Towards a Scalable and Robust DHT

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

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

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

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

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

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

7. DHT by Karger et al. data 0 1 sites Towards a Scalable and Robust DHT

8. 0 1 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 Towards a Scalable and Robust DHT

9. 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 Towards a Scalable and Robust DHT

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

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

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

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

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

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

16. 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 Towards a Scalable and Robust DHT

17. What is the problem? • Adversary can select requests to different data items at same region • Any medicine against that??? 0 1 Towards a Scalable and Robust DHT

18. Yes!! Towards a Scalable and Robust DHT

19. 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 Towards a Scalable and Robust DHT

20. 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 Towards a Scalable and Robust DHT

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

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

23. 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 Towards a Scalable and Robust DHT

24. 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 Towards a Scalable and Robust DHT

25. Questions? Towards a Scalable and Robust DHT

26. 0 1 Hash table data sites Towards a Scalable and Robust DHT