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

### Ahmad Kamal, 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,nâ‰¥2k-1. We also show that our proposed method is information theoretic secure against a semi-honest adversary.

Download#### 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