Asymptotically Optimal Tree-based Group Key Management Schemes

TL;DR

This paper analyzes and improves tree-based group key management schemes for secure multicast, demonstrating asymptotic optimality for withdrawal costs and proposing a new scheme that also considers join costs, with simulation validation.

Contribution

It proves the asymptotic optimality of the Selcuk-Sidhu scheme and introduces a new scheme that optimizes both join and withdrawal costs.

Findings

Selcuk-Sidhu scheme is asymptotically optimal for withdrawal costs.

Proposed scheme is asymptotically optimal for both join and withdrawal costs.

Simulation shows good performance of the new scheme in nonasymptotic cases.

Abstract

In key management schemes that realize secure multicast communications encrypted by group keys on a public network, tree structures are often used to update the group keys efficiently. Selcuk and Sidhu have proposed an efficient scheme which updates dynamically the tree structures based on the withdrawal probabilities of members. In this paper, it is shown that Selcuk-Sidhu scheme is asymptotically optimal for the cost of withdrawal. Furthermore, a new key management scheme, which takes account of key update costs of joining in addition to withdrawal, is proposed. It is proved that the proposed scheme is also asymptotically optimal, and it is shown by simulation that it can attain good performance for nonasymptotic cases.