Inevitability of Encrypted Traffic Side-Channel Leakage in the Multi-Class Setting

The Side-Channel Existence Theorem proves $I(X;Y)>0$ in the binary, undefended setting, but is confined to pairwise arguments and ignores active defenses. We extend it to $k$ classes via the per-class decomposition $I(X;Y)=\sum_iπ_i D_{\mathrm{KL}}(P_{Y|i}\|P_Y)$, with defense cost modelled by per-c