1. Towards a Scalable and Robust DHT Baruch Awerbuch Johns Hopkins University Christian Scheideler Technical University of Munich

2. 2Towards a Scalable and Robust DHT Holy Grail of Distributed Systems Scalability and Robustness Adversarial behavior increasingly pressing issue!

3. 3Towards a Scalable and Robust DHT Why is this difficult??? Scalability: minimize resources needed for operations Robustness: maximize resources needed for attack Scalable solutions seem to be easy to attack!

4. 4Towards a Scalable and Robust DHT Distributed Hash Table Problem: maintain a hash table of data items across multiple sites Basic operations: Join(s): site s joins the system Join(s): site s joins the system Leave(s): site s leaves the system Leave(s): site s leaves the system Insert(d): insert data item d into hash table Insert(d): insert data item d into hash table Lookup(name): lookup data item with given name Lookup(name): lookup data item with given name data sites

5. 5Towards a Scalable and Robust DHT Distributed Hash Table Scalable DHT: Bounded-degree overlay network Few copies per data item data sites

6. 6Towards a Scalable and Robust DHT Distributed Hash Table Robust DHT: Network can sustain constant fraction of adversarial sites Data layer can handle arbitrary collection of insert and lookup requests data sites

7. 7Towards a Scalable and Robust DHT DHT by Karger et al. 01 data sites

8. 8Towards a Scalable and Robust DHT Robust Overlay Network Two central conditions (given n sites): Balancing condition: only O(log n) sites in intervals of size (c log n)/n Majority condition: adv. sites in minority in all intervals of size (c log n)/n Balancing condition: scalability Majority condition: robustness via majority decision 01

9. 9Towards a Scalable and Robust DHT How to satisfy conditions? Chord: uses cryptographic hash function to map sites to points in [0,1) randomly distributes honest sites does not randomly distribute adversarial sites

10. 10Towards a Scalable and Robust DHT How to mix adversarial sites? CAN: map sites to random points in [0,1)

11. 11Towards a Scalable and Robust DHT How to mix adversarial sites? Group spreading [AS04]: Map sites to random points in [0,1) Limit lifetime of points Too expensive!

12. 12Towards a Scalable and Robust DHT How to mix adversarial sites? Our approach: n honest nodes (not under control of adversary) and  n adversarial nodes Adversary can adaptively join and leave with its nodes Oblivious join operation that can maintain conditions under any adversary Naive solution: perturb everything after each join operation

13. 13Towards a Scalable and Robust DHT How to mix adversarial sites? Card shuffling [Diaconis & Shahshahani 81]: random transposition  (n log n) transpositions: random permutation  (log n) transpositions per join operation??

14. 14Towards a Scalable and Robust DHT Random transpositions Cannot preserve balancing condition!!

15. 15Towards a Scalable and Robust DHT How to mix adversarial sites? Rule that works: k-cuckoo rule evict k/n-region n honest  n adversarial   < 1-1/k

16. 16Towards a Scalable and Robust DHT Are we done? Dilemma: we cannot randomly distribute the data Reason: data unsearchable! So we need hash function, but then open to adversarial attacks on insert, lookup operations

17. 17Towards a Scalable and Robust DHT What is the problem? Adversary can select requests to different data items at same region Any medicine against that??? 01

18. 18Towards a Scalable and Robust DHT Yes!!

19. 19Towards a Scalable and Robust DHT Robust Data Management Long, long ago… Deterministic PRAM simulation: Pioneered by Mehlhorn and Vishkin 84 Problem: simulate PRAM of n processors and m memory cells on complete network of n processors with memory Central ideas: Choose 2c-1 fixed hash functions with expansion properties, c=  (log m) Majority trick: update and lookup any c copies

20. 20Towards a Scalable and Robust DHT Robust Data Management Why deterministic strategies? Randomness expensive in dynamic systems with adversarial presence! More complex for dynamic networks: Congestion during routing Contention at destination regions

21. 21Towards a Scalable and Robust DHT Robust Data Management Expansion properties (probabilistic proof): simple threshold rule sufficient sources

22. 22Towards a Scalable and Robust DHT Robust Data Management Strategy: Run several attempts In each attempt: For each remaining request, route 2c-1 packets, one for each copy For each remaining request, route 2c-1 packets, one for each copy Discard packets at congested nodes Discard packets at congested nodes If c packets of a request successful, then request successful If c packets of a request successful, then request successful How many attempts???

23. 23Towards a Scalable and Robust DHT Robust Data Management Answer: O(log n) many attempts with congestion threshold O(polylog). Theorem 1: For any set of n lookup requests, one request per node, the lookup protocol can serve all requests in O(polylog) communication rounds. Theorem 2: Same for insert requests

24. 24Towards a Scalable and Robust DHT Conclusion We presented high-level solution for a scalable and robust DHT. Open problems: Low-level attacks (DoS!) Adversary controls join-leave behavior of adversarial and honest nodes Elementary random number generator

25. 25Towards a Scalable and Robust DHT Questions?

26. 26Towards a Scalable and Robust DHT Hash table data sites 01