Structural Decomposability of Encrypted Traffic Side-Channel Leakage

Abstract

Existing side-channel theories treat leakage as a holistic quantity $I(X;Y)$, without characterizing its internal structure. This paper studies the \emph{structural decomposability} of encrypted-traffic side-channel leakage. Via the structural causal model $X\!\to\!Y_{\mathrm{size}}\!\to\!Y_{\mathrm{dir}}\!\to\!Y_{\mathrm{time}}$ and the mutual-information chain rule, total leakage is decomposed into three sequential increments for packet size, direction, and timing. Defenses are formalized as mechanism replacement by a strategy variable~$D$; coupling information $C_{\mathrm{size,dir}}=I(Y_{\mathrm{size}};Y_{\mathrm{dir}}\!\mid\!X)$ measures inter-dimensional dependence, and the Markov residual gives a testable condition for a single-dimension defense to sever downstream leakage. Causal efficacy~$η_d$ quantifies per-unit-cost suppression, and a Fisher-geometric approximation $I(X;Y)\approx\frac{1}{2\ln 2}\mathrm{Tr}(GΣ_θ)$ holds under small perturbations. On the Wang dataset (95 websites), $Y_{\mathrm{dir}}$ dominates undefended leakage (0.637\,bits), while Tor's fixed 512-byte cells make $Y_{\mathrm{size}}$ degenerate; FRONT suppresses the direction term by 63\%, yet its Markov residual of 0.021\,bits (95\% CI $[0.016,0.027]$) shows it cannot sever timing leakage; $η_{\mathrm{dir}}=0.97$ vs. $η_{\mathrm{time}}\approx 0$ confirms FRONT's design intent. This yields a computable, structured leakage-accounting method for multi-dimensional joint defense design.