## Cryptology ePrint Archive: Report 2005/177

Secret sharing on the $d$-dimensional cube

Laszlo Csirmaz

Abstract: 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 $1/d$.

Category / Keywords: foundations / Secret sharing scheme, polymatroid, information theory