Approximation Algorithms for Key Management in Secure Multicast

TL;DR

This paper develops approximation algorithms for optimizing key management in secure multicast systems, minimizing communication costs during group updates, and addresses the problem's computational complexity.

Contribution

It introduces a polynomial-time approximation scheme and a constant-factor approximation algorithm for key hierarchy optimization considering routing costs.

Findings

Polynomial-time approximation scheme for minimizing multicast messages.

NP-hardness of the problem on tree networks with uniform update frequencies.

A constant-factor approximation algorithm for general weighted graphs with nonuniform update frequencies.

Abstract

Many data dissemination and publish-subscribe systems that guarantee the privacy and authenticity of the participants rely on symmetric key cryptography. An important problem in such a system is to maintain the shared group key as the group membership changes. We consider the problem of determining a key hierarchy that minimizes the average communication cost of an update, given update frequencies of the group members and an edge-weighted undirected graph that captures routing costs. We first present a polynomial-time approximation scheme for minimizing the average number of multicast messages needed for an update. We next show that when routing costs are considered, the problem is NP-hard even when the underlying routing network is a tree network or even when every group member has the same update frequency. Our main result is a polynomial time constant-factor approximation algorithm for the general case where the routing network is an arbitrary weighted graph and group members have nonuniform update frequencies.