| Summary: | We consider the problem of binary hypothesis testing using a distributed wireless sensor network. Identical binary quantizers are used on the sensor's observations and the outputs are encrypted using a probabilistic cipher. The third party (enemy) fusion centers are unaware of the presence of the probabilistic encipher. We find the optimal (minimum-probability-of-error) fusion rule for the ally (friendly) fusion center subject to a lower bound on the the probability of error for the third-party fusion centers.
To obtain the minimum probability of error, we first prove the quasi-convexity of error probability with respect to the sensor's threshold for a given cipher and show the existence of a unique positive minimum for error probability of the ally fusion center. The threshold corresponding to the minimum error-probability is evaluated numerically and the appropriate cipher that deteriorates the performance of the third-party fusion center below the required limits is obtained.
Our results show that, by adjusting the sensor threshold and the encryption parameters, it is possible to achieve acceptable performance for the ally fusion center while causing significant degradation to the performance of the third party fusion center.
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