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Resilient Detection in the Presence of Integrity Attacks

Mo, Yilin and Hespanha, João P. and Sinopoli, Bruno (2014) Resilient Detection in the Presence of Integrity Attacks. IEEE Transactions on Signal Processing, 62 (1). pp. 31-43. ISSN 1053-587X.

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We consider the detection of a binary random state based on m measurements that can be manipulated by an attacker. The attacker is assumed to have full information about the true value of the state to be estimated as well as the values of all the measurements. However, the attacker can only manipulate n of the m measurements. The detection problem is formulated as a minimax optimization, where one seeks to construct an optimal detector that minimizes the “worst-case” probability of error against all possible manipulations by the attacker. We show that if the attacker can manipulate at least half the measurements (n ≥ m/2) then the optimal worst-case detector should ignore all m measurements and be based solely on the a-priori information. When the attacker can manipulate less than half of the measurements (n < m/2), we show that the optimal detector is a threshold rule based on a amming-like distance between the (manipulated) measurement vector and two appropriately defined sets. For the special case where n=(m-1)/2, our results provide a constructive procedure to derive the optimal detector. We also design a heuristic detector for the case where n « m, and prove the asymptotic optimality of the detector when m → ∝. Finally we apply the proposed methodology in the case of i.i.d. Gaussian measurements.

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Additional Information:© 2013 IEEE. Manuscript received February 22, 2013; revised June 04, 2013 and September 04, 2013; accepted September 21, 2013. Date of publication October 01, 2013; date of current version December 03, 2013. The associate editor coordinating the review of this manuscript and approving it for publication was Prof. Xiao-Ping Zhang. This work was supported by Grant W911NF-09-0553 from the Army Research Office Foundation and Grants CNS-1135895 and ECCS-0955111 from NSF.
Funding AgencyGrant Number
Army Research Office (ARO)W911NF-09-0553
Subject Keywords:Detection algorithms, robustness, fault tolerance
Issue or Number:1
Record Number:CaltechAUTHORS:20140303-153552196
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Official Citation:Mo, Y.; Hespanha, J.P.; Sinopoli, B., "Resilient Detection in the Presence of Integrity Attacks," Signal Processing, IEEE Transactions on , vol.62, no.1, pp.31,43, Jan.1, 2014 doi: 10.1109/TSP.2013.2284145
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:44111
Deposited By: Ruth Sustaita
Deposited On:03 Mar 2014 23:54
Last Modified:03 Oct 2019 06:14

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