powerful technique for encoding Reed-Solomon codes, enables private computation in many cases of interest. In particular, we present a scheme that enables private computation of polynomials of any degree on Lagrange encoded data, while being robust to Byzantine and straggling servers, and to servers colluding to attempt to deduce the identities of the functions to be evaluated. Moreover, incorporating ideas from the well-known Shamir secret sharing scheme allows the data itself to be concealed from the servers as well. Our results extend private computation to high degree polynomials and to data-privacy, and reveal a tight connection between private computation and coded computation.