Natural Generalizations of Threshold Secret Sharing
- Cite this paper as:
- Farràs O., Padró C., Xing C., Yang A. (2011) Natural Generalizations of Threshold Secret Sharing. In: Lee D.H., Wang X. (eds) Advances in Cryptology – ASIACRYPT 2011. ASIACRYPT 2011. Lecture Notes in Computer Science, vol 7073. Springer, Berlin, Heidelberg
We present new families of access structures that, similarly to the multilevel and compartmented access structures introduced in previous works, are natural generalizations of threshold secret sharing. Namely, they admit an ideal linear secret sharing schemes over every large enough finite field, they can be described by a small number of parameters, and they have useful properties for the applications of secret sharing. The use of integer polymatroids makes it possible to find many new such families and it simplifies in great measure the proofs for the existence of ideal secret sharing schemes for them.