How to reconstruct (anonymously) a secret cellular automaton

Luca Mariot; Federico Mazzone; Luca Manzoni; Alberto Leporati

How to reconstruct (anonymously) a secret cellular automaton

Luca Mariot
, Federico Mazzone
, Luca Manzoni
, Alberto Leporati

Research output: Working paper › Preprint › Academic

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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.

Original language	English
Publisher	ArXiv.org
Publication status	Published - 13 Apr 2026

Keywords

cs.CR
math.CO

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2604.11362v1Final published version, 199 KB

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AU - Leporati, Alberto

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N2 - 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.

AB - 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.

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M3 - Preprint

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ER -

How to reconstruct (anonymously) a secret cellular automaton

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