Beyond Yao's Millionaires: Secure Multi-Party Computation of Non-Polynomial Functions

TL;DR

This paper introduces an unconditionally secure multi-party comparison scheme based on Shamir secret sharing that efficiently compares multiple private inputs without revealing any individual data, and can be adapted to compute various non-polynomial functions.

Contribution

It presents the first information-theoretically secure scheme for comparing multiple private numbers with improved efficiency and versatility for computing non-polynomial functions.

Findings

Achieves unconditionally secure comparison of N private inputs.

Reduces computational complexity compared to two-input comparison schemes.

Enables computation of functions like minimum, median, and rank from secret inputs.

Abstract

In this paper, we present an unconditionally secure $N$-party comparison scheme based on Shamir secret sharing, utilizing the binary representation of private inputs to determine the $\max$ without disclosing any private inputs or intermediate results. Specifically, each party holds a private number and aims to ascertain the greatest number among the $N$ available private numbers without revealing its input, assuming that there are at most $T < \frac{N}{2}$ honest-but-curious parties. The proposed scheme demonstrates a lower computational complexity compared to existing schemes that can only compare two secret numbers at a time. To the best of our knowledge, our scheme is the only information-theoretically secure method for comparing $N$ private numbers without revealing either the private inputs or any intermediate results. We demonstrate that by modifying the proposed scheme, we can compute other well-known non-polynomial functions of the inputs, including the minimum, median, and rank. Additionally, in the proposed scheme, before the final reveal phase, each party possesses a share of the result, enabling the nodes to compute any polynomial function of the comparison result. We also explore various applications of the proposed comparison scheme, including federated learning.