Proposition 1 — Measurement Symmetry
Let F be any feature a defender computes from voltage samples
V captured at rate fs and resolution b. An adversary with
b′ ≥ b and f′s ≥ fs records V′ with
|F(V) − F(V′)| ≤ ε, where ε is bounded by the two converters' quantization.
Any classifier that accepts F(V) within tolerance δ > ε
must also accept F(V′).
No choice of feature escapes it. Raw samples, rise/fall times, ringing, spectral shape —
all are functions of the same voltage trace, and a faithful copy carries every one of
them at once. The adversary does not model the fingerprint. It re-emits the exact signal
that produced it. This is why the operative attack is replay, not imitation.
Wired is the easy case
Channel variability — multipath, fading — is the only partial defense against
physical-layer replay. An impedance-controlled, transformer-coupled 1553 bus has
essentially none of it. The doctrine is weakest exactly where it is deployed most
confidently.
The fidelity gap favors the attacker
A 14-bit converter resolves the waveform to ~0.6 mV; an 8-bit defender scope
has a ~39 mV noise floor — 65× larger. Any replay artifact sits
six bits below the defender's least-significant bit.
The cost asymmetry is permanent
Every increment of defender resolution costs an instrument upgrade. The attacker's
answer is a few-dollar RC filter that smooths any residual step below the new floor.
The attacker filters more cheaply than the defender can measure.