Validation: Time, Frequency & Spectral Analysis
Empirical Validation: Three Domains
Analog Guard’s security claims are not merely theoretical — they are measured in reproducible simulation. Validation across the time domain, frequency domain, and spectral coherence tells a consistent story: with the matched key, recovery is exact in simulation; without it, the output is statistically indistinguishable from noise in the tested cases, with no usable partial signal observed. The figures below show each stage of that process directly.
Time domain. The first trace shows the analog-encoded original signal. The second shows the same data after PLTNM encryption — a physically distinct waveform bearing no visible resemblance to the input. The third shows the signal after decryption with the matched key, recovering the original waveform. The encrypted trace shares no structure with the original; the decrypted trace reproduces it.
Frequency domain. Comparing spectral distributions makes the transformation measurable rather than visual. The original signal and the matched-key decryption show corresponding spectral content — the recovery is faithful across the spectrum, not just in the time trace. The encrypted signal’s spectrum differs substantially from the original. And critically, the mismatched-key decryption produces a spectral distribution markedly different from the encrypted signal’s — confirming that an incorrect key does not partially reverse the transformation toward the original, but maps to an unrelated output.
Spectral coherence. Coherence measures how related two signals are across frequency, on a scale from 0 (unrelated) to 1 (identical). Three comparisons define the result. Original versus encrypted: coherence varies erratically between 0 and 1, indicating no stable relationship — the encrypted signal carries no consistent trace of the original. Original versus matched-key decryption: coherence holds flat at 1 across all frequencies — complete, faithful recovery. Original versus mismatched-key decryption: coherence again varies erratically between 0 and 1 — a wrong key yields no coherent relationship to the original, even for the near-miss keys tested.
Time and frequency show the transformation. Coherence confirms it: a flat line at 1 with the key, no stable relationship without it.
Simulated Recovery Metrics
Matched key: exact recovery. Mismatched key: ~50% bit error — statistically random. No intermediate values were observed for an adversary to climb toward or close in on.
This binary outcome — exact recovery or noise — is not a property of the software layer. It is a property of the physics.
This binary outcome — exact recovery or noise-level output — is not a feature of the software layer. It is a property of the physics.
AI & Machine Learning Resistance
Structural Resistance to Learning-Based Attack
Analog Guard was tested in four experiments against deep convolutional neural networks — GoogLeNet and Inception-ResNet-v2 — retrained through transfer learning on Continuous Wavelet Transform scalograms of encrypted output waveforms. The networks were asked to sort encrypted files by which of two analog keys had been used (Tests 1–2), or by which of two messages had been encrypted (Tests 3–4). They could not do either: in every test, accuracy was about 50% — a coin flip.
Training accuracy converged to approximately 100%: the models readily memorized the specific waveform instances they were shown. Validation accuracy, however, did not rise above chance in these tests — and additional training iterations did not move it. The models learned the examples but learned nothing that generalized to unseen ones.
That divergence is the result. When a model can memorize a training set perfectly yet predicts no better than chance on held-out data, it indicates the models found no generalizable structure to learn. In these tests, the limit was not computational — it did not yield to more data, more parameters, or more training. The evidence points to a structural limit, arising from the high-order nonlinearity and continuous parameterization of the analog key space.
The models memorized every example and generalized none of them. The tested models found no learnable key structure — and more training did not change that.