  In this paper, an anti-eavesdropping estimation problem is investigated. A
linear encryption scheme is utilized, which first linearly transforms
innovation via an encryption matrix and then encrypts some components of the
transformed innovation. To reduce the computation and energy resources consumed
by the linear encryption scheme, both stochastic and deterministic intermittent
strategies which perform the linear encryption scheme only at partial moments
are developed. When the system is stable, it is shown that the mean squared
error (MSE) of the eavesdropper converges under any stochastic or deterministic
intermittent strategy. Also, an analytical encryption matrix that maximizes the
steady-state of the MSE is designed. When the system is unstable, the
eavesdropper's MSE can be unbounded with arbitrary positive encryption
probabilities and decision functions if encryption matrices are chosen
appropriately. Then, the relationship between the aforementioned encryption
parameters and the eavesdropper's MSE is analyzed. Moreover, a single
intermittent strategy which only encrypts one message is discussed. This
strategy can be unavailable for stable systems, but can make the eavesdropper's
MSE unbounded in unstable systems for the encrypted message satisfies a linear
matrix inequality (LMI) condition. The effectiveness of the proposed methods is
verified in the simulation.
