Secure Estimation and Zero-Error Secrecy Capacity

We study the problem of 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 such that a security criterion is satisfied ensuring that the eavesdropper obtains as little state information as possible. Two security criteria are considered. A sufficient condition on the uncertain wiretap channel, i.e., the pair formed by the uncertain channel from encoder to estimator and the uncertain channel from encoder to 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. The zero-error secrecy capacity of uncertain wiretap channels is studied. M. Wiese, T. J. Oechtering and M. Skoglund are with the Department for Communication Theory, KTH Royal Institute of Technology, Osquldas väg 10, SE-10044 Stockholm, Sweden. K. H. Johansson and H. Sandberg are with the Department for Automatic Control, KTH Royal Institute of Technology, Osquldas väg 10, SE-10044 Stockholm, Sweden. P. Papadimitratos is with the Networked Systems Security Group, KTH Royal Institute of Technology, Osquldas väg 6, SE-10044 Stockholm, Sweden. e-mail: {moritzw, oech, kallej, papadim, hsan, skoglund}@kth.se This paper was presented in part at the 2016 IEEE International Symposium on Information Theory in Barcelona, Spain and at the 55th IEEE Conference on Decision and Control in Las Vegas, USA. ar X iv :1 61 2. 05 55 2v 1 [ cs .S Y ] 1 6 D ec 2 01 6