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EBSCO Publishing : eBook Collection (EBSCOhost) - printed on 2/16/2016 3:37 AM via CGC-GROUP OF COLLEGES (GHARUAN) AN: 779681 ; Heard, Nicholas, Adams, Niall M..; Data Analysis for Network Cyber-security Account: ns224671
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Rapid Detection of Attacks by Quickest Changepoint Detection Methods 51 Further improvement may be achieved by using either mixtures or adaptive versions with generalized likelihood ratio-type statistics similar to (2.10) – (2.11). Also, an improvement can be obtained by running several CUSUM (or SR) algorithms in parallel, each tuned to its own value of ( q, δ ). This multichart CUSUM and SR procedures are robust and very efficient (Tartakovsky and Polunchenko, 2007, 2008). In Tartakovsky et al. (2006a,b), we conjectured that in certain con- ditions splitting packets in “bins” and considering multichannel detectors helps localize and detect attacks more rapidly. Consider the multichannel scenario where the vector data X (1) n , . . . , X ( N ) n are used to decide on the presence of anomalies. Here X ( i ) n is a sample obtained at time n in the i th channel. For example, in the case of UDP flooding attacks the channels correspond to packet sizes (size bins), while for TCP SYN attacks they correspond to IP addresses (IP bins). Similarly to the single-channel case, for i = 1 , . . . , N , introduce the score functions S ( i ) n = C i 1 Y i n + C i 2 ( Y i n ) 2 C i 3 (or any other reasonable scores in channels) and the corresponding score-based CUSUM and SR statistics W ( i ) n = max 0 , W ( i ) n 1 + S ( i ) n , W ( i ) 0 = 0; R ( i ) n = (1 + R ( i ) n ) exp S ( i ) n , R ( i ) 0 = 0 . (2.17) Typically, the statistics W ( i ) n and log R ( i ) n ( i = 1 , . . . , N ) remain close to zero in normal conditions; when the change occurs in the j th channel, the j th statistics W ( j ) n and log R ( j ) n start rapidly drifting upward. The “MAX” algorithm previously proposed by Tartakovsky et al. (2006a,b) is based on the maximal statistic W max ( n ) = max 1 i N W ( i ) n , which is compared to a threshold h that controls FAR, i.e., the algorithm stops and declares the attack at T max ( h N ) = min { n 1 : W max ( n ) h N } . (2.18) This method shows very high performance and is the best one can do when attacks are visible in one or very few channels. The latter conclu- sion can be explained as follows. If the attack is visible in the i th channel (and only in this channel), then analogously to (2.14) the average delay to detection SADD i ( T max ) = sup ν 0 E ν,i ( T max ν | T max > ν ) is approximated as SADD i ( T max ) h N /Q i , where Q i = lim n →∞ 1 n E 0 ,i n k =1 S ( i ) k is the “signal-to-noise” ratio (related to the attack intensity relative to the back- ground traffic) in the i th channel. In the N -channel system, the threshold Copyright © 2014. Imperial College Press. All rights reserved. May not be reproduced in any form without permission from the publisher, except fair uses permitted under U.S. or applicable copyright law.
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