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

2. 1 1 Overview (hidden slide) Anomaly Detection —Problem with High Speed networks Sketch Based Approaches and their problems —What is a sketch ? —How does it help ? —Its current problem: not reversible Reverse Hashing algorithms —Taking Intersections –Its problems —Modular Hashing —IP Mangling Dealing with Multiple Anomalies Evaluation Conclusions Future Work

3. 2 2 Overview Anomaly Detection Sketch Based Approaches and their problems Reverse Hashing algorithms Dealing with Multiple Anomalies Evaluation Conclusions Future Work

4. 3 3 Overview Anomaly Detection Sketch Based Approaches and their problems Reverse Hashing algorithms Dealing with Multiple Anomalies Evaluation Conclusions Future Work

5. 4 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 !

6. 5 5 Overview Anomaly Detection Sketch Based Approaches and their problems Reverse Hashing algorithms Dealing with Multiple Anomalies Evaluation Conclusions Future Work

7. 6 6 What is a sketch ? Probabilistic summary of data streams —Widely used in database research to handle massive data streams SpaceAccuracy Hash tablePer-key state100% SketchCompact With probabilistic guarantees (better for larger values) Array of hash tables: T j [K] (j = 1, …, H)

8. 7 7 What is a sketch ? 1 j H 01K-1 … … … hj(k)hj(k) hH(k)hH(k) h1(k)h1(k) Update (k, u): T j [ h j (k)] += u (for all j) Estimate v(S, k): sum of updates for key k

9. 8 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 !

10. 9 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 ! ? ?

11. 10 Overview Anomaly Detection Sketch Based Approaches and their problems Reverse Hashing algorithms Dealing with Multiple Anomalies Evaluation Conclusions Future Work

12. 11 Our contribution ? ? How can we figure out the keys without storing them explicitly ?

13. 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 b 1, b 2, b 3, b 4, b 5 Intersect A 1, A 2, A 3, A 4, A 5  really small set ! E[x] << 1 for 5 hash tables (ref. our paper )

14. 13 The problem with simple intersection Why is this difficult ? —One to many mapping Each set A i can be very large ! —E.g. for IP addresses Key space is 2 32. For 2 12 buckets  2 20 keys per bucket !

15. 14 Problem with Intersections How do we store these huge mappings ? How de we take intersections of these huge sets ? Modular hashing Partition the key into separate words Hash each word separately 32 bits 8 bits 10010100101010111001010110100011

16. 15 Modular hashing reduces the set size 32 bits 8 bits 10010100101010111001010110100011 h 1 ()h 2 ()h 3 ()h 4 () 010110001101 010 110 001 101 Greatly reduces size of reverse mapped sets

17. 16 Modular hashing Only 32 elements per partition For 8 bit to 3 bit hashing : Each bucket maps to 2 5 = 32 keys  small ! 2 8 /2 3

18. 17 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) logarithmic in key space poly-log in key space

19. 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

20. 19 Without IP mangling: skewed !

21. 20 IP Mangling removes correlations Key idea : randomize the input data to destroy correlations Must be reversible also !

22. 21 Theory of Modular Linear Equations f(x)  a·x mod n To be invertible: Must be relatively prime a is chosen randomly Can be easily reversed: replace a by a -1 ! This function is highly effective in resolving the skewed distribution

23. 22 With IP mangling: uniform !

24. 23 Recap Intersections of reverse mapped sets Converges to culprit key Modular Hashing Makes intersection time and space efficient IP Mangling Removes un-uniformity of modular hashing

25. 24 Overview Anomaly Detection Sketch Based Approaches and their problems Reverse Hashing algorithms Dealing with Multiple Anomalies Evaluation Conclusions Future Work

26. 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…

27. 26 Handling Multiple Intersections… Multiple possibilities…. Take union of keys from each hash table, and then intersection  False positives

28. 27 Handling Multiple Intersections… Multiple possibilities…. Try all possible combinations of intersections…. Expensive and inaccurate(?)

29. 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

30. 29 Overview Anomaly Detection Sketch Based Approaches and their problems Reverse Hashing algorithms Dealing with Multiple Anomalies Evaluation Conclusions Future Work

31. 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

32. 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

33. 32 Our methods are quite effective Detection quite accurate, even upto 20 heavy changes False positives and false negatives very less

34. 33 The bucket vector algorithm is important For multiple changes, the method of intersection quite important E.g. w/o bucket vector algorithm:

35. 34 We can make the sketch more accurate Use 6 hash tables, instead of 5 —Makes intersections very accurate, less false negatives

36. 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

37. 36 Overview Anomaly Detection Sketch Based Approaches and their problems Reverse Hashing algorithms Dealing with Multiple Anomalies Evaluation Conclusions Future Work

38. 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