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

**Category / Keywords: **cryptographic protocols / Secure Multi-Party Computation, MPC, Secure Multiplication, Secret Sharing

**Original Publication**** (with minor differences): **7th International Conference on Information Systems Security and Privacy (ICISSP 2021)

**Date: **received 31 Jan 2021

**Contact author: **ahmad at sec ee kagu tus ac jp

**Available format(s): **PDF | BibTeX Citation

**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.

**Version: **20210201:072612 (All versions of this report)

**Short URL: **ia.cr/2021/113

[ Cryptology ePrint archive ]