Reverse Hashing for Sketch Based Change Detection in High Speed Networks

1. Reverse Hashing for Sketch Based Change Detection in High Speed Networks Ashish GuptaElliot Parsons with Robert Schweller, Theory Group Advisor: Yan Chen Class Presentation, June 2004, Network Security Computer Science Department, Northwestern University

2. Overview • Anomaly Detection • Sketch Based Approaches and their problems • Reverse Hashing algorithms • Dealing with Multiple Anomalies • Evaluation • Conclusions • Future Work

3. Overview • Anomaly Detection • Sketch Based Approaches and their problems • Reverse Hashing algorithms • Dealing with Multiple Anomalies • Evaluation • Conclusions • Future Work

4. Anomaly Detection • Goes beyond signature detection • Two popular types: • Heavy Hitter Detection • Change detection : very broad  simple change to statistical methods • Online real-time  difficult • Heavy hitter: some solutions proposed • Heavy Change  ? • Scalability with High speed traffic • Large Number of flows: large memory required • Performance penalty • Scalable Change Detection: Sketch to the rescue !

5. Overview • Anomaly Detection • Sketch Based Approaches and their problems • Reverse Hashing algorithms • Dealing with Multiple Anomalies • Evaluation • Conclusions • Future Work

6. What is a sketch ? • Probabilistic summary of data streams • Widely used in database research to handle massive data streams • Array of hash tables: Tj[K] (j = 1, …, H)

7. … h1(k) 0 1 K-1 Estimate v(S, k): sum of updates for key k 1 … hj(k) j hH(k) … H What is a sketch ? Update (k, u): Tj [ hj(k)] += u (for all j)

8. Using Sketch for anomaly detection • Requires very little space: • E.g. 5 hash tables with 16 K buckets = 360 K • High speed memory usable • Still able to reconstruct the values with high accuracy • Its main problem • To know the value of a key, must know the key. • Can know the anomalies, not the keys !

9. ? ? Using Sketch for anomaly detection • Requires very little space: • E.g. 5 hash tables with 16 K buckets = 360 K • High speed memory usable • Still able to reconstruct the values with high accuracy • Its main problem • To know the value of a key, must know the key. • Can know the anomalies, not the keys !

10. Overview • Anomaly Detection • Sketch Based Approaches and their problems • Reverse Hashing algorithms • Dealing with Multiple Anomalies • Evaluation • Conclusions • Future Work

11. How can we figure out the keys without storing them explicitly ? ? ? Our contribution

12. Step 1: Taking Intersections • Each hash table  independent hash function • Each key maps to different bucket in each table • Each bucket maps to a large set of keys • Example: Key maps to b1, b2, b3, b4, b5 • Intersect A1, A2, A3, A4, A5  really small set ! • E[x] << 1 for 5 hash tables (ref. our paper )

13. The problem with simple intersection • Why is this difficult ? • One to many mapping • Each set Ai can be very large ! • E.g. for IP addresses Key space is 232. For 212 buckets  220 keys per bucket !

14. Modular hashing 32 bits 10010100 10101011 10010101 10100011 8 bits Problem with Intersections • How do we store these huge mappings ? • How de we take intersections of these huge sets ? • Partition the key into separate words • Hash each word separately

15. h1() h2() h3() h4() 010 110 001 101 010 110 001 101 Modular hashing reduces the set size 32 bits 10010100 10101011 10010101 10100011 8 bits Greatly reduces size of reverse mapped sets

16. Modular hashing 28/23 Only 32 elements per partition • For 8 bit to 3 bit hashing : Each bucket maps to 25 = 32 keys  small !

17. logarithmic in key space • poly-log in key space Modular Hashing is Efficient • Very efficient in space and time: • If n is the key space, m is hash space, q is number of words, • Space = • Run time (intersections) = Set q = O(log n)

18. An Important problem: spatial locality • This hashing scheme is not uniform and biased • In network streams, strong spatial locality in IP addresses • E.g. many addresses fall into 120.105.56.* • These would be mapped into very few buckets  large number of collisions  low sketch accuracy IP Mangling

19. Without IP mangling: skewed !

20. IP Mangling removes correlations • Key idea : randomize the input data to destroy correlations • Must be reversible also !

21. To be invertible: Must be relatively prime Theory of Modular Linear Equations • a is chosen randomly • Can be easily reversed: replace a by a-1 ! • This function is highly effective in resolving the skewed distribution f(x)  a·x mod n

22. With IP mangling: uniform !

23. Modular Hashing Makes intersection time and space efficient IP Mangling Removes un-uniformity of modular hashing Recap Intersections of reverse mapped sets Converges to culprit key

24. Overview • Anomaly Detection • Sketch Based Approaches and their problems • Reverse Hashing algorithms • Dealing with Multiple Anomalies • Evaluation • Conclusions • Future Work

25. Handling Multiple Intersections… • A more complex problem  Illustration How do we take intersections now ? • Each hash table contains two anomalies now  two culprit keys…

26. Handling Multiple Intersections… • Multiple possibilities…. • Take union of keys from each hash table, and then intersection False positives

27. Handling Multiple Intersections… • Multiple possibilities…. • Try all possible combinations of intersections…. • Expensive and inaccurate(?)

28. Handling Multiple Intersections… • Bucket Vector Algorithm: a new algo • Efficient • Similar to all possible intersections but takes polynomial time • Documented in our technical report

29. Overview • Anomaly Detection • Sketch Based Approaches and their problems • Reverse Hashing algorithms • Dealing with Multiple Anomalies • Evaluation • Conclusions • Future Work

30. Evaluation • Got traffic traces from a large ISP • Each 5 min interval  7.5 GB of traces • Used the Change Detection Method described earlier

31. Evaluation • Efficacy depends on number of heavy changers • Depends on change threshold, • Less threshold  large number of heavy changes • To verify our results, used a naïve multi-pass algo  the Ground Truth

32. Our methods are quite effective • Detection quite accurate, even upto 20 heavy changes • False positives and false negatives very less

33. The bucket vector algorithm is important • For multiple changes, the method of intersection quite important • E.g. w/o bucket vector algorithm:

34. We can make the sketch more accurate • Use 6 hash tables , instead of 5 • Makes intersections very accurate, less false negatives

35. Conclusions • Sketches a powerful method for scalable change detection • Our main contribution : can reverse them • Greatly enhances their applicability in online systems • We can extract heavy changes from the sketchs, without storing any key information • Methods are accurate • Low number of false positives and false negatives • Methods are efficient • Runtime: Only poly-logarithmic in key space • Space: logarithmic in key space

36. Overview • Anomaly Detection • Sketch Based Approaches and their problems • Reverse Hashing algorithms • Dealing with Multiple Anomalies • Evaluation • Conclusions • Future Work

37. Future Work: Three areas • Application to Online real-time systems • Performance evaluation • Hardware design of our methods • More advanced applications: • Hierarchical change detection • Output the prefix changes not just the key changes ! • E.g. 129.105.100.* shows a big change ! • Advanced change detection methods: • Statistical methods