Secret sharing schemes have been proven to be useful in various fields of interest such as cryptologic key management and multi-party secure protocols. Recent developments show the importance of what is called multiple-secret sharing schemes. This paper gives a new and order theoretic approach to this topic. Its advantage is the capability of modelling implications in a set of involved secrets. We introduce a concept of homogeneity and adapt classical notions like that of information rate and perfectness to the generalized context. Our main results are conceptual and furthermore yield constructions of large classes of homogeneous and perfect control schemes using unital modules and their automorphism groups.
|Title of host publication||Recent advances in geometry and topology : the 6th International workshop on differential geometry and its applications : the 3rd German-Romanian Seminar on geometry, Cluj-Napoca, 1-6 Sept. 2003|
|Number of pages||8|
|Publication status||Published - 2004|