On secret sharing schemes, matroids and polymatroids

Abstract

The complexity of a secret sharing scheme is defined as the ratio between the maximum length of the shares and the length of the secret. The optimization of this parameter for general access structures is an important and very difficult open problem in secret sharing. We explore in this paper the connections of this open problem with matroids and polymatroids.

Keywords

• secret sharing
• optimization of secret sharing schemes for general access structures
• ideal secret sharing schemes
• matroids
• polymatroids