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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.

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