Reverse Hashing for High-speed Network Monitoring: Algorithms, Evaluation, and Applications Robert Schweller 1, Zhichun Li 1, Yan Chen 1, Yan Gao 1, Ashish Gupta 1, Yin Zhang 2, Peter Dinda 1, Ming-Yang Kao 1, Gokhan Memik 1 1 Lab for Internet and Security Technology (LIST), Northwestern Univ. 2 University of Texas at Austin

The Spread of Sapphire/Slammer Worms

Motivation (online change detection) Online network anomaly/intrusion detection over high speed links –Small memory usage –Small # of memory access per packet –Scalable to large key space size Primitives for online anomaly detection –Heavy hitters (lots of prior work) –Heavy changes: enabler for aggregate queries over multiple data streams Asymmetric routing demands spatial aggregation Time Series Analysis (TSA) need temporal aggregation

Outline Background on k-ary sketch Reversible sketch problem Modular hashing IP mangling Reverse hashing Evaluation Conclusion

[Krishnamurthy, Sen, Zhang, Chen, 2003] First to detect flow-level heavy changes in massive data streams at network traffic speeds K-ary sketch 1 j H 01K-1 … … …

k-ary 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 [Krishnamurthy, Sen, Zhang, Chen, 2003] APIs: + =  S=COMBINE( ,S1, ,S2):

? ? Main problem –Cannot efficiently report keys with heavy change INFERENCE(S,t) –Important function for anomaly detection! Our Contribution –Determine set of keys that have “large” estimates in a sketch Reverse Sketch Problem

Reversible sketch framework Streaming data recording reversible k-ary sketch value stored value Modular hashing IP mangling key Heavy change detection reversible k-ary sketch Reverse hashing Reverse IP mangling heavy change keys change threshold

Outline Background on k-ary sketch Reversible sketch problem Modular hashing IP mangling Reverse hashing Evaluation Conclusion

Intersect A 1, A 2, A 3, A 4, A 5 Taking Intersections H = 5 K = 2 12 #keys = 2 32 (IP addresses) E[false positives] << 1

The problem with simple intersection Each set A i can be very large ! H = 5 K = 2 12 #keys = 2 32 (IP addresses) |A 1 | = 2 32 / 2 12 = 2 20

The problem with simple intersection Each set A i can be very large ! Solution: Modular hashing

Modular hashing reduces the set size 32 bits 8 bits h() 12 bits

Modular hashing reduces the set size 32 bits 8 bits h 1 ()h 2 ()h 3 ()h 4 () Greatly reduces size of reverse mapped sets

Modular hashing reduces the set size b1b1 b2b2 b4b4 b5b5 b3b3 A 1 : 2 5 * 2 5 * 2 5 * 2 5 Intersection: Only 32 elements per word set

b1b1 b2b2 b4b4 b5b5 b3b3 A 1 : 2 5 * 2 5 * 2 5 * 2 5 A 2: 2 5 * 2 5 * 2 5 * 2 5 Intersection: Modular hashing reduces the set size

Problem: Too many collisions * 32 bits 12 bits

Problem: Too many collisions * 32 bits 12 bits IP Mangling with GF (Galois Extension Field) Solution: IP Mangling: a bijective mapping function for breaking the key space continuity

Outline Background on k-ary sketch Reversible sketch problem Modular hashing IP mangling Reverse hashing Evaluation Conclusion

Handling Multiple Intersections… b1b1 b2b2 b4b4 b5b5 b3b3 b3b3 b1b1 b2b2 b4b4 b5b5 2 H different intersections Much more difficult – Solution: Reverse Hashing algorithms Step 1: Reverse hashing for each module Step 2: Infer the whole key through bucket index matching among candidates from each module

Reverse Hashing for Each Module H=5, r=1, K=2 12 r tolerance level candidate set of the first word in Hash table i All possible values of the first word in the sketch Take the first word as an example { 2,3,5} { 2, 6,9,10} {0,2,3} { 2,3,8,10} { 3,6,7,9} {2}{2,3}

