Asymptotically Optimal Stochastic Encryption for Quantized Sequential Detection in the Presence of Eavesdroppers

TL;DR

This paper analyzes the asymptotic performance of stochastic encryption in quantized sequential detection with eavesdroppers, proposing optimal encryption strategies that maximize the performance gap between legitimate and eavesdropping fusion centers.

Contribution

It characterizes the asymptotic expected sample size under stochastic encryption and derives the globally optimal encryption scheme for enhancing security in sequential detection.

Findings

Symmetric stochastic encryption is ineffective when error probabilities are equal.

Encryption increases the expected sample size at the legitimate center, degrading detection performance.

Optimal encryption flips only one type of quantized bits to maximize security gap.

Abstract

We consider sequential detection based on quantized data in the presence of eavesdropper. Stochastic encryption is employed as a counter measure that flips the quantization bits at each sensor according to certain probabilities, and the flipping probabilities are only known to the legitimate fusion center (LFC) but not the eavesdropping fusion center (EFC). As a result, the LFC employs the optimal sequential probability ratio test (SPRT) for sequential detection whereas the EFC 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 when the detection error probabilities are set to be the same at the LFC and EFC, every symmetric stochastic encryption is ineffective in the sense that it leads to the same expected sample size at the LFC and EFC. Next, in the asymptotic regime of small detection error probabilities, we show that every stochastic encryption degrades the performance of the quantized sequential detection at the LFC by increasing the expected sample size, and the expected sample size required at the EFC is no fewer than that is required at the LFC. Then the optimal stochastic encryption is investigated in the sense of maximizing the difference between the expected sample sizes required at the EFC and LFC. Although this optimization problem is nonconvex, we show that if the acceptable tolerance of the increase in the expected sample size at the LFC induced by the stochastic encryption is small enough, then the globally optimal stochastic encryption can be analytically obtained; and moreover, the optimal scheme only flips one type of quantized bits (i.e., 1 or 0) and keeps the other type unchanged.