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Abstract-The problem of binary hypothesis testing is considered in a bandwidth-constrained densely populated low-power wireless sensor network operating over insecure links. Observations of the sensors are quantized and encrypted before transmission. The encryption method maps the output of the quantizer to one of the possible quantizer output levels randomly according to a probability matrix. The intended (ally) fusion center (AFC) is aware of the encryption keys (probabilities) while the unauthorized (third party) fusion center (TPFC) is not. A constrained optimization problem is formulated from the point of view of AFC in order to design its decision rule along with the encryption probabilities. The objective function to be minimized is the error probability of AFC and the constraint is a lower bound on the error probability of TPFC. In the binary case the optimal solution is found and in the nonbinary case a good suboptimal solution is analytically obtained. Numerical results are presented to show that it is possible to degrade the error probability of TPFC significantly and still achieve very low probability of error for AFC. The proposed method which may be considered a PHY-layer security scheme is highly scalable since it does not increase the packet overhead or transmit power of the sensors and has very low computational complexity. A scheme is described to randomize the keys so as to defeat any key space exploration attack.Index Terms-Decentralized detection, decision fusion rule, information security, soft decision, wireless sensor networks.

The problem of binary hypothesis testing is considered in a bandwidth-constrained densely populated low-power wireless sensor network operating over insecure links. Observations of the sensors are quantized and encrypted before transmission. The encryption method maps the output of the quantizer to one of the possible quantizer output levels randomly according to a probability matrix. The intended (ally) fusion center (AFC) is aware of the encryption keys (probabilities) while the unauthorized (third party) fusion center (TPFC) is not. A constrained optimization problem is formulated from the point of view of AFC in order to design its decision rule along with the encryption probabilities. The objective function to be minimized is the error probability of AFC and the constraint is a lower bound on the error probability of TPFC. In the binary case the optimal solution is found and in the nonbinary case a good suboptimal solution is analytically obtained. Numerical results are presented to show that it is possible to degrade the error probability of TPFC significantly and still achieve very low probability of error for AFC. The proposed method which may be considered a PHY-layer security scheme is highly scalable since it does not increase the packet overhead or transmit power of the sensors and has very low computational complexity. A scheme is described to randomize the keys so as to defeat any key space exploration attack.

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Handwritten character recognition has been an active area of research. However, because of the recent advancements in mobile devices with limited amount of memory and computational power, efficient and simple algorithms for both online and offline character recognition have become more appealing. In this work, an efficient character recognition systems is proposed using LDA Analysis followed by a Bayesian discriminator function based on the Mahalonobis distance. Since LDA is tailored for Gaussian distributed data and the samples dimensionality is high, a couple of preprocessing steps have been applied to reduce dimensionality and cluster the data into semiGaussian subclasses. In the first step, affine transformations are applied to the training samples in order to make the scheme robust against distortion. Scaling and Rotation are among those popular distortions which have been considered in this work. Inactive pixels are cut off using a simple algorithm in the next step. Then, principal component analysis (PCA) and k-means clustering are applied. The results from preprocessing showed a great potential in dimensionality reduction using transformations that can preserve useful information. Numerical results on the MNIST dataset reached 3% error rate which is lower than the other linear approaches. The proposed linear techniques are discussed in a way that make it easier to have a much clearer understanding of the method and why it works compared to the other classification methods.

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