Rate-Distortion Function for Encrypted Traffic Side-Channel Defense

2026-07-20

AI Summary

This work addresses a critical gap in existing encrypted traffic defenses: the absence of a computable and provable lower bound on information leakage under quality-of-service cost constraints. Modeling semantic label sequences as a source and post-defense feature sequences as observations, the study introduces and fully characterizes, for the first time within the class of i.i.d. defenses, a side-channel rate–distortion function where defense cost is measured by the Wasserstein-1 distance. Leveraging information theory, optimal transport, and convex optimization, the authors reveal that optimal defenses exhibit an exponential tilting structure and form a Pareto frontier, and they derive the maximum distortion for binary symmetric-prior tasks. Experiments demonstrate that state-of-the-art schemes—Front, WTF-PAD, and TrafficSliver—exhibit information leakage gaps of 0.028, 0.034, and 0.124 bits, respectively, from the theoretical optimum.

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.

Problem

• side-channel defense
• rate-distortion function
• encrypted traffic
• information leakage
• Wasserstein distance

Innovation

• side-channel rate-distortion
• encrypted traffic defense
• Wasserstein-1 distance
• Pareto frontier
• exponential tilting