On Complexity and Approximability of Optimal DoS Attacks on Multiple-Tree P2P Streaming Topologies

We investigate the hardness of malicious attacks on multiple-tree topologies of push-based Peer-to-Peer streaming systems. In particular, we study the optimization problem of finding a minimum set of target nodes to achieve a certain damage objective. For this, we differentiate between three natural and increasingly complex damage types: global packet loss, service loss when using Multiple Description Coding, and service loss when using Forward Error Correction. We show that each of these attack problems is NP-hard, even for an idealized attacker with global knowledge about the topology. Despite tree-based topologies seem susceptible to such attacks, we can even prove that (under strong assumptions about NP) there is no polynomial time attacker, capable of guaranteeing a general solution quality within factors of c₁ log(n) and c₂2log^1-δn (with n topology nodes, δ = 1/log log^d n for d <; 1/2 and constants c₁, c₂), respectively. To our knowledge, these are the first lower bounds on the quality of polynomial time attacks on P2P streaming topologies. The results naturally apply to major real-world DoS attackers and show hard limits for their possibilities. In addition, they demonstrate superior stability of Forward Error Correction systems compared to Multiple Description Coding and give theoretical foundation to properties of stable topologies.