How to reconstruct (anonymously) a secret cellular automaton

2026-04-13

AI Summary

This work addresses the challenge of achieving anonymous reconstruction in cellular automaton (CA)-based threshold secret sharing without relying on participants’ identity information. The authors propose a novel (2, n) threshold scheme by defining the secret space as a family of mutually orthogonal Latin squares (MOLS), enabling the original CA rule—i.e., the secret—to be reconstructed solely from the shares themselves. This approach realizes truly anonymous reconstruction, as no participant identifiers are required during the recovery phase. Furthermore, the study uncovers an inherent trade-off between the number of shareable secrets and the computational complexity of reconstruction, offering new insights for privacy-preserving distributed storage systems.

Technology Category

• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Machine Learning: Privacy
• Search and Optimization: Distributed Search

Application Category

• Security and Privacy: Large-scale security measurements
• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems

Abstract

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.

Problem

• cellular automata
• secret sharing
• anonymous reconstruction
• threshold scheme
• MOLS

Innovation

• anonymous reconstruction
• cellular automata
• threshold secret sharing
• Mutually Orthogonal Latin Squares
• secret sharing scheme