我们研究基于元胞自动机(CA)的门限秘密共享方案,该方案支持匿名重构,即仅依据份额即可恢复秘密,而无需知晓参与者的身份。为此,我们重新审视了基于CA的(2,n)门限方案的基本刻画——该刻画以相互正交拉丁方(MOLS)为理论基础,并将秘密空间重新定义为MOLS族本身;由此构造的新方案可实现对秘密CA规则的匿名重构。最后,我们讨论了可共享的秘密CA数量与恢复阶段计算复杂度之间的权衡关系。
We consider threshold secret sharing schemes based on cellular automata (CA) that allows for anonymous reconstruction, meaning that the secret can be recovered only as a function of the shares, without knowing the participants' identities. To this end, we revisit the basic characterization of $(2,n)$ threshold schemes based on CA in terms of Mutually Orthogonal Latin Squares (MOLS), and redefine the secret space as the MOLS family itself, showing that the new resulting scheme enables anonymous reconstruction of secret CA rules. Finally, we discuss the trade-off between the number of secret CA that can be shared and the computational complexity of the recovery phase.