Rate-Distortion Function for Encrypted Traffic Side-Channel Defense

Parameter selection for encrypted traffic defense has long relied on empirical tuning, yet the fundamental question -- 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 side-channel rate-distortion function R sc(D) within the stationary memoryless defense class iid and provide its complete characterization. We prove that R 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 iid. For binary equal-prior tasks, D = 2 W 1(P 0,P 1) via Kantorovich--Rubinstein duality. On real-world website-fingerprinting defenses, the framework locates Front (gap = 0.028,bits), WTF-PAD (0.034,bits), and TrafficSliver (0.124,bits) above the theoretical curve, quantifying their suboptimality gaps.