Computer Sciences Dept.

Cristian Estan

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Bitmap algorithms for counting active flows on high speed links
Cristian Estan, George Varghese, Mike Fisk
IEEE/ACM Transactions on Networking, October 2006

This paper presents a family of bitmap algorithms that address the problem of counting the number of distinct header patterns (flows) seen on a high speed link. Such counting can be used to detect DoS attacks and port scans, and to solve measurement problems. Counting is especially hard when processing must be done within a packet arrival time (8 nsec at OC-768 speeds) and, hence, must require only a small number of accesses to limited, fast memory. A naive solution that maintains a hash table requires several Mbytes because the number of flows can be above a million. By contrast, our new probabilistic algorithms take very little memory and are fast. The reduction in memory is particularly important for applications that run multiple concurrent counting instances. For example, we replaced the port scan detection component of the popular intrusion detection system Snort with one of our new algorithms. This reduced memory usage on a ten minute trace from 50 Mbytes to 5.6 Mbytes while maintaining a 99.77% probability of alarming on a scan within 6 seconds of when the large-memory algorithm would. The best known prior algorithm (probabilistic counting) takes 4 times more memory on port scan detection and 8 times more on a measurement application. Fundamentally, this is because our algorithms can be customized to take advantage of special features of applications such as a large number of instances that have very small counts or prior knowledge of the likely range of the count.

Paper in PDF and Postscript. The conference version of this paper has an appendix with the derivation of the variance of estimates based on virtual bitmap and multiresolution bitmap. The implementation of the bitmap counting algorithms is publicly available.

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