Secret sharing on the d-dimensional cube

Secret sharing on the d-dimensional cube

We prove that for d > 1 the information rate of the perfect secret sharing scheme based on the edge set of the d-dimensional cube is exactly 2/d. Using the technique developed, we also prove that the information rate of the infinite d-dimensional lattice is 1/d.

On Converting Secret Sharing Scheme to Visual Secret Sharing Scheme

Traditional Secret Sharing (SS) schemes reconstruct secret exactly the same as the original one but involve complex computation. Visual Secret Sharing (VSS) schemes decode the secret without computation, but each share is m times as big as the original and the quality of the reconstructed secret image is reduced. Probabilistic visual secret sharing (Prob.VSS) schemes for a binary image use only...

Notes on Secret Sharing

These are lecture notes from the first two lectures in Fall 2016, focusing on technical material we saw for secret sharing (including a proof by reduction using the hybrid proof technique). The notes do not include the general introduction to the course and modern crypto, as well as some discussion and motivation for secret sharing. Also not covered here is Shamir’s secret sharing, which we saw...

On-Line Secret Sharing

We propose a new construction for computationally secure secret sharing schemes with general access structures where all shares are as short as the secret. Our scheme provides the capability to share multiple secrets and to dynamically add participants on-line, without having to redistribute new shares secretly to the current participants. These capabilities are gained by storing additional aut...

Large k-D Simplices in the d-Dimensional Cube