Unique Keys Enabling Multithreshold Schemes

. We present a generalization of Shamir's threshold scheme [5]. The Shamir's scheme shows how to divide a key D into n pieces such that it is easily reconstructable from any k pieces, but that even complete knowledge of k \Gamma 1 pieces reveals no information about D. Shamir calls it a (k,n) threshold scheme. We propose a system with s security levels, each of them requiring k l partial keys for computation of a secret key D l for level l. The higher is the security level, the more keys are required. We call our scheme a (k l ; s; n) multithreshold scheme, l = 1; \Delta \Delta \Delta ; s. 1 Introduction We consider the following scenario. A group of ten experts is responsible for operating a protected system. To perform some minor changes in the system, at least three of them must be present. If they want to change more sensitive parts, more experts from the group have to agree. The more of them are involved, the more sensitive parts of the system under protection are accessible. W..