Secure Quantized Sequential Detection in the Internet of Things with Eavesdroppers

We consider sequential detection based on one-bit quantized data in the Internet of Things (IoT) with an eavesdropper. A lightweight physical-layer encryption algorithm, called stochastic encryption, is employed as a counter measure that flips the quantization bits at each IoT sensor according to certain probabilities, and the flipping probabilities are only known to the legitimate cloud (LC) but not the eavesdropping cloud (EC). Due to the optimality of the sequential probability ratio test (SPRT), the LC employs the SPRT for sequential detection whereas the EC employs a mismatched SPRT (MSPRT). We characterize the asymptotic performance of the MSPRT in terms of the expected sample size as a function of the vanishing error probabilities. We show that every symmetric stochastic encryption is ineffective in the sense that it leads to the same expected sample size at the LC and EC when the LC and EC have the same detection accuracy. Next, in the asymptotic regime of small detection error probabilities, we show that every stochastic encryption degrades the performance of the EC to a greater extent in the sense that the expected sample size required at the EC is no fewer than that is required at the LC. Moreover, the optimal stochastic encryption is derived in the sense of maximizing the difference between the expected sample sizes required at the EC and LC.