Patrick P. C. Lee, Vishal Misra, Dan Rubenstein Distributed Algorithms for Secure Multipath Routing in Attack-Resistant Networks Patrick P. C. Lee, Vishal Misra, Dan Rubenstein 授課教授：林永松教授 學生：D96725006 陳霈語 　　　R95725004 楊琇珊 　　　R95725016 王貝瑜

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 The network will then constitute a set of critical links, defined as the links whose attack costs cannot be further decreased without increasing . 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 represents the actual proportion of data loss for the data session Number of executions of Preflow-push Routing overhead The total number of routing packets transmitted during the simulation. Routing overhead: The total number of routing packets transmitted during the simulation.

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

Experiment 1 – Bound-Control Number of executions of the Preflow-Push algorithm

Experiment 1 – Bound-Control Routing overhead

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.

Experiment 3 Lex-Control algorithm subject to different scales of uniform link attacks.

Experiment 4 Lex-Control algorithm subject to the proportional and worst-case multi-link attacks 同時能reduce 兩種情況的 attack cost，按attack cost比例攻擊 / 只攻擊highest attack cost (worst-case)

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 severe attack costs (e.g., the second and third worst-case link attacks)

Attack-resistant network a specialized network that protects end hosts by surrounding them with a defensive architecture Example SOS (Secure Overlay Services) Two crucial but contradicting criteria (1) resiliency: the network should offer alternate paths in the face of node failures (2) security: the network should confine the damage caused by compromised nodes. To evaluate their trade-off via simulation 重疊網路(Overlay Network)係指利用Proxy 等技術，將某應用伺服器多點散布在廣大的 網路中，以達到增進網路安全之目的。在攻擊發生時，可以立刻有效的針對分散的攻擊加以阻擋來保 護伺服器。 SOS(Secure Overlay Services) 同樣使用 Overlay Network 技術來防禦。而 SOS 架構簡單 來說就是 Overlay 和 Filter。使用 Overlay 來隱藏行蹤並且用 Filter 來過濾攻擊封包。 以上兩個criteria雖然重要，但兩者相互抵觸，有trade-off關係。以simulation來取得兩者平衡

Example of an attack-resistant network

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: Simulation results for multi-link attacks