10-Party Sublinear Secure Computation from Standard Assumptions

Secure computation enables mutually distrusting parties to jointly compute a function on their secret inputs, while revealing nothing beyond the function output. A long-running challenge is understanding the required communication complexity of such protocolsin particular, when communication can be sublinear in the circuit representation size of the desired function. While several techniques have demonstrated the viability of sublinear secure computation in the two-party setting, known methods for the corresponding multi-party setting rely either on fully homomorphic encryption, non-standard hardness assumptions, or are limited to a small number of parties. In this work, we expand the study of multi-party sublinear secure computation by demonstrating sublinear-communication 10-party computation from various combinations of standard hardness assumptions. In particular, our contributions show:

-8-party homomorphic secret sharing under the hardness of (DDH or DCR), the superpolynomial hardness of LPN, and the existence of constant-depth pseudorandom generators; -A general framework for achieving (N + M )-party sublinear secure computation using M -party homomorphic secret sharing for NC 1 and correlated symmetric PIR.

Together, our constructions imply the existence of a 10-party MPC protocol with sublinear computation. At the core of our techniques lies a novel series of computational approaches based on homomorphic secret sharing.