—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 ns at OC-768 speeds) and, hence, may perform only a small number of accesses to limited, fast memory. A naive solution that maintains a hash table requires several megabytes because the number of flows can be above a million. By contrast, our new probabilistic algorithms use 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 to 5.6 MB while maintaining a 99...