1. Network Coding and Reliable Communications Group A Multi-hop Multi-source Algebraic Watchdog Muriel Médard † Joint work with MinJi Kim †, João Barros ‡ † Massachusetts Institute of Technology ‡ University of Porto

2. Network Coding and Reliable Communications Group Background Secure network coding – Network error correction [Yeung et al. 2006] – Resilient coding in presence of Byzantine adversaries [Jaggi et al. 2007] – Confidential coding scheme [Vilela et al. 2008] – Signature scheme [Charles et al. 2006][Zhao et al. 2007] – Locating attackers [Siavoshani et al. 2008] – NOTE: downstream nodes check for adversaries, the upstream nodes unaware. Watchdog and pathrater [Marti et al. 2000] – Extensions of Dynamic Source Routing – Detect/mitigate misbehavior of the next node – Use wireless medium: promiscuous monitoring Algebraic Watchdog [Kim et al. 2009] – Combine the benefits of network coding and watchdog – Extend to multi-hop, multi-source setting

3. Network Coding and Reliable Communications Group Problem Statement Wireless network G = (V, E 1,E 2 ). – V : Set of nodes in the network – E 1 : Set of hyperedges for connectivity/wireless links – E 2 : Set of hyperedges for interference Transition probability known (Binary symmetric channel) Intended transmission in E 1 Overhearing with noise in E 2 Is v m+1 consistent with… Overheard packets from v 2, v 3,… v m ? Channel statistics?

4. Network Coding and Reliable Communications Group Problem Statement How can upstream nodes ( v 1, v 2, …,v m ) detect misbehaving node ( v m+1 ) with high probability? Routing: Packets individually recognizable Network Coding: Packets are mixed Errors from BSC channel : Probabilistic detection Few bit errors can make dramatic change in the algebraic interpretation Intended transmission in E 1 Overhearing with noise in E 2

5. Network Coding and Reliable Communications Group Packet Structure A node v i that receives messages x j ’s and transmits p i – Note: hash is contained in one hop, dependent on in-degree Goal: If v i transmits x i = e + Σ α j x j where e≠0, detect it with high probability. – Even if | e | small, the algebraic interpretation may change dramatically. a j ’sxixi coding coefficients a j ’s coded data x i = Σ α j x j with error- correcting code C i = (n, k i, d i ) p i = h(x j ) hash of received messages h(x j ) h(x i ) hash of message h(x i ) a j ’sh(x j ) h(x i ) header: protected with error correction codes

6. Network Coding and Reliable Communications Group Threat Model Adversary – Eavesdrops its neighbors’ transmissions – Injects/corrupts packets – Computationally unbounded – Knows the channel statistics, but does not know the specific realization of the channel errors Adversary’s objective: Corrupt information flow without being detected by other nodes Our objective: limit errors introduced by the adversaries to be at most that of the channel

7. Network Coding and Reliable Communications Group Algebraic Watchdog Focus on v 1 – Listens to neighbors and infer the messages: Using transition matrix T – Combines the inferred messages to “guess” what the next hop node should transmit: Watchdog trellis & Viterbi-like algorithm – Check the “guessed message” with next-hop node’s transmission: Inverse transition matrix T -1

8. Network Coding and Reliable Communications Group Transition Matrix/List T Relates the overheard information from source v i to list of candidates (inferred list of x i ) Overheard information Start state Overheard information Inferred information x i y Edge iff Edge weight proportional to probability of receiving given y is original message:

9. Network Coding and Reliable Communications Group Watchdog Trellis Uses overheard & inferred information (candidates) to generate a list of “guesses” on what v m+1 should send Layer 1 α 1 x 1 Start state Layer 2 α 1 x 1 +α 2 x 2 Layer 3 α 1 x 1 +α 2 x 2 +α 3 x 3 Layer m-1 Σ 1≤i≤m-1 α i x i Layer m Σ 1≤i≤m α i x i What v 1 already has Combine infor- mation from v 2 Combine infor- mation from v m-1 Combine infor- mation from v m “guesses” are states with positive weight at Layer m

10. Network Coding and Reliable Communications Group Inverse Transition Matrix T -1 Using the “guesses” generated, checks that v m+1 is well-behaving Same as T, just inverse Overheard information [x̃ m+1,h(x m+1 )] Guesses Σ 1≤i≤m α i x i Inferred linear combinations (guesses) Σ 1≤i≤m α i x i End node y Edge iff Edge weight proportional to probability of receiving given y is original message:

11. Network Coding and Reliable Communications Group Decision Making Total weight of end state = p* = probability of overhearing given channel statistics Can use various decision policy, such as threshold decision rule p*>t – Depending on the rule, different false positive/false negative probabilities Layer 1 α 1 x 1 Start state Layer 2 α 1 x 1 +α 2 x 2 Layer 3 α 1 x 1 +α 2 x 2 +α 3 x 3 Layer m-1 Σ 1≤i≤m-1 α i x i Layer m Σ 1≤i≤m α i x i Overheard information [x̃ m+1,h(x m+1 )] “Guesses” End state

12. Network Coding and Reliable Communications Group Simulation Results: Varying adversarial attack All channel noise: 10%, i.e. BSC(0.1) 3 sources 10-bit field size 2-bit hash size Adversarial relay (flips bit with probability p adv ) Honest relay (does not inject errors) When adversary injects more than channel noise (10%), the p* adv and p* relay have different distribution!

13. Network Coding and Reliable Communications Group Conclusions Probabilistically police downstream neighbors in a multi-hop, multi-source network using network coding – Only discussed multi-source, two-hop setting Trellis-like graphical model: – Capture inference process – Compute/approximate probabilities of consistency within the network (Viterbi-like algorithm) Preliminary simulation results agree with the intuition Future Work: – Combine with reputation based protocol and some practical considerations

14. Network Coding and Reliable Communications Group EXTRA SLIDES

15. Network Coding and Reliable Communications Group Multi-hop Algebraic Watchdog As long as the min-cut to any node from the source is not dominated by adversarial node, can detect malicious behavior

16. Network Coding and Reliable Communications Group Multi-hop Algebraic Watchdog edges in E 1 S0S0 S1S1 S2S2 v1v1 v2v2 v3v3 v5v5 v4v4 v6v6 v7v7 v8v8 As long as the min-cut to any node from the source is not dominated by adversarial node, can detect malicious behavior S 0 monitors v 5 S 1 monitors v 7 S 1 monitors v 8 S 2 monitors v 4

17. Network Coding and Reliable Communications Group Simulation Results: Varying hash size All channel noise & adversarial attack level: 10%, i.e. BSC(0.1) 3 sources 10-bit field size Adversarial relay (flips bit with probability 10%) Honest relay (does not inject errors) Hash size > 1 bit sufficient Hash size (in bits)

18. Network Coding and Reliable Communications Group Simulation Results: Varying channel noise Adversarial relay (flips bit with probability 10%) Honest relay (does not inject errors) Channel noise between sources Adversarial attack level: 10%, i.e. BSC(0.1) 3 sources 10-bit field size 2-bit hash size When channel noise > 10% (adversarial attack level), then may not be able to detect the adversary!

19. Network Coding and Reliable Communications Group Simulation results: Varying number of sources Adversarial relay (flips bit with probability 10%) Honest relay (does not inject errors) Number of sources All channel noise & adversarial attack level: 10%, i.e. BSC(0.1) 3 sources 10-bit field size 2-bit hash size When only one source, v 1 can detect adversary with high probability v 1 can detect (even by itself) when there are moderate number of sources v 1 can not detect by itself when many sources Need more hash or better overhearing channel Does not take into account other nodes vi’s independent watchdog