skip to main content


Title: Asymptotic analysis of a new low complexity encryption approach for the Internet of Things, smart cities and smart grid
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.  more » « less
Award ID(s):
1702555
NSF-PAR ID:
10049235
Author(s) / Creator(s):
;
Date Published:
Journal Name:
2017 IEEE International Conference on Smart Grid and Smart Cities (ICSGSC)
Page Range / eLocation ID:
200 to 204
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
More Like this
  1. 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. 
    more » « less
  2. In large-scale wireless sensor networks, sensor-processor elements (nodes) are densely deployed to monitor the environment; consequently, their observations form a random field that is highly correlated in space.We consider a fusion sensor-network architecture where, due to the bandwidth and energy constraints, the nodes transmit quantized data to a fusion center. The fusion center provides feedback by broadcasting summary information to the nodes. In addition to saving energy, this feedback ensures reliability and robustness to node and fusion-center failures. We assume that the sensor observations follow a linear-regression model with known spatial covariances between any two locations within a region of interest. We propose a Bayesian framework for adaptive quantization, fusion-center feedback, and estimation of the random field and its parameters. We also derive a simple suboptimal scheme for estimating the unknown parameters, apply our estimation approach to the no-feedback scenario, discuss field prediction at arbitrary locations within the region of interest, and present numerical examples demonstrating the performance of the proposed methods. 
    more » « less
  3. Summary

    Many methods for estimation or control of the false discovery rate (FDR) can be improved by incorporating information about π0, the proportion of all tested null hypotheses that are true. Estimates of π0 are often based on the number of p-values that exceed a threshold λ. We first give a finite sample proof for conservative point estimation of the FDR when the λ-parameter is fixed. Then we establish a condition under which a dynamic adaptive procedure, whose λ-parameter is determined by data, will lead to conservative π0- and FDR estimators. We also present asymptotic results on simultaneous conservative FDR estimation and control for a class of dynamic adaptive procedures. Simulation results show that a novel dynamic adaptive procedure achieves more power through smaller estimation errors for π0 under independence and mild dependence conditions. We conclude by discussing the connection between estimation and control of the FDR and show that several recently developed FDR control procedures can be cast in a unifying framework where the strength of the procedures can be easily evaluated.

     
    more » « less
  4. Abstract

    In recent years, cyber‐security of networked control systems has become crucial, as these systems are vulnerable to targeted cyberattacks that compromise the stability, integrity, and safety of these systems. In this work, secure and private communication links are established between sensor–controller and controller–actuator elements using semi‐homomorphic encryption to ensure cyber‐security in model predictive control (MPC) of nonlinear systems. Specifically, Paillier cryptosystem is implemented for encryption‐decryption operations in the communication links. Cryptosystems, in general, work on a subset of integers. As a direct consequence of this nature of encryption algorithms, quantization errors arise in the closed‐loop MPC of nonlinear systems. Thus, the closed‐loop encrypted MPC is designed with a certain degree of robustness to the quantization errors. Furthermore, the trade‐off between the accuracy of the encrypted MPC and the computational cost is discussed. Finally, two chemical process examples are employed to demonstrate the implementation of the proposed encrypted MPC design.

     
    more » « less
  5. Information fusion is a procedure that merges information locally contained at the nodes of a network. Of high interest in the field of distributed estimation is the fusion of local probability distributions via a weighted geometrical average criterion. In numerous practical settings, the local distributions are only known through particle approximations, i.e., sets of samples with associated weights, such as obtained via importance sampling (IS) methods. Thus, prohibiting any closed-form solution to the aforementioned fusion problem. This article proposes a family of IS methods—called particle geometric–average fusion (PGAF)—that lead to consistent estimators for the geometrically-averaged density. The advantages of the proposed methods are threefold. First, the methods are agnostic of the mechanisms used to generate the local particle sets and, therefore, allow for the fusion of heterogeneous nodes. Second, consistency of estimators is guaranteed under generic conditions when the agents use IS-generated particles. Third, a low-communication overhead and agent privacy are achieved since local observations are not shared with the fusion center. Even more remarkably, for a sub-family of the proposed PGAF methods, the fusion center does not require the knowledge of the local priors used by the nodes. Implementation guidelines for the proposed methods are provided and theoretical results are numerically verified. 
    more » « less