Estimation Theoretic Secure Communication via Encoder Randomization

Abstract

Estimation theoretic secure transmission of a scalar random parameter is investigated in the presence of an eavesdropper. The aim is to minimize the estimation error at the receiver under a secrecy constraint at the eavesdropper; or, alternatively, to maximize the estimation error at the eavesdropper for a given estimation accuracy limit at the receiver. In the considered setting, the encoder at the transmitter is allowed to use a randomized mapping between two one-to-one and continuous functions and the eavesdropper is fully aware of the encoding strategy at the transmitter. For small numbers of observations, both the eavesdropper and the receiver are modeled to employ linear minimum mean-squared error (LMMSE) estimators, and for large numbers of observations, the expectation of the conditional Cramér-Rao bound (ECRB) metric is employed for both the receiver and the eavesdropper. Optimization problems are formulated and various theoretical results are provided in order to obtain the optimal solutions and to analyze the effects of encoder randomization. In addition, numerical examples are presented to corroborate the theoretical results. It is observed that stochastic encoding can bring significant performance gains for estimation theoretic secrecy problems.

Parameter Encoding for ECRB Minimization in the Presence of Jamming

“…In the presence of eavesdropping, secure transmission of scalar and vector parameters is investigated in an estimation theoretic framework in [2]- [4]. In particular, the optimal encoding strategy for a scalar parameter is investigated in [2] by minimizing the expectation of the conditional Cramér-Rao bound (ECRB) at the intended receiver under a constraint on the mean-squared error (MSE) at the eavesdropper.…”

“…In particular, the optimal encoding strategy for a scalar parameter is investigated in [2] by minimizing the expectation of the conditional Cramér-Rao bound (ECRB) at the intended receiver under a constraint on the mean-squared error (MSE) at the eavesdropper. In [4], the optimal encoding strategy for estimation theoretic security is analyzed, where the transmitter is allowed to perform randomization between two one-to-one and continuous encoding functions and the eavesdropper is fully aware of the encoding strategy at the transmitter.…”

Optimal Power Allocation for Secure Estimation of Multiple Parameters

“…E STIMATION theoretic secrecy has been investigated in various settings as an alternative to information theoretic secrecy, where the aim is the secure transmission of parameters to intended users in the presence of eavesdroppers [1]- [8]. In the literature, various approaches such as parameter encoding [4], beamforming [9], [10], [11], artificial noise generation [6], and encoder randomization [5] were adopted to maximize estimation accuracy at intended users while achieving secrecy. In [2], optimal deterministic encoding of a scalar parameter was proposed to minimize the expectation of the conditional Cramér-Rao bound of the parameter at an intended receiver under an estimation theoretic secrecy constraint.…”

Optimal Parameter Design for Estimation Theoretic Secure Broadcast

“…In [4], secure transmission of a vector parameter is investigated and practical encoding strategies are introduced. In [5], estimation theoretic security is investigated when the encoder at the transmitter is allowed to use a randomized mapping with two functions and the eavesdropper is fully aware of the encoding strategy.…”