Problem statement • Our goal:

• build intrusion tolerant replicated service• good performance over WANs

• Our approach:• intrusions are Byzantine faults• use Byzantine quorum systems• deploy on WANs

• Performance measures:• average client response time• network congestion

Quorum systems

• Quorum system:• collection of sets with nonempty intersection

• Byzantine (b):• tolerate up to b failures• intersection size masks failures

• Quorum placement:• mapping from quorum elements to nodes of network

Measures

• Average delay over all clients: Avgclients(Expquorums(delay(client,quorum)))

• Congestion:Maxedges(rel. congestion(edge))

Large-scale intrusion tolerant services over WANsFlorian Oprea, Michael K. Reiter, Carnegie Mellon University

April 27, 2006

3

4

5

delay = 5

congestion = 3

Problem definition and results • (QPPD, QPPC) Given quorum system Q, access strategy p, network G with node and edge capacities, find placement f , so that:

• average delay or congestion minimized• load(v) ≤ capacity(v) for all nodes v

• Finding optimal placements for arbitrary quorums is NP-hard for both problems; for one case of QPPC, hard to approximate within any constant.• constant approximation algorithms for QPPD provided node capacities exceeded by a small factor:

• (5a/(a-1), 2) for arbitrary quorum systems• (5, 1) for Majority and Grid [GMOR05]

• two models for QPPC: multiple paths and single paths• polylog(size(G)) approximation algorithms for each model, provided exceed node capacities by a factor of 2 [GGMOR06]

Preliminary experimental results

[GMOR05] : A. Gupta, B. Maggs, F. Oprea, M. K Reiter. Quorum placement in networks to minimize access delays. PODC 2005. [GGMOR06] : D. Golovin, A. Gupta, B. Maggs, F. Oprea, M. K. Reiter. Quorum placement in networks: Minimizing network congestion. PODC 2006.