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When IDSs were first contemplated in the 1970s and 1980s, many focused on anomaly detection Researchers continue to devote energy to this method, but pattern-based detection has been the dominant strategy for the last decade Pattern-based detection prevailed for a few simple reasons First, it was easier for developers to implement Searching a packet or reassembled stream for a string of characters is conceptually simple Ever-increasing traffic loads and deployment of encryption frustrate this approach, but pattern matching survives Second, it is easier for analysts to understand If an analyst knows the detection product is watching for a certain pattern, it makes sense when the IDS reports seeing that pattern If the pattern does not indicate a malicious event occurred, it's not the IDS's fault Verification has been lacking, but NSM approaches and integration of assessment techniques make pattern matching increasingly effective Third, it is much easier to deploy a rule based on a new pattern than it is to implement a new algorithm for anomaly-based intrusion detection Snort rules are released within hours of the discovery of a new worm, exploit, and other malicious code Engineers and analysts can plug the new rule into their product and validate or tune it as necessary Anomaly detection is not dead, however Pattern-matching systems are frequently compared to signature-based antivirus products If an antivirus product strictly relied on patterns to intercept and defeat malware, users would suffer infections much more often Antivirus products supplement their pattern-matching features with heuristic detection algorithms Heuristic techniques concentrate more on the acts the malware take, like opening network sockets, sending e-mail, and so on, and less on the code used to bring these acts to life Implementing heuristic detection or anomaly-based detection requires knowing what is normal, suspicious, and malicious We encountered those terms earlier in the book with respect to manual inspection of security events In some sense a human analyst is an anomaly detection device An experienced human analyst develops a sense of what is normal for the organizations he or she monitors Seeing an alert or session that falls outside those boundaries of normality prompts the analyst to investigate Validating these unusual events requires access to high-fidelity network traffic, as is provided by session data and full content data Network profiling is related to anomaly detection It's the idea that organizations should develop a formal sense of the devices and traffic patterns required for normal operational use Introduction of new devices or traffic types should raise an alarm Marcus Ranum calls this technique first seen nomaly detection: "[A first seen anomaly detection] system treats the first time it sees an instance of a thing as an anomaly It's accurate that something never seen before is always anomalous, in at least a few senses of the word When I was looking at statistical anomaly detection for IDS I realized that the first seen anomaly was 99% of what you'd get [with statistical anomaly detection products]".

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Let us denote by v a sample from the distribution of V Then a sample Z (k) (G) of Z(G) can be deduced from a sample Z (k) (Gv ) of Z(Gv ) by Z (k) (G) = H + (1 pH )Z (k) (Gv ) If s and t are merged into a nal single node, the unreliability of Gv is equal to 0 and then Z (k) (G) = H + (1 pH ) 0 = H If s and t are not connected, the unreliability of Gv is equal to 1 and then Z (k) (G) = H + (1 pH ) 1 = 1 Otherwise, we have found an st-cut in Gv and we proceed again as before The main interest of this procedure is that Gv is smaller than G, and sometimes much smaller, because of the series parallel simpli cations, deletions and contractions performed A function which returns a trial of Z(G) can be summarized as follows: TRIAL-RVR(G, K) 1 Check end recursion condition: If |K| = 1 return(0) If G is not K-connected return(1) 2 Construct sp-red(G) by applying series parallel reductions to G 3 Find a K-cut in sp-red(G): = {l1 , , lH } 4 Compute the probability H that all links in are down 5 Compute the probability mass function distribution of the random variable V 6 Generate a trial v of V 7 Construct the network Gv = sp-red((G l1 l2 lv 1 ) lv ) 8 Recursive step: return( H + (1 H ) Trial-RVR(Gv , Kv )) The memory space complexity of the function TRIAL-RVR(G, K) is of order O(|E|(|E| + |V|)) and time complexity is, in the worst case, of order O(|E|(|K|2 |E||V|2 )) The worst case corresponds to a version using a maximal ow procedure in order to select a K-cut at step 3 of the above algorithm By calling the function TRIAL-RVR(G K) N times, we obtain N independent trials Z (k) (G) of Z(G), 1 k N The sample mean Z(G) of these trials leads to an estimate of Q = 1 R and the variance is estimated by VRV R 1 = N (N 1).

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To the best of our knowledge, the CE-MP method [37] which uses the cross-entropy technique to further improve the performance of the merge process method [29] and the RVR technique which exploits eries parallel reductions and a minimum cost st-cut strategy [13], where each link l has value ln(ql ), are the most suitable procedures published in the literature to compute network reliability in a rare event context In this section we present some numerical illustrations of these methods For the examples, we consider highly reliable grid topologies G3 and G6 (see Figure 71), where links are assigned equal unreliability q = 10 3 or q = 10 6 as in [37] and K is the set of the four corner nodes For those networks exact values of Q = 1 R are tabulated in column 3 of Table 71 Each exact unreliability Q is used in the computation of the relative error parameter which helps to appreciate the quality of the estimates produced by the two estimators considered Tables 72 and 73 show that both methods lead to small relative errors and the RVR method offers the most accurate estimates In the general case, we do not know the exact values Then, the best estimator in terms of accuracy is the one with smallest variance for a xed sample size N , leading to smallest lengths of con dence intervals Column 6 of Table 73 shows that the RVR method signi cantly reduces the variance with respect to the CE-MP method, and the best gains are obtained for highly reliable cases To illustrate the behavior of the RVR method on dense networks, let us now consider the evaluation of complete topologies for which we calculate the exact.

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