Paper 2024/1152 Original: eprint.iacr.org/2024/1152 ↗

Secure Multiparty Computation of Symmetric Functions with Polylogarithmic Bottleneck Complexity and Correlated Randomness

Abstract

Bottleneck complexity is an efficiency measure of secure multiparty computation (MPC) protocols introduced to achieve load-balancing in large-scale networks, which is defined as the maximum communication complexity required by any one player within the protocol execution. Towards the goal of achieving low bottleneck complexity, prior works proposed MPC protocols for computing symmetric functions in the correlated randomness model, where players are given input-independent correlated randomness in advance. However, the previous protocols with polylogarithmic bottleneck complexity in the number of players $n$ require a large amount of correlated randomness that is linear in $n$, which limits the per-party efficiency as receiving and storing correlated randomness are the bottleneck for efficiency. In this work, we present for the first time MPC protocols for symmetric functions such that bottleneck complexity and the amount of correlated randomness are both polylogarithmic in $n$, assuming collusion of size at most $n-o(n)$ players. Furthermore, one of our protocols is even computationally efficient in that each player performs only $\mathrm{polylog}(n)$ arithmetic operations while the computational complexity of the previous protocols is $O(n)$. Technically, our efficiency improvements come from novel protocols based on ramp secret sharing to realize basic functionalities with low bottleneck complexity, which we believe may be of interest beyond their applications to secure computation of symmetric functions.