Paper 2025/269

10-Party Sublinear Secure Computation from Standard Assumptions

Abstract

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 protocols – in 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 NC1 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.