The paper establishes a strict property hierarchy: unobservability ⇒ anonymity, and sender/recipient anonymity ⇒ relationship anonymity. Unobservability is strictly stronger than anonymity because it additionally requires undetectability against all uninvolved subjects — the IOI's very existence must be hidden — while anonymity only hides the subject's relationship to the IOI.

Global anonymity is maximized when the anonymity set is large and behavior is uniformly distributed: 'global anonymity is maximal iff all subjects within the anonymity set are equally likely.' Strong global anonymity does not protect individual 'likely suspects' — even in a strong-anonymity system, one user with distinctive behavior may have weak individual anonymity. Strong or even maximal global anonymity does not imply strong anonymity of each particular subject.

§3 defense

Adding dummy traffic to any anonymity mechanism yields the corresponding kind of unobservability: 'A mechanism to achieve some kind of anonymity appropriately combined with dummy traffic yields the corresponding kind of unobservability.' DC-nets achieve sender anonymity and MIX-nets achieve relationship anonymity; with dummy traffic both achieve the corresponding sender and relationship unobservability respectively.

§8 defense

Pseudonymity uses persistent identifiers other than real names, enabling accountability while providing partial unlinkability; however, use of the same pseudonym across different contexts enables linkability: the attacker can link all data related to a pseudonym. Unlinkability of two messages requires that the attacker cannot sufficiently distinguish whether they share a sender or recipient; for a scenario with n senders, this holds iff the probability of common authorship is sufficiently close to 1/n.

§4, §9, §11 defense

Undetectability of a message requires that it be indistinguishable from 'random noise' — an attacker cannot sufficiently distinguish whether the message exists or not. This is distinct from anonymity, which protects only the relationship between an IOI and a subject, not the IOI's existence itself. Undetectability is possible only for subjects not involved in the IOI; senders and recipients cannot achieve it against each other.

§6 defense

A three-stage detection pipeline exploiting the "dual-role" behavioral fingerprint of single-IP circumvention relays achieved 23.2% recall (96/414 ground-truth relays) with a 0.18% false-positive rate against 97,651 benign TLS servers, for an overall accuracy of 99.5%. The ground-truth set covered OpenVPN, WireGuard, and SOCKS relays identified in a 17 TB single-day backbone trace (WIDE Project, April 9, 2025).

2026-almutairi-server §3.4, Table 1 traffic-shapedpiflow-correlation

NATA (Non-invasive Active Traffic-correlation Analysis) injects low-frequency bandwidth waveforms (sinusoidal, square-wave, triangular) into Tor TCP connections at an upstream gateway without endpoint compromise, payload decryption, or Tor-browser modification. BM-Net, a selective state-space classifier trained on the exit-side observations, achieves a 99.65% binary detection F1 score distinguishing watermarked from natural traffic on a 20,000-trace real-world dataset.

2026-fan-activeflowmark-assessing-tor §IV, §VI.D, Table III flow-correlationtraffic-shapeml-classifier

BM-Net achieves a 99.65% binary detection F1 score for distinguishing bandwidth-watermarked Tor flows from natural traffic, outperforming all evaluated baselines (next best: TikTok at 75.96% F1). The accuracy gap stems from active perturbation imposing a deterministic low-frequency throughput constraint rather than relying on subtle natural metadata, making the detection task fundamentally easier than passive website fingerprinting.

2026-fan-activeflowmark-assessing-tor §VI-D, Table III–IV flow-correlationtraffic-shapeml-classifier

BM-Net achieves a 99.65% binary detection F1 score distinguishing watermarked from natural Tor flows, and a 97.5% macro-F1 score for fine-grained modulation classification across sinusoidal, square-wave, and triangular patterns. The fine-grained test set contains 201 held-out samples collected from ten clients across five geographic regions (Europe, North America, Australia, Southeast Asia, East Asia), with training traces including traffic collected under WTF-PAD and Walkie-Talkie defenses.

2026-fan-activeflowmark-assessing-tor §VI-D, Table III, Table V flow-correlationml-classifiertraffic-shape

Active bandwidth perturbation has an inherent detectability–stability trade-off: overly aggressive low-rate phases cause Tor SENDME-based flow control stalls, retransmissions, timeouts, or circuit replacement before sufficient correlation evidence is collected. The paper selects a 30-second modulation period and an empirically determined minimum shaping rate; the usable shaping range varies with relay load, path length, TCP congestion control behavior, and Tor multiplexing.

2026-fan-activeflowmark-assessing-tor §VII-A flow-correlationtraffic-shape

BM-Net achieves a 97.5% macro-F1 score for fine-grained classification of three modulation geometries (sinusoidal, square-wave, triangular) from noisy exit-side Tor observations using only 201 labeled test samples collected across cross-continental Tor paths. Residual errors concentrate between natural traffic and square-wave modulation, as abrupt low-rate transitions are partially smoothed by Tor multiplexing and network jitter.

2026-fan-activeflowmark-assessing-tor §VI-D, Table V flow-correlationml-classifiertraffic-shape