Quantum ($t$,$n$) Threshold Multi-Secret Sharing based on Cluster States

TL;DR

This paper introduces a practical quantum ($t$,$n$) threshold multi-secret sharing protocol using cluster states, enabling secure, efficient, and multi-secret transmission with minimal quantum operations and proven security.

Contribution

It presents the first quantum ($t$,$n$) threshold multi-secret sharing protocol based on cluster states and Lagrangian interpolation, enhancing security and practicality.

Findings

Protocol is secure against external and internal attacks.

Experimental validation confirms correctness and feasibility.

Requires only common quantum operations, suitable for current technology.

Abstract

Quantum secret sharing is an encryption technique based on quantum mechanics, which utilizes uncertainty principle to achieve security in transmission. Most protocols focus on the study of quantum ($n,n$) or ($t,n$) threshold single secret sharing. In this paper, the first quantum ($t,n$) threshold multi-secret sharing protocol based on Lagrangian interpolation and cluster states is proposed, which requires only $t$ instead of $n$ participants to reconstruct multiple quantum secrets. The protocol exploits the security properties of the cluster state to transmit shared information in two parts, quantum and classical, where the shares remain private after reconstructing quantum secrets. Meanwhile, extending the new measurement basis in cluster states enables participants to transmit quantum information without preparing particles. In the presented protocol, the dealer can be offline after sending secrets. And required quantum operations are all common quantum operations, thus the protocol is practical under the current technical conditions. It is proven to be theoretically secure against external and internal attacks by analyzing the protocol under several common external attacks and internal attacks. In addition, experiments on IMB Q prove that the protocol satisfies correctness and feasibility.