We investigate the structure of quantizer rules at the local sensors in distributed detection networks, in the presence of eavesdroppers (Eve), under asymptotic regime (number of sensors tending to infinity) for binary hypotheses. These local quantizers are designed in such a way that the confidentiality of sensor data is preserved while achieving optimal detection performance at the fusion center (FC). In the case of Eve with noisier channels, for a general channel model, we show that these optimal quantizer rules at the local sensors are always on the boundaries of the achievable region of sensor's ROC. If there is a constraint on the Eve's performance, based on our numerical results, we conjecture that the structure of an optimal quantizer is LRT-based. The above argument is corroborated with a numerical example using BSC channels for the Eve and ideal channels for the FC. In the case of Eve with better channels, we prove that the quantizer rules that can provide confidentiality along with optimal detection performance, cannot send any useful information to the fusion center (FC). We propose a jamming scheme for the FC against Eve and evaluate the optimal distribution for the Gaussian jamming signal that requires minimum energy to make both FC and Eve's channel similar in distributed detection performance.