Bucket Index Matrix of Candidates H=5, r=1, K=2 12 For each x in I 1, we can get B 1 (x), a vector of the heavy bucket sets which x hashes to b 11 b 21 b 42 b 51 b 32 b 31 b 12 b 22 b 41 b b 11 b 21 b 42 b 51 b 32 b 31 b 12 b 22 b 41 b b 11 b 21 b 42 b 51 b 32 b 31 b 12 b 22 b 41 b *.*.* hash to the red heavy buckets

Prefix Extension Algorithm I1I1 I2I2 B1B1 B2B = * more than r=1 Ignore! Ignore! Path discovery algorithm

+= I3I3 B3B3 + = 75 I4I4 B4B4 Prefix Extension Algorithm

Recap: Streaming data recording reversible k-ary sketch value stored value Modular hashing IP mangling key Heavy change detection reversible k-ary sketch Reverse hashing Reverse IP mangling heavy change keys change threshold n is the size of key space

Outline Background on k-ary sketch Reversible sketch problem Modular hashing IP mangling Reverse hashing Evaluation Conclusion

Evaluation Dataset –A large US ISP (330M Netflow records) –NU (19M Netflow records) Efficient data recording For the worst case traffic, all 40-byte packets –Software: 526Mbps on P4 3.2Ghz PC –Hardware: 16Gbps on a single FPGA broad –Only a few hundred KB to a couple of MB memory used –Only 15 memory access per packet for 48 bit reversible sketches and 16 per packet for 64 bit reversible sketches Efficient heavy change detection and key inference –0.34 seconds for 100 changes seconds for 1000 change

Key Inference Accuracy True positives and false positives of 16bit reversible sketches for 32bit IP addresses [Deltoids]: S.Muthukrishnan and Graham Cormode, What's New: Find Significant Differences in Network Data Streams. Infocom 2004

Stress test with larger dataset still accurate Scalable to larger key space size: similar results for 64bit IP pairs Built anomaly/intrusion detection system to detect, e.g., SYN flooding and port scans [ICDCS 2006] More Results

Conclusions Proposed the first reversible sketches which Record high speed network streams online Detect the heavy changes and infer the keys online Small memory usage, small # of memory access per packet Scalable to large key space size

Backup Slides

Related work Compare with [deltoids] –Accuracy better –Scalable to large key space better –# of Memory access less [PCF, IMC2004]: not reversible [Q. Zhao et al, IMC2005] [S.Venkataraman, NDSS2005]: unique fan-out (fan-in) estimation.

Modular Hashing Optimal Hashing

However… Not reversible Lack of an inference API: INFERENCE(S,t) Important function for anomaly detection! Decouple the recording stage of sketches from the detection stage to enable efficient combine and inference. Given a threshold t, report keys whose corresponding sum of updates are larger than the threshold. Our contribution: an efficient algorithm for inference Reversible sketch problem

? ?

Problem: Too many collisions * 32 bits 12 bits IP Mangling with Solution:

IP-mangling Use GF (Galois Extension Field) function for attack resilience

Modular Hashing Modular Hashing with IP Mangling Optimal Hashing

Reverse Hashing for Each Module b 11 b 21 b 42 b 51 b 32 b 31 b 12 b 22 b 41 b 52 H=5, r=1, K=2 12 all possible value of the first word for the No. j heavy bucket in Hash table i all possible value of the first word in Hash table i All possible value of the first word in the sketch Take the first word as an example

False positive reduction by original sketch verifying Estimate (, 180) Threshold 150 (, 180) Final result Verified original k -ary sketch

[Krishnamurthy, Sen, Zhang, Chen, 2003] K-ary sketch [Krishnamurthy, Sen, Zhang, Chen, 2003] first to detect flow-level heavy changes in massive data streams at network traffic speeds APIs –UPDATE(S,k,u): T j [ h j (k)] += u (for all j) –ESTIMATE(S, k): sum of updates for key k –Linear combination: S=COMBINE( ,S 1, ,S 2 ) + = 