Rate-Distortion Function for Encrypted Traffic Side-Channel Defense

• URL: http://arxiv.org/abs/2607.17889v1
• Date: Mon, 20 Jul 2026 12:38:49 GMT
• Title: Rate-Distortion Function for Encrypted Traffic Side-Channel Defense
• Abstract summary: We prove that the optimal defense has an exponential-tilting structure governed by KKT conditions.<n>On real-world website-fingerprinting defenses, the framework locates Front ($_mathrmgap=0.028$,bits), WTF-PAD ($0.034$,bits, and TrafficSliver ($0.124$,bits) above the theoretical curve.
• Score: 23.361601797200475
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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