Secret sharing on the $d$-dimensional cube
arXiv:1310.4640v118 citations
Originality Incremental advance
AI Analysis
This solves a specific problem in cryptography and information theory by establishing exact bounds for secret sharing schemes on geometric structures.
The paper determined the optimal information ratio for perfect secret sharing on the d-dimensional cube, proving it is exactly d/2, and extended this to show the infinite d-dimensional lattice has an information ratio of d.
We prove that for $d>1$ the best information ratio of the perfect secret sharing scheme based on the edge set of the $d$-dimensional cube is exactly $d/2$. Using the technique developed, we also prove that the information ratio of the infinite $d$-dimensional lattice is $d$.