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Distributed denial of service (DDoS) attacks continue to plague the Internet. Defense against these attacks is complicated by spoofed source IP addresses, which make it difficult to determine a packet's true origin. We propose Pi (short for path identifier), a new packet marking approach in which a path fingerprint is embedded in each packet, enabling a victim to identify packets traversing the same paths through the Internet on a per packet basis, regardless of source IP address spoofing. Pi features many unique properties. It is a per-packet deterministic mechanism: each packet traveling along the same path carries the same identifier This allows the victim to take a proactive role in defending against a DDoS attack by using the Pi mark to filter out packets matching the attackers' identifiers on a per packet basis. The Pi scheme performs well under large-scale DDoS attacks consisting of thousands of attackers, and is effective even when only half the routers in the Internet participate in packet marking. Pi marking and filtering are both extremely lightweight and require negligible state. We use traceroute maps of real Internet topologies (e.g. CAIDA's Skitter (2000) and Burch and Cheswick's Internet Map (1999, 2002)) to simulate DDoS attacks and validate our design.