Rate-Distortion Function for Encrypted Traffic Side-Channel Defense
2026-07-20 • Cryptography and Security
Cryptography and Security
AI summaryⓘ
The authors study how well encrypted traffic defenses can hide information while keeping quality of service within a budget. They define a mathematical function to describe the trade-off between privacy leakage and defense cost, focusing on a specific type of simple defense strategy. They show that this function has nice properties like being smooth and convex, and they find the best possible defense within their model. They also compare existing real-world defenses to this theoretical limit, showing how far those methods are from the best possible performance.
encrypted traffic defenseside-channel attackrate-distortion functionWasserstein distancestationary memoryless defensePareto frontierKKT conditionsKantorovich-Rubinstein dualitywebsite fingerprinting
Authors
Guangjie Liu, Guang Cheng, Weiwei Liu, Yutong Wang
Abstract
Parameter selection for encrypted traffic defense has long relied on empirical tuning, yet the fundamental question -- \emph{given a QoS cost budget $D$, how low can the leakage rate go under sustained observation?} -- lacks a provable, computable baseline. Taking the semantic label sequence $X^n$ as the source, the defended feature sequence $Y^n$ as the observation, and Wasserstein-1 distance as the defense cost, we define the \emph{side-channel rate-distortion function} $R^{\mathrm{sc}}(D)$ within the stationary memoryless defense class $Θ_{\mathrm{iid}}$ and provide its complete characterization. We prove that $R^{\mathrm{sc}}(D)$ is monotone decreasing, convex, and continuous, with exact endpoints; the optimal defense has an exponential-tilting (Boltzmann) structure governed by KKT conditions; and the curve constitutes the exact Pareto frontier within $Θ_{\mathrm{iid}}$. For binary equal-prior tasks, $D_{\max} = \tfrac{1}{2}W_1(P_0,P_1)$ via Kantorovich--Rubinstein duality. On real-world website-fingerprinting defenses, the framework locates Front ($Δ_{\mathrm{gap}}{=}0.028$\,bits), WTF-PAD ($0.034$\,bits), and TrafficSliver ($0.124$\,bits) above the theoretical curve, quantifying their suboptimality gaps.