Randomized and set-system based collusion resistant key predistribution schemes

Abstract

One problem that frequently arises is the establishment of a secure connection between two network nodes. There are many key establishment protocols that are based on Trusted Third Parties or public key cryptography which are in use today. However, in the case of networks with frequently changing topology, such an approach is difficult to apply. In this paper we give a formal definition of collusion resistant key predistribution schemes and then propose such a scheme based on probabilistically created set systems. The resulting key sets are shown to have a number of desirable properties that ensure the confidentiality of communication sessions against collusion attacks by other network nodes. Moreover we associate our deterministic key pre-distribution scheme with the theory of set family construction methods showing that the mathematical properties possessed by the sets of such families lead to key sets with the aforementioned desirable properties.