Secure Estimation and Zero-Error Secrecy Capacity

Moritz Wiese

Published Jan 23, 2020• 32 citations

Abstract

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.

DOI: 10.1109/tac.2018.2849620

Related papers

Secure Estimation and Zero-Error Secrecy Capacity

Moritz Wiese, Tobias J. Oechtering, Karl Henrik Johansson +3 more

arXiv:1612.05552IEEE Transactions on Automatic ControlJun 21, 20180 citations

Secrecy capacity of wiretap channels with the bit error rate criterion

Ryutaroh Matsumoto

The coding problem over wiretap channels is to realize an encoder and a decoder such that the legitimate receiver can correctly decode transmitted secret messages while the eavesdropper knows little about the secret messages. Traditionally, the secrecy of messages to the eavesdropper has been measured in terms of mutual information. Recently, several researches on the wiretap channels employ the bit error rate after decoding by the eavesdropper as a secrecy measure. In this note, we show that the secrecy capacity with respect to the bit error rate criterion is different from that with the traditional mutual information criterion. In addition to that, the encoder can be deterministic for the bit error rate criterion, while it must be stochastic for the mutual information criterion.

IEICE Communications ExpressJan 1, 20160 citations

Wiretap Channel With Causal State Information and Secure Rate-Limited Feedback

Alejandro Cohen, Asaf Cohen

In this paper, we consider the secrecy capacity of a wiretap channel in the presence of causal state information and secure rate-limited feedback. In this scenario, the causal state information from the channel is available to both the legitimate transmitter and the legitimate receiver. In addition, the legitimate receiver can send secure feedback to the transmitter at a limited rate Rf. We derive upper and lower bounds on the secrecy capacity and show that, when the channel to the eavesdropper is degraded, the bounds are tight and the secrecy capacity is completely characterized. The capacity achieving scheme is based on Wyner, Csiszár, and Körner wiretap coding and two steps of shared-key generation: one from the state information and one via the noiseless feedback. The upper bound is more involved and requires a nontrivial recursive lemma extending previous results in the literature to include both state and feedback. We conclude the paper by showing that a few interesting known results can be seen as special cases of the above, as well as discussing the case where the source of local randomness at the encoder is limited.

IEEE Transactions on CommunicationsJan 7, 201624 citations

On the ergodic secrecy capacity of the wiretap channel under imperfect main channel estimation

Zouheir Rezki, Ashish J. Khisti, Mohamed‐Slim Alouini

The ergodic secrecy capacity of the wiretap channel is known when the main channel (between the transmitter and the legitimate receiver) state information (CSI) is perfect at the transmitter and the coherence period is sufficiently large to enable random coding arguments in each block. In a fast fading scenario, when the codeword length spans many coherence periods, the secrecy capacity is still not known. In this paper, we present a framework that characterizes this secrecy capacity under imperfect main channel estimation at the transmitter. Inner and outer bounds on the ergodic secrecy capacity are derived for a class of independent identically distributed (i.i.d.) fading channels. The achievable rate is a simple on-off scheme using a Gaussian input. The upper bound is obtained using an appropriate correlation scheme of the main and the eavesdropper channels. The upper and the lower bounds coincide with recently derived ones in the perfect main CSI extreme. Furthermore, the lower bound matches the upper bound in no main CSI extreme, where the secrecy capacity is equal to zero. Numerical results are provided for independent identically distributed (i.i.d.) Rayleigh fading channels.

Asilomar Conference on Signals, Systems and Computers (ACSSC)Nov 1, 201120 citations

Wiretap channel with causal state information and secure rate-limited feedback

Alejandro Cohen, Asaf Cohen

In this paper, we consider the secrecy capacity of a wiretap channel in the presence of causal state information and secure rate-limited feedback. In this scenario, the causal state information from the channel is available to both the legitimate transmitter and legitimate receiver. In addition, the legitimate receiver can send secure feedback to the transmitter at a limited rate Rf. We shown that the secrecy capacity is bounded by Cs ≥ max {p(u|v) p(x|u,v)max min{I(U;Y|v) - I(U;Z|V) + H(V|Z) + Rf, I(U;Y|V)},p(u)p(x|u,v)max min{H(V|Z,U) + Rf, I(U;Y|V)}}. Moreover, when the channel to the legitimate receiver is less noisy than the channel to the eavesdropper, the bound is shown to be tight. The capacity achieving scheme is based on both the Wyner wiretap coding and two steps of shared-key generation: one from the state information and one via the noiseless feedback. Finally, we consider several special cases. When state information is available only at the legitimate receiver, the analysis suggests that unlike previous results involving feedback, it is better to use the feedback to send the state information to the transmitter (when possible), rather than send a random key.

Allerton Conference on Communication, Control, and ComputingOct 1, 20131 citation

Wiretap Channel With Causal State Information and Secure Rate-Limited Feedback

Alejandro Cohen, Asaf Cohen

In this paper, we consider the secrecy capacity of a wiretap channel in the presence of causal state information and secure rate-limited feedback. In this scenario, the causal state information from the channel is available to both the legitimate transmitter and legitimate receiver. In addition, the legitimate receiver can send secure feedback to the transmitter at a limited rate Rf . We shown that the secrecy capacity is bounded. Moreover, when the channel to the legitimate receiver is less noisy than the channel to the eavesdropper, the bound is shown to be tight. The capacity achieving scheme is based on both the Wyner wiretap coding and two steps of shared-key generation: one from the state information and one via the noiseless feedback. Finally, we consider several special cases. When state information is available only at the legitimate receiver, the analysis suggests that unlike previous results involving feedback, it is better to use the feedback to send the state information to the transmitter (when possible), rather than send a random key.

arXiv:1308.6736Aug 30, 20131 citation