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In Internet of Things (IoT) applications requiring parameter estimation, sensors often transmit quantized observations to a fusion center through a wireless medium where the observations are susceptible to unauthorized eavesdropping. The fusion center uses the received data to estimate desired parameters. To provide security to such networks, some low complexity encryption approaches have been proposed. In this paper, we generalize those approaches and present an analysis of their estimation and secrecy capabilities. We show that the dimension of the unknown parameter that can be efficiently estimated using an unbiased estimator when using these approaches, is upper bounded. Assuming that an unauthorized eavesdropper is aware of the low complexity encryption process but is unaware of the encryption key, we show successful eavesdropping, even with a large number of observations, is impossible with unbiased estimators and independent observations for these approaches. Numerical results validating our analysis are presented.

Abstract (WSN) using encrypted non-binary quantized data is studied. In a WSN, sensors transmit their observations to a fusion center through a wireless medium where the observations are susceptible to unauthorized eavesdropping. Encryption approaches for WSNs with fixed threshold binary quantization were previously explored. However, fixed threshold binary quantization limits parameter estimation to scalar parameters. In this paper, we propose a stochastic encryption approach for WSNs that can operate on non-binary quantized observations and has the capability for vector parameter estimation. We extend a binary stochastic encryption approach proposed previously, to a nonbinary generalized case. Sensor outputs are quantized using a quantizer with R + 1 levels, where R in {1.2. 3 ...}, encrypted by flipping them with certain flipping probabilities, and then transmitted. Optimal estimators using maximum-likelihood estimation are derived for both a legitimate fusion center (LFC) and a third party fusion center (TPFC) perspectives. We assume the TPFC is unaware of the encryption. Asymptotic analysis of the estimators is performed by deriving the Cramer-Rao lower bound for LFC estimation, and the asymptotic bias and variance for TPFC estimation. Numerical results validating the asymptotic analysis are presented.