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.

翻译：如何高效地在多个参与者之间共享秘密是密钥管理中一个非常重要的问题。本文提出了一种基于GHZ态的多秘密共享方案。首先，分发者利用单调张成程序对秘密进行编码，生成相应的秘密份额分发给参与者。然后，每个参与者使用广义泡利算子将其自身的秘密份额嵌入到传输粒子中。想要获取秘密的参与者可以通过执行GHZ态联合测量同时获取多个秘密。此外，该方案基于单调张成程序，其访问结构比(t,n)门限访问结构更具一般性。与其他方案相比，本文提出的方案效率更高且计算开销更小。