Uncertain Wiretap Channels and Secure Estimation

Uncertain wiretap channels are introduced. Their zero-error secrecy capacity is defined. If the sensor-estimator channel is perfect, it is also calculated. Further properties are discussed. The problem of estimating a dynamical system with nonstochastic disturbances is studied where the sensor is connected to the estimator and an eavesdropper via an uncertain wiretap channel. The estimator should obtain a uniformly bounded estimation error whereas the eavesdroppers error should tend to infinity. It is proved that the system can be estimated securely if the zero-error capacity of the sensor-estimator channel is strictly larger than the logarithm of the systems unstable pole and the zero-error secrecy capacity of the uncertain wiretap channel is positive.