On secret sharing schemes, matroids and polymatroids - Martí-Farré Jaume; Padró Carles (Journal of mathematical cryptology, 2010)
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.