What is Access Structure

In secret sharing, a secret is distributed between various participants in a manner that an authorized group of participants in the appropriate access structures can recover 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 chapter discusses a computationally secure publicly verifiable secret sharing scheme constructed using the three-dimensional cellular automata (3D CA). The initial configuration of the 3D CA is the secret. 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, the authors added a verifiability layer such that a dealer posts a public share and a private share to each shareholder. The NIST test suite has been used to calculate the randomness of the shares.