Paper 2021/113

Improvement of Secure Multi-Party Multiplication of (k,n) Threshold Secret Sharing Using Only N=k Servers (Revised Version)

Ahmad Akmal Aminuddin Mohd Kamal and Keiichi Iwamura

Abstract

Secure multi-party computation (MPC) allows a set of n servers to jointly compute an arbitrary function of their inputs, without revealing these inputs to each other. A (k,n) threshold secret sharing is a protocol in which a single secret is divided into n shares and the secret can be recovered from a threshold k shares. Typically, multiplication of (k,n) secret sharing will result in increase of polynomial degree from k-1 to 2k-2, thus increasing the number of shares required from k to 2k-1. Since each server typically hold only one share, the number of servers required in MPC will also increase from k to 2k-1. Therefore, a set of n servers can compute multiplication securely if the adversary corrupts at most k-1<n/2 of the servers. In this paper, we differentiate the number of servers N required and parameter n of (k,n) secret sharing scheme, and propose a method of computing (k-1) sharing of multiplication ab by using only N=k servers. By allowing each server to hold two shares, we realize MPC of multiplication with the setting of N=k,n&#8805;2k-1. We also show that our proposed method is information theoretic secure against a semi-honest adversary.

Note: **This is the revised version of the paper submitted in the Proceedings of the 7th International Conference on Information Systems Security and Privacy (ICISSP 2021). The revised version had corrected a few mistakes in the original publication.