Synchronized Laser Spoofing and Quantum Defense

• Synchronized laser spoofing is an attack where adversaries inject timed laser pulses into LIDAR receivers to create false detection events or mask genuine returns.
• Quantum illumination protocols employing polarization encoding and non-phase-sensitive coincidence detection improve spoofing resilience by identifying abnormal error rate elevations.
• Detection relies on statistical analysis of signal and idler photon coincidences, enabling discrimination between adversarial injections and authentic returns.

Synchronized laser spoofing refers to an adversarial attack on active optical sensing systems in which an intruder injects carefully-timed laser pulses, synchronized with the legitimate system's timing, into the receiver's signal path. The intent is to create false detection events or to mask the presence of genuine returns, thereby undermining the integrity of object detection and range-finding tasks. This attack vector is particularly critical in low-light LIDAR regimes utilizing conventional or quantum illumination (QI), where signal-to-noise ratios can be low and detection is photon-limited. Recent work has established how quantum illumination protocols, notably those incorporating polarization encoding, nonsimultaneous phase-insensitive coincidence detection, and careful background subtraction, provide enhanced resilience against such attacks when compared to classical illumination approaches (Murchie et al., 27 Oct 2025).

1. Quantum Illumination Protocol for Spoofing Resilience

In the QI LIDAR protocol, a twin-beam photon source—commonly type-II SPDC—generates signal-idler photon pairs described by the joint state

$$\rho_0 = \sum_{n,m=0}^{\infty} p_{nm} |n\rangle_s \langle n| \otimes |m\rangle_i \langle m|,$$

which in the weak mean-photon-number regime ($n, m \in \{0, 1\}$) is truncated. Polarization encoding is implemented in two mutually unbiased bases: rectilinear (H/V) and diagonal (D/A), with the basis chosen at random for each pulse. The idler photons are measured locally using Geiger-mode detectors. Upon an idler "click" in basis $X \in \{ H, V, D, A \}$, the corresponding signal photon is expected in the correlated polarization mode.

Signal photons are directed to the target. Reflected signals, background noise, and potentially injected spoof pulses are collected and measured in the same basis as preparation, with signal detection events time-tagged for later correlation with the corresponding idler "click." Coincidences are determined within a defined temporal window, which is not phase-sensitive.

2. Detection Statistics: Probabilities and Error Rates

The key detection probabilities are:

• $\Pr[I:X]$: Probability of an idler click in polarization mode $X$.
• $\Pr[S:Z \mid I:X]$: Probability of a signal click in mode $Z$ conditioned on an idler click in $X$.

From these, the protocol computes:

• Correct-coincidence probability $(\Pr^a_c)$: Indicates authentic, correlated events.
• Wrong-coincidence probability $(\Pr^a_w)$: Events with the same polarization but lacking the nonclassical correlation.
• Double-coincidence probability $(\Pr^a_{wc})$: Multiple simultaneous clicks.

An adversary ("Eve") may introduce her own contributions with probabilities parameterized by a relative basis angle $\theta$, yielding $\Pr^e_{c,w,wc}(\theta)$. Background is accounted for via $\Pr^B_{c,w,wc}$. For intercept-resend attacks, the observed coincidence rates in "real" and "false" channels are weighted combinations of untampered, adversarial, and background contributions, factoring in partial spoofing probabilities $p$, $p_r$, and $p_f$.

Quantitative spoofing assessment hinges on:

• $k$-factor:

$k = \frac{\Pr^e_c - \Pr^B_c}{\Pr^e_w - \Pr^B_w}$

• Eve’s error rate:

$e_E = \frac{1}{k+1}$

• Threshold error for spoofing detection (partial attack $p$):

$$e_T = e_E \cdot \frac{p(\Pr^e - \Pr^B)}{p(\Pr^e - \Pr^B) + (1-p)(\Pr^a - \Pr^B)}$$

Alice sets an offset threshold $e_{T,\mathrm{off}}$ using measured real/false click rates, subtracting background estimates.

