# Communication-Efficient (Client-Aided) Secure Two-Party Protocols and Its Application

## TL;DR

This paper introduces communication-efficient two-party secure computation protocols using Beaver triple extension, significantly reducing communication rounds and bits, thus improving performance in high-latency environments like the Internet.

## Contribution

It presents novel semi-honest secure protocols that minimize communication rounds and bits, leveraging Beaver triple extension for efficient multi-fan-in gate computation.

## Key findings

- Reduced communication rounds to three for less-than comparison.
- Decreased communication bits by 38.4%.
- Achieved 56.1% shorter total online execution time.

## Abstract

Secure multi-party computation (MPC) allows a set of parties to compute a function jointly while keeping their inputs private. Compared with the MPC based on garbled circuits,some recent research results show that MPC based on secret sharing (SS) works at a very high speed. Moreover, SS-based MPC can be easily vectorized and achieve higher throughput. In SS-based MPC, however, we need many communication rounds for computing concrete protocols like equality check, less-than comparison, etc. This property is not suited for large-latency environments like the Internet (or WAN). In this paper, we construct semi-honest secure communication-efficient two-party protocols. The core technique is Beaver triple extension, which is a new tool for treating multi-fan-in gates, and we also show how to use it efficiently. We mainly focus on reducing the number of communication rounds, and our protocols also succeed in reducing the number of communication bits (in most cases). As an example, we propose a less-than comparison protocol (under practical parameters) with three communication rounds. Moreover, the number of communication bits is also $38.4\%$ fewer. As a result, total online execution time is $56.1\%$ shorter than the previous work adopting the same settings. Although the computation costs of our protocols are more expensive than those of previous work, we confirm via experiments that such a disadvantage has small effects on the whole online performance in the typical WAN environments.