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

Ahmad Kamal, Keiichi Iwamura

2021

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≥2k-1. We also show that our proposed method is information theoretic secure against a semi-honest adversary.

Paper Citation

in Harvard Style

Kamal A. and Iwamura K. (2021). Improvement of Secure Multi-Party Multiplication of (k, n) Threshold Secret Sharing Using Only N = k Servers.In Proceedings of the 7th International Conference on Information Systems Security and Privacy - Volume 1: ICISSP, ISBN 978-989-758-491-6, pages 77-88. DOI: 10.5220/0010206400770088

in Bibtex Style

@conference{icissp21,
author={Ahmad Kamal and Keiichi Iwamura},
title={Improvement of Secure Multi-Party Multiplication of (k, n) Threshold Secret Sharing Using Only N = k Servers},
booktitle={Proceedings of the 7th International Conference on Information Systems Security and Privacy - Volume 1: ICISSP,},
year={2021},
pages={77-88},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0010206400770088},
isbn={978-989-758-491-6},
}

in EndNote Style

TY - CONF

JO - Proceedings of the 7th International Conference on Information Systems Security and Privacy - Volume 1: ICISSP,
TI - Improvement of Secure Multi-Party Multiplication of (k, n) Threshold Secret Sharing Using Only N = k Servers
SN - 978-989-758-491-6
AU - Kamal A.
AU - Iwamura K.
PY - 2021
SP - 77
EP - 88
DO - 10.5220/0010206400770088