# Efficient Quantum Secret Sharing Scheme Based On Monotone Span Program

## TL;DR

This paper introduces an efficient multi-secret sharing scheme using GHZ states and monotone span programs, enabling flexible access structures and simultaneous secret retrieval with reduced computational cost.

## Contribution

It presents a novel quantum secret sharing scheme based on monotone span programs that improves efficiency and generalizes access structures beyond traditional threshold schemes.

## Key findings

- More efficient than existing schemes
- Supports general access structures
- Allows simultaneous retrieval of multiple secrets

## Abstract

How to efficiently share secrets among multiple participants is a very important problem in key management. In this paper, we propose a multi-secret sharing scheme based on the GHZ state. First, the distributor uses monotone span program to encode the secrets and generate the corresponding secret shares to send to the participants. Then, each participant uses the generalized Pauli operator to embed its own secret share into the transmitted particle. The participant who wants to get the secrets can get multiple secrets at the same time by performing a GHZ-state joint measurement. Futhermore, the scheme is based on a monotone span program, and its access structure is more general than the access structure (t,n) threshold. Compared with other schemes, our proposed scheme is more efficient, less computational cost.