3. Synchronized Attack Model and Coincidence Detection

A synchronized laser spoofing adversary replicates Alice's timing to inject pulses coinciding with expected legitimate signals. However, nonsimultaneous phase-insensitive coincidence detection—requiring only temporal correlation between idler and signal "click" events within a window—exploits quantum correlations inaccessible to the adversary. The mismatch in photon-number correlations distinguishes injected (uncorrelated) pulses from genuine returns, as spoofed pulses increase wrong- and double-coincidence rates more than correct coincidences, elevating the observed error ($e_{\mathrm{obs}}$) beyond the established threshold $e_{T,\mathrm{off}}$. The adversary’s lack of access to the idler precludes anti-correlated spoofing without causing a detector-blinding regime.

4. Adversarial Basis Optimization

A sophisticated attacker may attempt to minimize induced errors by measuring intercepted pulses in a polarization basis rotated by angle $\theta$ relative to Alice's preparation, and resending in the measured polarization. The error induced by Eve is given by

$e_E(\theta) = \frac{1}{1 + k(\theta)}$

where $k(\theta)$ is maximized for certain $\theta^*$ determined by the system's detector efficiencies ($\eta$) and noise levels. Empirical results indicate an optimal $\theta^* \approx 0$ for typical mismatched detector efficiencies, but without precise knowledge of Alice's system parameters, Eve cannot minimize her detection probability reliably. Deviations or attempted bias strategies by Eve manifest as asymmetries in Alice's observed error rates across bases, which can be counteracted through rebalancing of basis choices.

5. Quantum versus Classical Illumination under Spoofing

When compared to a classical prepare-and-measure protocol (e.g., BB84-inspired LIDAR using weak coherent pulses $|\alpha\rangle$, $\bar n_\alpha \ll 1$), quantum illumination exhibits superior signal-to-noise ratio (SNR) and a higher threshold for spoofing detectability $(e_T)$. The error metrics and detection probabilities for both quantum and classical schemes can be computed using analogous models of loss and noise. Numerically, quantum illumination demonstrates greater resilience: the sensitivity to spoofed pulses remains significant at comparable signal and noise levels, allowing Alice to detect intrusions that would be indistinguishable from background in the classical case (Murchie et al., 27 Oct 2025).

6. Regimes: Detectability and Blinding

The distinction between detectable spoofing and detector blinding is governed by the condition:

• Detectable: $\Pr^e_w - \Pr^B_w > 0$—Eve's injected pulses raise the wrong-coincidence rate above background, so $e_{\mathrm{obs}} > e_{T,\mathrm{off}}$ enables detection and rejection.
• Blinding: If background noise drives $\Pr^e_w - \Pr^B_w \leq 0$, Alice’s detector cannot distinguish spoofing, but object detection itself is no longer feasible, warranting abandonment of the measurement.

For partial spoofing ($p<1$ vs. full $p=1$), Alice can employ $k$-factor analysis or solve the protocol's system of equations to isolate her genuine channel and reject spurious ones.

7. Practical Implementation and Trade-Offs

Essential practical considerations include maintaining low mean photon number ($\bar n \ll 1$) to suppress vulnerabilities to multiphoton events, precise calibration of detector quantum efficiencies (as mismatches directly influence SNR but not the relative advantage), and rigorous estimation of noise via sufficient measurement statistics (e.g., as determined by Skellam-distribution or Monte Carlo methods). Rapid randomization or scrambling of polarization bases is critical for preventing the adversary from exploiting fixed-basis strategies. The protocol's tolerance to timing jitter, by virtue of phase-insensitive, nonsimultaneous coincidence windows, facilitates implementation using conventional Geiger-mode detectors without photon-number resolution.

Quantum illumination, leveraging the nonclassical correlations present in entangled photon-pair sources, provides a robust framework for identifying and mitigating synchronized laser spoofing. Monitoring the elevation of wrong-coincidences above a well-characterized noise background, and leveraging statistical techniques such as $k$-factor subtraction, enables both reliable intrusion detection and discrimination of genuine returns for consequent imaging or ranging operations (Murchie et al., 27 Oct 2025).