Multicast key distribution schemes based on Stinson-Van Trung designs
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MULTICAST KEY DISTRIBUTION SCHEMES BASED ON STINSON–VAN TRUNG DESIGNS A. N. Alekseichuk† and S. N. Konyushok ‡
UDC 621.391:517.95
The efficiency characteristics of multicast key distribution schemes based on ( u, b , r, l )-designs are investigated. The stability and connectivity of such designs are estimated. These estimates generalize and enhance the well-known estimates for the efficiency characteristics of multicast key distribution schemes based on incomplete block designs. Keywords: key distribution scheme, broadcast encoding, covering problem, combinatory design, block design, block code. INTRODUCTION A multicast key distribution scheme (MKDS) is a cryptographic protocol, using which an agent that functions as a key distribution center (KDC) transmits some auxiliary confidential information to abonents of a communication network. This information will allow the abonents that belong to a certain privileged coalition to restore a private key transmitted in an encoded form from the KDC by a broadcast communication channel (this is why MKDSs are also called broadcast encryption schemes). Multicast key distribution schemes are proposed in [1, 2]. At present, publications on the analysis of properties of such schemes and methods of their construction number in the tens. Noteworthy are the reviews [3, 4] and studies [5–7], which, in particular, address various aspects of the practical application of MKDSs. A general approach to constructing multicast key distribution schemes based on coverings of a set V of abonents by certain subsets was proposed in [8] (and later independently in [5]). Each such a subset B (a covering block) is associated with a private key generated in the KDC. Then a set of private keys corresponding to subsets B that contain x is transmitted to each abonent x ÎV by a protected communication channel. The private key to be passed to some privileged coalition P Í V is encoded using private keys of abonents from P that correspond to certain subsets B Í P, which form the covering of the set P. The authors of [8] estimated also the parameters that characterize practical efficiency of the MKDS in which the subsets B are defined as blocks of balanced incomplete block designs with the set of elements V [9, 10]. The purpose of the present paper is to analyze the characteristics of a more general class of multicast key distribution schemes that correspond to the so-called ( u, b , r, l )-designs introduced by D. R. Stinson and T. van Trung [11]. The MKDSs under study are unconditionally (information-theoretic) stable and include, as a special case, MKDSs based on the block designs from [8] and on the block codes from [12]. The results obtained in the paper show that though MKDSs based on ( u, b , r, l )-designs rank below one of the best unconditionally stable MKDSs (so-called CST schemes) [5], they are more efficient than schemes from [8]. In particular, the total number of private keys in MKDSs that correspond to ( u, b , r, l )-design can be less than the number of network abonents, which is fundame
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