A combinatorial interpretation of ramp schemes

Ramp schemes are means by which a (large) secret can be shared among a group of participants in such a way that only sets of at least k participants can reconstruct the secret and the amount of information that of less than k participants can obtain is strictly controlled. This is of the concept of a threshold scheme. The current theory concerning ramp schemes will be here alongside some new results. We consider the class of strong ramp schemes and provide a combinatorial classification of optimal ramp schemes by showing their equivalence to ideal threshold schemes. A review of the previous literature will be presented.