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We propose a framework and methodology for quantifying the effect of denial of service (DoS) attacks on a distributed system. We present a systematic study of the resistance of gossip-based multicast protocols to DoS attacks. We show that even distributed and randomized gossip-based protocols, which eliminate single points of failure, do not necessarily eliminate vulnerabilities to DoS attacks. We propose Drum - a simple gossip-based multicast protocol that eliminates such vulnerabilities. Drum was implemented in Java and tested on a large cluster. We show, using closed-form mathematical analysis, simulations, and empirical tests, that Drum survives severe DoS attacks.