lattice-analysis/results/report.html

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<title>LUX Lattice — Reciprocal-Space Security Analysis</title>
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<div class="header">
    <h1>LUX Lattice — Reciprocal-Space Security Analysis</h1>
    <p>Dragonfire Research | 2026-03-21T10:38:16Z</p>
    <p>Ring Degree: 1024 | Samples: 10000</p>
</div>

<div class="methodology">
    <h2>Methodology: Reciprocal-Space Analysis</h2>
    <p>Lattice-based cryptographic security depends on the hardness of finding short vectors in
    high-dimensional lattices. The noise added during encryption (from a Gaussian distribution)
    is what makes the lattice problem hard. However, when this noise is transformed into the
    Number Theoretic Transform (NTT) domain — the discrete analogue of reciprocal space in
    solid-state physics — structural anomalies may become visible that are hidden in direct space.</p>

    <p>This analysis examines the LUX lattice implementation by:</p>
    <p>1. Capturing raw Gaussian noise samples from the sampler (direct space)<br>
    2. Applying NTT transformation to move into reciprocal space<br>
    3. Comparing statistical properties across both domains<br>
    4. Computing power spectral density to detect hidden periodicity<br>
    5. Measuring autocorrelation to identify exploitable structure<br>
    6. Timing crypto operations to detect side-channel leakage</p>

    <p>The physical analogy: just as phonon dispersion reveals defects in a crystal lattice that
    are invisible to direct inspection, spectral analysis of cryptographic noise can reveal
    implementation weaknesses that are invisible to standard statistical tests.</p>
</div>

<h2>Go Harness Findings</h2>
<div class="go-findings">
    <ul><li>TIMING: Gaussian_Sample_Real has CV=0.342 — non-constant-time risk</li>
<li>TIMING: NTT_Forward_Real has CV=0.140 — non-constant-time risk</li>
<li>TIMING: INTT_Backward_Real has CV=0.108 — non-constant-time risk</li>
<li>SPECTRAL: reciprocal_space has kurtosis=-1.1925 — non-Gaussian tails</li>
<li>RECIPROCAL: Variance ratio (direct/reciprocal) = 0.00 — significant energy redistribution in frequency domain</li>
</ul>
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<h2>Spectral Analysis Results</h2>
<div class="chart"><h3>Distribution</h3><img src="charts/distribution_comparison.png" /></div>
<div class="chart"><h3>Psd</h3><img src="charts/psd_analysis.png" /></div>
<div class="chart"><h3>Autocorrelation</h3><img src="charts/autocorrelation.png" /></div>


<h2>Detailed Findings</h2>

        <div class="finding info">
            <h3>Direct Space Distribution</h3>
            <pre>{
  "name": "Direct Space Distribution",
  "n": 10000,
  "mean": -0.006,
  "std": 3.2270983870963708,
  "variance": 10.414163999999998,
  "skewness": 0.07002761103342017,
  "kurtosis": 0.07464858285995923,
  "min": -12.0,
  "max": 12.0,
  "normality_test": "D'Agostino-Pearson",
  "normality_stat": 10.438236109312696,
  "normality_p": 0.005412100198788883,
  "is_gaussian": "False"
}</pre>
        </div>
        
        <div class="finding info">
            <h3>Direct Space Spectral</h3>
            <pre>{
  "name": "Direct Space Spectral",
  "psd_mean": 20.605750770855902,
  "psd_max": 29.02559861240613,
  "psd_peak_freq": 0.03515625,
  "spectral_flatness": 0.9862111852975296,
  "is_white_noise": "True",
  "max_autocorrelation_lag1_10": 0.02125353750910795,
  "has_structure": false
}</pre>
        </div>
        
        <div class="finding info">
            <h3>Reciprocal Space Distribution</h3>
            <pre>{
  "name": "Reciprocal Space Distribution",
  "n": 1024,
  "mean": 21990232554241.01,
  "std": 645308229335358.8,
  "variance": 4.16422710847936e+29,
  "skewness": -0.024240938988069657,
  "kurtosis": -1.1925365596921327,
  "min": -1125631967668576.0,
  "max": 1124983497145603.0,
  "normality_test": "Shapiro-Wilk",
  "normality_stat": 0.9550780996000607,
  "normality_p": 3.631961308521301e-17,
  "is_gaussian": "False"
}</pre>
        </div>
        
        <div class="finding info">
            <h3>Reciprocal Space Spectral</h3>
            <pre>{
  "name": "Reciprocal Space Spectral",
  "psd_mean": 8.357475151673109e+29,
  "psd_max": 1.709649625264889e+30,
  "psd_peak_freq": 0.48828125,
  "spectral_flatness": 0.9213490085045406,
  "is_white_noise": "True",
  "max_autocorrelation_lag1_10": 0.07065912131571873,
  "has_structure": true
}</pre>
        </div>
        
        <div class="finding warning">
            <h3>Cross-Domain Comparison</h3>
            <pre>{
  "name": "Cross-Domain Comparison",
  "direct_variance": 10.414163999999998,
  "reciprocal_variance": 4.16422710847936e+29,
  "variance_ratio": 2.5008636005452908e-29,
  "verdict": "WARNING: Significant energy redistribution between domains"
}</pre>
        </div>
        

<div class="footer">
    <p>Generated by Dragonfire Research Rig v0.1 | LUX Lattice Reciprocal-Space Analysis</p>
    <p>This report analyses placeholder data unless the Go harness has been integrated with the actual LUX lattice library.</p>
</div>

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