Robust metering schemes for general access structures

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. They show that one should be able 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. In this paper we extend the linear algebra approach from Nikov et al. 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.