Publicly verifiable threshold secret sharing based on three-dimensional-cellular automata

Secret sharing schemes are being widely used to distribute a secret between various participants so that an authorized subset of participants belonging to appropriate access structures can reconstruct this secret. However, a dealer might get corrupted by adversaries and may influence this secret sharing or the reconstruction process. Verifiable secret sharing (VSS) overcomes this issue by adding a verifiability protocol to the original secret sharing scheme. This article proposes a computationally secure publicly verifiable secret sharing scheme based on the three-dimensional cellular automata (3D-CA). Unlike the more widely used linear secret sharing schemes or secret sharing scheme based on the Chinese remainder theorem, our proposed scheme performs the secret sharing using 3D-CA. The secret is considered one of the initial configurations of the 3D-CA, and the following configurations are devised to be the shares distributed among the participants. Update mechanisms and various rules make it hard for an adversary to corrupt or duplicate a share. To make it even more efficient, we have added a verifiability layer such that a dealer posts a public share and private share to each shareholder. The verifiability layer reduces the interaction between dealer and participants and hence increases the security. The randomness of the shares has been calculated using the National Institute of Standards and Technology statistical test suite.