A ramp scheme for Key Predistribution System against collusion of users and centers

In this paper, we consider a ramp scheme for Key Predistribution System (KPS). In the ramp scheme, it can be regarded as one kind of generalization of KPS, and the required resources can be reduced at the cost of a security degradation which depends on the size of users. We define a ramp scheme for KPS, show lower bound on the amount of user' s information needed to generate a common key, and design a protocol that realize a ramp scheme for KPS.