Distributed Algorithms for Secure Multipath Routing Patrick P. C. Lee, Vishal Misra, Dan Rubenstein Distributed Network Analysis (DNA) Lab, Columbia University March 17, 2005

Outline Motivation: Security objectives Distributed algorithms: Why do we use multipath routing to achieve security? Security objectives Distributed algorithms: Bound-Control algorithm Lex-Control algorithm Simulation results

Motivation Problem of single-path routing: source sink An attack/failure shuts down the entire session.

Motivation Protection with multipath routing: source sink An attack/failure causes less damage.

Goals Determine the multipath routes that achieve the “best” security: Minimize the worst-case data loss with/without bandwidth constraints Minimize “severe” data loss with/without bandwidth constraints based on lexicographic optimization Implement a distributed solution: No need to know the global network topology Allow nodes to locally decide link costs Suitable for independently administered networks (e.g., RON)

Previous Work Lexicographic optimization: Minimize a non-increasing link-cost sequence a = (a1, a2, …, an) Find a*, where a* = (a1*, a2*, …, an*) ≤ a = (a1, a2, …, an) for every link-cost sequence a Georgiadis et al.’s solution [ToN ’02]: Recursively solve minimax problems on subgraphs Limitations: Centralized solution Does not consider varied bandwidth constraints

Our Work Develop two distributed algorithms Bound-Control and Lex-Control: Support fixed-rate model and maximal-rate model Fixed rate: a data session sends data at a fixed rate Maximal rate: a data session sends data at the maximal rate across all network links (i.e., equiv. to min-cut) Suitable for overlay networks and ad hoc networks Prove their optimality in response to single-link attacks. Evaluate the algorithms via simulations in response to single-link and multi-link attacks.

Model Assumptions Static network topology Single source-sink pair Easily generalized to networks with multiple customers/providers Infrequent link attacks/failures Optimize solutions for single-link attacks Evaluate performance for both single-link and multi-link attacks

How to Quantify the Cost of a Single-link Attack? Attack cost of link l: al = xl * cl xl – proportion of session data allocated to link l cl - security constant Measure the vulnerability of link l to an attack Possible physical interpretations: Attack success probability Proportion of xl lost during an attack In practice, security constants can be obtained from security monitoring systems or statistical measurements

Example of Setting Security Constants More vulnerable to attacks (e.g., cl = 0.9) Wireless link sink source Wired link Less vulnerable to attacks (e.g., cl = 0.1) In subsequent discussion of objectives, assume cl = 1 for all links, i.e., attack cost = data loss.

One possible data allocation. Objective 1 One possible data allocation. 5 5 Fixed data rate 10Mb/s 5 source sink 5 5 5 Minimize the worst-case data loss under the single-link attack

Another possible data allocation. Objective 1 Another possible data allocation. Fixed data rate 10Mb/s 5 5 5 5 source 5 sink 5

Another possible data allocation. Objective 1 Another possible data allocation. 5 5 Fixed data rate 10Mb/s 5 5 source 5 sink 5 Worst-case data loss cannot be less than 50%

Bandwidth-limited link Objective 2 6 6 Fixed data rate 10Mb/s 6 source sink Bandwidth-limited link (Only 4Mb/s allowed) 4 4 4 Minimize the worst-case data loss subject to bandwidth constraints

Lexicographic Optimization Objective 3 Lexicographic Optimization (6, 6, 6, 4, 4, 4, 0, 0, 0, 0)  (6, 4, 3, 3, 3, 3, 2, 2, 2, 2) 2 sink 3 source 4 6 sink 6 4 source Fixed data rate 10Mb/s Bandwidth-limited link (Only 4Mbs allowed) Minimize the ith worst-case data loss subject to bandwidth constraints, given already minimized attack costs for the worst-case, 2nd worst-case,…, (i-1)th worst-case.

Solving Objective 1: Preflow-Push Map minimax problem to max-flow problem Preflow-push algorithm [Goldberg & Tarjan, 89]: Nodes find the maximum flow from source to sink in a distributed fashion. Basic idea of solving Objective 1 [Ahuja, 86]: Each node sets capacity constraints of its outgoing links: cap(l) = 1/cl. Nodes solve max-flow problem under capacity constraints in a distributed fashion. Each node allocates data for its outgoing links: (link flow) / (max flow).

Solving Objective 2: Bound-Control Bandwidth constraint: fraction bound bl bl = (bandwidth of link l) / (session data rate) Capacity constraint: cap(l) = min(1/cl, bl*f) f = flow reaching the sink Upper bound in max-flow problem Basic idea of solving Objective 2: Repeat Distributed execution of Preflow-Push Each node adjusts capacity constraints for its outgoing links Until capacity constraints satisfied

Solving Objective 3: Lex-Control Basic idea – solve lexicographic optimization: Repeat Distributed execution of Bound-Control Each node identifies critical links among its outgoing links Until all critical links spotted Critical Links Links whose data allocation has to be fixed to preserve the optimal attack cost In practice, Lex-Control provides the necessary resilience in 3 or 4 lexicographic iterations. Lexicographic iteration

Recap of Algorithms Lex-Control algorithm Bound-Control algorithm Preflow-Push algorithm Hierarchical solution to the three security objectives

Experimental Setup Consider three random networks generated by BRITE: 200 nodes, 600 links 200 nodes, 800 links 200 nodes, 1000 links Randomly assign security constants (0 to 1) and bandwidths (1 to 5 Mb/s) for all links Metrics: Attack cost Number of executions of Preflow-push Routing overhead

Experiment 1 – Bound-Control Minimized worst-case attack cost vs. different session throughputs

Experiment 1 – Bound-Control Network setting Attack cost 200 nodes, 600 links 0.73 200 nodes, 800 links 0.72 200 nodes, 1000 links 0.78 Single shortest path approach Network setting Attack cost 200 nodes, 600 links 0.34 200 nodes, 800 links 0.19 200 nodes, 1000 links 0.16 Bound-Control (for maximal-rate model) Bound-Control reduces the worst-case attack cost by 50-70%.

Experiment 2 – Lex-Control Number of links with severe attack cost vs. number of lexicographic iterations. Attack cost is severe if it’s at least 25% of the worst-case attack cost. E.g., for the attack-cost sequence (1, 0.5, 0.25, 0.1, 0.1), number of links with severe attack cost is 3.

Summary of Experiments Bound-Control vs. Single-Path Routing: Reduce the worst-case attack cost by 50-70% Lex-Control vs. Bound-Control Reduce # of links with severe attack costs by ~50% Reduce aggregate attack cost in multi-link attacks: by ~40% in the uniform 50-link attack by ~23% in the proportional 5-link attack by ~12% in the worst-case 5-link attack 3 or 4 lexicographic iterations are enough

Conclusions In this talk: More details in the paper: Proposed two distributed algorithms Bound-Control and Lex-Control that optimize respective security objectives. Illustrated performance of Bound-Control and Lex-Control via simulation analysis. More details in the paper: Optimality proof Simulation results for multi-link attacks