Infinite Classes of Conference key Distribution Systems Constructed from Difference Families

Abstract

Combinatorial designs are a powerful tool because of their beautiful combinatorial structure that can help in many applications, such as coding theory or cryptography. A conference key distribution system is a scheme to design a conference key, and then to distribute this key to only participants attending the conference in order to communicate with each other securely. In this paper, we present an efficient conference key distribution system using difference families. Using techniques for creating the conference key and for performing authentication based on identification information, the communication protocol is designed. Applying the known results on difference families, we obtain many new infinite classes of conference key distribution systems. In special classes of difference families, the message overhead is $O(v\sqrt{tv})$, where $v$ is the number of participants and $t$ is the number of the $k$-elements subsets that consist of the difference family. The security of the presented protocol, which is an important problem in the construction of a secure system, is proved to be as computationally difficult to calculate as factoring and discrete logarithms.