QRNG Systems: Physical Measurement Nuances & Mathematical Post-Processing

In any hardware random number generator based on physical quantum entropy, true unpredictable randomness relies on two interconnected entities:

• The measurement equipment itself with its physical detector nuances.
• The mathematical post-processing and debiasing applied to the digitized stream.

1. The Measurement Equipment: Physical Detector Nuances

In our live hardware project (QRNGabri), we capture the spontaneous radioactive alpha-decay timing of Radon-222 atoms.

While the decay intervals are fundamentally non-deterministic and dictated by quantum mechanics, the physical detection apparatus introduces measurement boundaries:

• Chamber Geometry & Ionization Thresholds: The detection chamber geometry, sensor dead-time, and environmental capacitance influence pulse registration thresholds.
• Time-Windowed Sampling: Alpha-decay events are aggregated within discrete counter intervals rather than continuous timestamps. Because events fall into discrete time windows, raw sampled counts carry slight physical skew that must be corrected.

2. Mathematical Post-Processing: Debiasing

To transform raw physical readings into a cryptographically uniform distribution, we apply two complementary mathematical methods:

John von Neumann Debiasing

The classic John von Neumann extractor inspects non-overlapping successive bit pairs:

Bit Pair	Action	Output Bit
00	Discard	—
11	Discard	—
01	Keep	0
10	Keep	1

Because the transition probabilities are identical regardless of underlying bias $p$:

Von Neumann debiasing completely eliminates first-order bias from independent bits, producing an unbiased stream at the expense of variable bit rate throughput.

Bitwise XOR Whitening

In parallel, XOR whitening folds consecutive bit intervals. When combining independent streams with bias ${\epsilon }_1$ and ${\epsilon }_2$, the combined bias decays exponentially:

Original discussion published on LinkedIn.