On Metering Schemes

In order to decide on advertisement fees for web servers, Naor and Pinkas introduced (threshold) metering schemes secure against coalitions of corrupt servers and clients. Several researchers have generalized the idea of Naor and Pinkas: first metering scheme with pricing and dynamic multi-threshold metering schemes have been proposed; later the solution has been extended to allow general access structures and an approach on linear algebra has been introduced. But all previous papers consider the following scenario a general (or threshold) access structure for the clients and a threshold access structure for the servers. We generalize the model allowing also a general access structure for the servers, moreover we strengthen it limiting the possibility of corrupt servers to help each other. A more efficient protocol satisfying the requirements of the new model is described. Naor and Pinkas show that one should be able also to detect illegal behavior of clients, i.e., one needs to verify the shares received from clients. Most metering schemes do not offer this feature. But Ogata and Kurosawa pointed out a minor flaw in the extension protocol by Naor and Pinkas providing detection of such illegal behavior and propose a correction. So, we extend the used linear algebra approach in order to build robust unconditionally secure general metering schemes. As a tool to achieve this goal we introduce doubly-labelled matrices and an operation on such matrices. Certain properties of this operation are proven.