The widespread adoption of TLS 1.3 and QUIC has rendered payload content invisible, shifting traffic analysis toward side-channel features. However, rigorous justification for why side-channel leakage is inevitable in encrypted communications has been lacking. This paper establishes a strict foundation from information theory by constructing a formal model \(Σ=(Γ,Ω)\), where \(Γ=(A,Π,Φ,N)\) describes the causal chain of application generation, protocol encapsulation, encryption transformation, and network transmission, while \(Ω\) characterizes observation capabilities. Based on composite channel structure, data processing inequality, and Lipschitz statistics propagation, we propose and prove the Side-Channel Existence Theorem: for distinguishable semantic pairs, under conditions including mapping non-degeneracy (\(\mathbb{E}[d(z_P,z_N)\mid X]\le C\)), protocol-layer distinguishability (expectation difference \(\ge\barΔ\)), Lipschitz continuity, observation non-degeneracy (\(ρ>0\)), and propagation condition (\(C<\barΔ/2L_\varphi\)), the mutual information \(I(X;Y)\) is strictly positive with explicit lower bound. The corollary shows that in efficiency-prioritized systems, leakage is inevitable when at least one application pair is distinguishable. Three factors determine the boundary: non-degeneracy constant \(C\) constrained by efficiency, distinguishability \(\barΔ\) from application diversity, and \(ρ\) from analyst capabilities. This establishes the first rigorous information-theoretic foundation for encrypted traffic side channels, providing verifiable predictions for attack feasibility, quantifiable benchmarks for defenses, and mathematical basis for efficiency-privacy tradeoffs.

翻译：TLS 1.3与QUIC的广泛部署使得载荷内容不可见，从而将流量分析转向侧信道特征。然而，关于加密通信中侧信道泄露为何必然存在的严格论证尚属空白。本文从信息论角度建立严格基础，构建形式化模型\(Σ=(Γ,Ω)\)：其中\(Γ=(A,Π,Φ,N)\)描述应用生成、协议封装、加密变换与网络传输的因果链，\(Ω\)表征观测能力。基于复合信道结构、数据处理不等式与Lipschitz统计量传播，我们提出并证明了侧信道存在定理：对于可区分的语义对，在满足映射非退化性（\(\mathbb{E}[d(z_P,z_N)\mid X]\le C\)）、协议层可区分性（期望差\(\ge\barΔ\)）、Lipschitz连续性、观测非退化性（\(ρ>0\)）及传播条件（\(C<\barΔ/2L_\varphi\)）时，互信息\(I(X;Y)\)严格为正且具有显式下界。推论表明，在效率优先的系统中，只要至少存在一个可区分的应用对，泄露就必然发生。边界由三个因素决定：受效率约束的非退化常数\(C\)、源于应用多样性的可区分度\(\barΔ\)，以及取决于分析者能力的观测参数\(ρ\)。这为加密流量侧信道建立了首个严格的信息论基础，为攻击可行性提供可验证的预测，为防御措施提供可量化的基准，并为效率与隐私的权衡奠定数学基础。