因果IPD-QIM网络流水印的排队稳定性准则
A Queueing-Stability Criterion for Causal IPD-QIM Network Flow Watermarking
浏览论文内容
中文总结 AI 辅助
研究因果QIM网络流水印在多跳加密链路突发流量中的稳定嵌入问题，将嵌入器建模为反射停留队列，给出稳定性准则及操作窗口，通过模拟验证准则有效性，为因果QIM网络流水印提供稳定嵌入性准则和量化步长配置基线。
中文摘要 AI 辅助
在诸如Tor和级联VPN等多跳加密链路上，隧道技术使数据包长度和协议字段扁平化，数据包间延迟（IPD）成为主动流归因的主要载体。因果关系使嵌入器能够延迟数据包但不能提前，所以每个量化索引调制（QIM）对齐会向延迟缓冲区注入非负停留时间；无界停留会破坏格对齐并使主机连接延迟到不可接受的程度。因果QIM水印在突发流量上是否能稳定嵌入很大程度上依赖于经验配置而非分析。我们将嵌入器建模为固定双格、等概率位规则下的反射停留队列，其中注入依赖于状态，由当前间隔和位决定而非外部因素。通过特定代换得到代数林德利形式恒等式，稳定性由大停留时的忙状态漂移决定。远离临界边界时，对于独立同分布背景，当\(\mu_d>\Delta/4\)（即\(\Delta<4\mu_d\)）时缓冲区稳定；对于平稳遍历和有限状态马尔可夫调制流量且有瞬时过载时，当时间平均强度\(\bar\rho<1\)时稳定。在外生解码下限\(\Delta\ge c\sigma_\xi\)（\(c = 4Q^{-1}(\epsilon/2)\)）条件下，得到操作窗口\(\Delta\in[c\sigma_\xi,4\bar\mu_d)\)。模拟证实仅由均值决定在\(\rho = 1\)处有急剧转变；在四条真实IPD轨迹上，每个模拟链限于单个流，该准则在流局部相关性和突发性下给出正确的稳定性方向，而汇总的跨流均值高估了余量。这些结果为因果QIM网络流水印提供了可测试的稳定嵌入性准则和量化步长配置基线。
英文摘要
On multi-hop encrypted links such as Tor and cascaded VPNs, tunneling flattens packet lengths and protocol fields, leaving inter-packet delay (IPD) as the main carrier for active flow attribution. Causality lets the embedder delay packets but never advance them, so each quantization-index-modulation (QIM) alignment injects nonnegative dwell into a delay buffer; unbounded dwell breaks lattice alignment and delays the host connection unacceptably. Whether a causal QIM watermark embeds stably on bursty traffic has largely been left to empirical configuration rather than analysis. We model the embedder as a reflected dwell queue under the fixed dual-lattice, equiprobable-bit rule, where injection is state-dependent -- set by the current interval and bit -- rather than exogenous. The substitution $Y_i=δ_i-r_i$ gives only an algebraic Lindley-form identity; stability is governed by the busy-state drift at large dwell, where the effective interval collapses to zero and the mean injection becomes $Δ/4$. Away from the critical boundary, the buffer is stable iff $μ_d>Δ/4$ (i.e. $Δ<4μ_d$) for i.i.d. backgrounds, and, under stationary-ergodic and finite-state Markov-modulated traffic with instantaneous overload, iff the time-average intensity $\barρ<1$. With the exogenous decoding floor $Δ\ge cσ_ξ$ ($c=4Q^{-1}(ε/2)$), this yields the operating window $Δ\in[cσ_ξ,4\barμ_d)$. Simulations confirm a sharp transition at $ρ=1$ set only by the mean; on four real IPD traces, with each simulated chain confined to a single flow, the criterion gives the correct stability direction under flow-local correlation and burstiness, while pooled cross-flow means overestimate the margin. These results give a testable stable-embeddability criterion and a quantization-step configuration baseline for causal QIM network flow watermarking.
