Secure Estimation and Zero-Error Secrecy Capacity

• Published in: IEEE transactions on automatic control Vol. 64; no. 3; pp. 1047 - 1062
• Main Authors: Wiese, Moritz, Oechtering, Tobias J., Johansson, Karl Henrik, Papadimitratos, Panagiotis, Sandberg, Henrik, Skoglund, Mikael
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.03.2019; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Channel coding; Channel estimation; Channels; Cybersecurity; Disturbances; Error analysis; Estimation error; Reliability; Secure state estimation; Security; uncertain wiretap channel; Wiretapping; zero-error secrecy capacity
• ISSN: 0018-9286; 1558-2523; 1558-2523
• DOI: 10.1109/TAC.2018.2849620

We study the problem of securely estimating the states of an unstable dynamical system subject to nonstochastic disturbances. The estimator obtains all its information through an uncertain channel , which is subject to nonstochastic disturbances as well, and an eavesdropper obtains a disturbed version of the channel inputs through a second uncertain channel. An encoder observes and block encodes the states in such a way that, upon sending the generated codeword, the estimator's error is bounded and a security criterion is satisfied, thereby ensuring that the eavesdropper obtains as little state information as possible. Two security criteria are considered and discussed with the help of a numerical example. A sufficient condition on the uncertain wiretap channel , i.e., the pair formed by the uncertain channel from the encoder to the estimator and the uncertain channel from the encoder to the eavesdropper is derived, which ensures that a bounded estimation error and security are achieved. This condition is also shown to be necessary for a subclass of uncertain wiretap channels. To formulate the condition, the zero-error secrecy capacity of uncertain wiretap channels is introduced, i.e., the maximal rate at which data can be transmitted from the encoder to the estimator in such a way that the eavesdropper is unable to reconstruct the transmitted data. Finally, the zero-error secrecy capacity of uncertain wiretap channels is studied.