SCATTER

Sequential CUSUM Analysis of Telemetry for Threat-Exposure Regions — an information-theoretic framework for the security of telemetry-based intrusion detection in decoy-state BB84 quantum key distribution, and the DEGENERACY attack, an eavesdropper that hides in cheap telemetry while stealing the key.

Pure Monte-Carlo simulation. No hardware required.

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Motivation

The textbook security signal of BB84 is the quantum bit error rate (QBER): if it stays below ~11 %, the key is accepted. But device-imperfection attacks (photon-number splitting, detector blinding, time-shift) leave the QBER at its honest value while leaking most of the key. Modern defenses add machine-learning intrusion detection on richer telemetry — detector click statistics, timing histograms, decoy residuals. This repository asks a sharper question:

How much telemetry must you observe, and for how long, before an eavesdropper is fundamentally undetectable?

We answer it with an information-theoretic bound rather than an empirical classifier score, and we exhibit an attack that saturates it.

Intercept-resend is caught (QBER past the abort threshold) but leaks little; PNS, time-shift, and stealthy blinding sit at honest QBER while Eve knows 35–100 % of the key.

The two contributions

1. SCATTER — detectability as an information-theoretic quantity

Each block of ~10⁴–10⁶ pulses produces a telemetry vector whose law is Gaussian by the central limit theorem. The detectability of an attack is the KL divergence between the honest and attacked telemetry laws, and by the Stein/Lorden theorem the minimum number of blocks any detector needs is

N*_T = log(1/α) / D_T ,      D_T = KL( P₁ ‖ P₀ )  on telemetry set T.

Two theorems drive every result:

• Data-processing inequality: dropping features (LIMITED ⊂ FULL) can only lower detectability, D_LIMITED ≤ D_FULL, so cheap telemetry strictly raises the detection delay.
• Stein floor: even an omniscient detector obeys N* ≥ log(1/α)/D, so D → 0 means undetectable at any latency.

The floor is validated against a Monte-Carlo CUSUM detector:

Empirical CUSUM detection delay stays above the information floor log(ARL₀)/D; small-D attacks (PNS) are fundamentally slow to detect.

2. The DEGENERACY attack — collapsing honest and attacked telemetry

The eavesdropper tunes gain-matched PNS so that, under LIMITED telemetry, the attacked telemetry law becomes observationally degenerate with honest operation — every cheap feature matches to within statistical noise — while she still learns the multi-photon bits. An analytic derivation predicts the single surviving trace (a decoy-channel residual) in closed form.

As Eve tunes her one free knob, cheap-telemetry detectability collapses into a valley (D≈0.08, 57 blocks to detect) while decoy telemetry still sees her (6.8 blocks). An 8× detection-delay penalty from cheap telemetry.

At the analytic optimum, all seven LIMITED features match honest to <0.2σ; the lone survivor is a single decoy residual — the degeneracy fingerprint.

Main results

The impossibility region. Sweeping attacks and duty cycles traces the Pareto frontier of leakage vs detectability. Under LIMITED telemetry the minimum detection delay stays high across all leakage levels; under FULL it collapses.

The security cost. Translated into finite-key terms, cheap telemetry lets the DEGENERACY attack steal 3–6× more certified-secret key before detection, across 25–100 km of fiber.

How much telemetry is enough? Greedily adding features shows the 1-knob attack is lifted out of degeneracy by a single decoy-gain residual, while the 2-knob attack resists the entire feature set — no observable catches it quickly.

Combined loopholes are sub-additive. On a receiver with detector-efficiency mismatch, a composite of PNS and time-shift leaks the sum of their information at roughly the detectability of the stealthier one alone — 57 % below the additive detection budget a defender would assume.

Physics validation. The simulator reproduces the textbook decoy-state result (no-decoy PNS key rate collapses at ~63 km; decoy-state extends secure range to ~173 km), certifying the analytic layer.

Repository structure

qkd/
  params.py       physical + protocol parameter containers
  source.py       weak coherent pulse (Poisson photon number)
  channel.py      fiber loss (Bernoulli thinning)
  detector.py     threshold detector pair (efficiency, dark counts, crosstalk)
  session.py      per-pulse Monte-Carlo pipeline with attack hooks
  attacks.py      intercept-resend, PNS, blinding, time-shift (+ calibration)
  telemetry.py    LIMITED vs FULL block-feature extraction
  keyrate.py      GLLP + decoy-state (Ma et al. 2005) key rates
  finitekey.py    epsilon-secure finite-key length (Lim et al. 2014)
  infometrics.py  Gaussian KL detectability + Stein floor        [SCATTER]
  sequential.py   CUSUM sequential detector                       [SCATTER]
  degeneracy.py   analytic gain-match + decoy residual            [DEGENERACY]
  subset.py       KL on feature subsets + greedy telemetry budget
  adversary.py    adversarial D_lim minimisation
  security.py     finite-key certified-but-stolen ledger
  dataset.py      block dataset generation
  mldetect.py     one-class SVM / isolation-forest baseline
experiments/      figure-generating scripts (see below)
tests/            regression + validation suite
METHOD.md         detailed method write-up

Experiments

Run any experiment from the repository root:

PYTHONPATH=. python experiments/<name>.py

script	output
fig1_decoy.py	decoy vs no-decoy key rate (validation anchor)
fig2_qber_blind.py	Eve-info vs QBER: QBER is blind to stealth attacks
fig3_ml_ablation.py	one-class SVM ROC, LIMITED vs FULL
exp_stein_validation.py	CUSUM delay respects the Stein floor
exp_frontier.py	detectability–leakage frontier + impossibility region
exp_degeneracy.py	the degeneracy valley
exp_fingerprint.py	per-feature degeneracy fingerprint
exp_stolen_key.py	certified-secret key stolen vs distance
exp_telemetry_budget.py	greedy telemetry budget: which feature lifts the attack
exp_composite.py	combined loopholes: detectability is sub-additive
exp_detectors.py	LLR vs one-class SVM vs isolation forest ROC
exp_residual_map.py	exact analytic decoy residual vs distance and decoy intensity
exp_finitekey_distance.py	epsilon-secure finite-key rate vs distance (Lim 2014)
exp_clt.py	telemetry Gaussianity (CLT validation)
smoke_attacks.py	attack telemetry-signature sanity table

Installation

python -m venv .venv && source .venv/Scripts/activate   # or conda env
pip install -r requirements.txt

Tests

python -m pytest tests/ -q

Covers key-rate limits, attack signatures, the data-processing inequality, the Stein floor, the analytic degeneracy prediction, and the security ledger.

References

• Gottesman, Lo, Lütkenhaus, Preskill, Quant. Inf. Comput. 4, 325 (2004).
• Ma, Qi, Zhao, Lo, "Practical decoy state for QKD," Phys. Rev. A 72, 012326 (2005).
• Lydersen et al., "Hacking commercial QKD systems by tailored bright illumination," Nat. Photonics 4, 686 (2010).
• Lorden, "Procedures for reacting to a change in distribution," Ann. Math. Stat. 42, 1897 (1971).