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.

翻译：我们考虑基于元胞自动机（CA）的阈值秘密共享方案，该方案支持匿名重构，即秘密仅能作为份额的函数而恢复，无需知晓参与者的身份。为此，我们重新审视了基于CA的 $(2,n)$ 阈值方案在互斥拉丁方（MOLS）框架下的基本刻画，并将秘密空间重新定义为MOLS族本身，从而证明新方案能够实现对秘密CA规则的匿名重构。最后，我们讨论了可共享秘密CA数量与恢复阶段计算复杂度之间的权衡。