Efficient polynomial operations in the shared-coefficients setting

Abstract. We study the design of efficient and private protocols for polynomial operations in the shared-coefficients setting. We propose efficient protocols for polynomial multiplication, division with remainder, polynomial interpolation, polynomial gcd, and a few other operations. All the protocols introduced in this paper are constant-round, and more efficient than the general MPC. The protocols are all composable, and can be combined to perform more complicated functionalities. We focus on using a threshold additively homomorphic public key scheme due to the applications of our protocols. But, our protocols can also be securely computed in the information-theoretic setting. Finally, we mention some applications of our protocols to privacy-preserving set-operations