Statistical anomaly detection in .NET

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Statistical anomaly detection
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For a sequence of uncorrelated data observations, x(n), n = 1, , N , with the mean of x and the standard deviation of x , the EWMA control chart rst performs the EWMA data smoothing as follows [1, 2, 4 6]: z (n) = x (n) + (1 ) z (n 1) , 0 < 1 (141)
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The smoothed data, z(n), has approximately a normal distribution with the following mean and standard deviation: z = x z = x 2 (142) (143)
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The EWMA control chart then monitors the smoothed data sequence, z(n), n = 1, , N If z(n) falls outside the range de ned by the Lower Control Limit (LCL) and Upper Control Limit (UCL), [LCLz , UCLz ], LCLz = z L z UCLz = z + L z , (144) (145)
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an anomaly is detected to signal an alarm for an attack The parameter, L, is de ned according to the desired Type-I error or false alarm rate For example, L is 196 for the 005 signi cance level of type-I error The EWMA control chart for time series data with autocorrelated data observations [1, 2, 4 6] monitors the prediction error, e(n), n = 1, , N , instead of the smoothed data, z(n) At rst, z(n 1), which is computed using Formula 141, is considered the one-step-ahead prediction of x(n) The prediction error for x(n) is the following: e (n) = x (n) z (n 1) (146)
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The prediction error data, e(n), n = 1, , N, is approximately independently and normally distributed with the mean of e = 0 and the standard deviation of e The estimate of e can be obtained as follows: e2 (n) = e2 (n) + (1 ) e2 (n 1) , 0 < 1 LCLe and UCLe of e(n) are de ned as follows: LCLe (n) = e L e (n 1) = L e (n 1) UCLe (n) = e + L e (n 1) = +L e (n 1) (148) (149) (147)
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Application of the ewma control chart to cyber attack detection
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Based on Formula 146, the EWMA control chart monitoring e(n) is equivalent to the EWMA control chart monitoring x(n) with the following control limits: LCLx (n) = z (n 1) L e (n 1) UCLx (n) = z (n 1) + L e (n 1) (1410) (1411)
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142 APPLICATION OF THE EWMA CONTROL CHART TO CYBER ATTACK DETECTION
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The Windows performance objects data described in 7 is used to test the application of the EWMA control charts to cyber attack detection The testing of the EWMA control charts on other data sets can be found in [5, 6] As described in 10, many data variables of the Windows performance objects have a certain degree of autocorrelation Hence, the EWMA control chart for autocorrelated data is applied to the Windows performance object data to detect the eleven attacks described in 7 In order to compare the detection performance of the EWMA control charts in this chapter, the ANN-based signature recognition models described in 13 and the cuscore-based attack norm separation models described in 17, the three techniques are tested using the data of the same variables which are involved in the attack characteristics in Table 131 Speci cally, two EWMA control charts are developed for each attack characteristic in Table 131 for the attack with that attack characteristic in combination with the text editing norm and the web browsing norm, respectively, using Formulas 141, 146, 147, 1410 and 1411 For example, the ARP Poison attack has the autocorrelation increase characteristic in Network Interface\Bytes Received/sec This data variable, Network Interface\Bytes Received/sec, is x in Formulas 141 and 146 As described in 7, Run 2 of the data collection for the ARP Poison attack contains the 10 minutes of the text editing data followed by the mixture of the text editing data and the ARP Poison attack data, and Run 3 of the data collection contains the 10-minute web browsing data followed by the mixture of the text editing data and the ARP Poison attack data Two EWMA control charts are developed, one for each of the two normal use activities: text editing and web browsing For the normal use activity of text editing, the rst half of the 10-minute text editing data from Run 2, which contains time series data of 300 data observations for the variable, x, is used as the training data The second half of the 10-minute text editing data and the ARP attack data from Run 2 for the variable, x, is used as the testing data Since the EWMA control chart is an anomaly detection technique and does not require the attack data for the training phase, the attack data from Run 1 of the data collection is not used to develop the EWMA control chart In the training and the testing, both and are set to 03, and L is set to 3, according to work in [5, 6] In the training phase of developing the EWMA control chart, z(0) is initialized to the average of the x values in the training data For each x(n) in the training data, Formula 141 is used to compute z(n), and Formula 146 is then used to compute e(n) At the beginning of the testing phase, z(0) is initialized to the average of z s computed from the training data, and e2 (0) is initialized to the average of e2 s from the training data For x(n) in the testing data from n = 1 to the last data observation, LCLx (n) and UCLx (n) are computed using Formulas 1410 and 1411 after computing z(n 1) using Formula 141 and e (n 1) using Formulas 146 and 147 If x(n) falls outside [LCLx (n, UCLx (n)], x(n) is considered as attack; otherwise, x(n) is
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Table 141 False alarms of EWMA control charts for attacks with the text editing (T) and web browsing (W) norms
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Attacks Apache T 14 1 3 11 12 14 12 2 2 3 6 1 1 5 14 14 13 3 0 34 23 43 23 14 32 3 14 4 20 15 12 5 12 16 0 2 1 3 2 5 2 21 21 34 34 2 2 0 0 1 0 2 18 2 15 12 7 1 13 5 0 10 2 16 3 1 2 3 W T W T W T W T W T W T W T W T ARP Distributed Fork FTP Hardware Remote Rootkit Security W Software Vulnerability T W T W
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