How to reconstruct (anonymously) a secret cellular automaton
This work addresses the problem of anonymous secret reconstruction in threshold schemes, which is relevant for privacy-preserving cryptographic applications.
The paper introduces a threshold secret sharing scheme based on cellular automata that enables anonymous reconstruction, where the secret is recovered from shares without participant identities. It redefines the secret space using Mutually Orthogonal Latin Squares and discusses trade-offs between the number of secrets and recovery complexity.
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.