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Protocol anomaly detection provides some very powerful capabilities that make it an xcellent mechanism for performing network intrusion detection First and foremost, because it does not require any prior signature to detect certain classes of attacks, it provides the ability to detect some zero-day attacks even before signatures are published This eliminates the window of vulnerability often created during the first hours or days after an exploit is published Another useful feature of the protocol anomaly detection technique is its resistance to evasion through polymorphism and other similar evasion techniques Since they do not rely on matching an explicit pattern, variations in the attack generally do not cause a failure to detect as they can in signature systems As they do not require constant signature updates, protocol anomaly detection systems can also provide a solution with lower administrative overhead Other solutions require weekly or even daily updates, often causing significant reductions in utility if these updates are not performed Even in modest networks, this level of maintenance quickly becomes a significant barrier to use Depending on the implementation, a protocol anomaly detection system may also scale better at higher network speeds The amount of comparison that needs to be performed is much smaller and much more static, therefore it is possible to implement very efficient models for detection One notable limitation of anomaly systems in general, however, is that they often provide less specific information than comparable explicit matching systems They usually identify items of concern descriptively or by some type of classification For example, a protocol anomaly detection system monitoring HTTP traffic may report observing a questionably encoded URL, while a signature system (properly updated) may report the same event as "Code Purple" While these labels are often fairly arbitrary names assigned to threats or exploits, once widely published they do provide a useful function by allowing security administrators to easily communicate about the threat or search for patches This is a fairly important consideration given the amount of coordination required across organisations during incident response situations This limitation is not a significant one, however Through various forms of classification work, a protocol anomaly detection system can be structured such that once anomalies are identified, additional work is performed to more specifically identify the event and provide additional reference information This can include common names, CVE (Common Vulnerabilities and Exposures) reference, BugTraq IDs, CERT advisories, and so on Done correctly, this can actually be quite a scalable approach, as the detection methods can be fairly lightweight and the data reduction prior to classification can be significant.

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can essentially ignore it The computer is much more likely to break Your job is secure Instead of using a shuffling technique, you can achieve the same result by choosing the pivot randomly instead of deterministically Take a random item in the array and swap it with the item in position l o w Take another random item and swap it with the item in position high Take a third random item and swap it with the item in the middle position Then continue as usual As before, degenerate partitions are always possible, but they now happen as a result of bad random numbers, not bad inputs Let us look at the differences between randomized and nonrandomized algorithms So far we have concentrated on nonrandomized algorithms When calculating their average running times, we assume that all inputs are equally likely This assumption does not hold, however, because nearly sorted input, for instance, occurs much more often than is statistically expected This situation can cause problems for some algorithms, such as quicksort But when we use a randomized algorithm, the particular input is no longer important The random numbers are important, and we get an expected running time, in which we average over all possible random numbers for any particular input Using quickselect with random pivots (or a shuffle preprocessing step) gives an O(N) expected time algorithm That is, for any input, including already sorted input, the running time is expected to be O(N), based on the statistics of random numbers On the one hand an expected time bound is somewhat stronger than an average-case time bound because the assumptions used to generate it are weaker (random numbers versus random input) but it is weaker than the corresponding worst-case time bound On the other hand, in many instances solutions that have good worst-case bounds frequently have extra overhead built in to assure that the worst case does not occur The O(N)worst-case algorithm for selection, for example, is a marvelous theoretical result but is not practical Randomized algorithms come in two basic forms The first, as already shown, always gives a correct answer but it could take a long time, depending on the luck of the random numbers The second type is what we examine in the remainder of this chapter Some randomized algorithms work in a fixed amount of time but randomly make mistakes (presumably with low probability) called false positives or false negatives This technique is commonly ccepted in medicine False positives and false negatives for most tests are actually fairly common, and some tests have surprisingly high error rates Furthermore, for some tests the errors depend on the individual, not random numbers, so repeating the test is certain to produce another false result In randomized algorithms we can rerun the test on the same input using different random numbers If we run a randomized algorithm 10 times and get 10 positives-and if a single false positive is an unlikely occurrence.

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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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