Quantum security computation on shared secrets

TL;DR

This paper introduces a new $(n,n)$ threshold quantum secret sharing scheme applicable for any number of participants, utilizing a quantum circuit with Clifford and Toffoli gates to enhance security analysis.

Contribution

It extends previous schemes to any number of participants and employs a quantum circuit-based approach for security evaluation.

Findings

Scheme works for any $n \\in Z^+$

Uses Clifford and Toffoli gates in the quantum circuit

Provides security analysis against dishonest participants

Abstract

Ouyang et al. proposed an $(n,n)$ threshold quantum secret sharing scheme, where the number of participants is limited to $n=4k+1,k\in Z^+$, and the security evaluation of the scheme was carried out accordingly. In this paper, we propose an $(n,n)$ threshold quantum secret sharing scheme for the number of participants $n$ in any case ( $n\in Z^+$ ). The scheme is based on a quantum circuit, which consists of Clifford group gates and Toffoli gate. We study the properties of the quantum circuit in this paper and use the quantum circuit to analyze the security of the scheme for dishonest participants.