QPP-RNG: A Conceptual Quantum System for True Randomness

TL;DR

The paper presents QSQS, a physics-inspired model in which true randomness arises from measuring two conjugate observables of a single permutation-sorting process: the modular permutation count $ ilde{n} = n_p mod 2^n$ and the modular sorting time $ ilde{t} = T_p mod 2^n$. By combining a deterministic permutation-sorting core (dQRNG) with live system jitter (qQRNG) through entropy reseeding, the authors realize QPP-RNG as a software-based TRNG that yields high-entropy, statistically uniform outputs without dedicated hardware. A central insight is that right-skewed raw distributions of $n_p$ and $T_p$ become nearly uniform after modulo reduction, due to internal degeneracies and physical noise, enabling robust entropy harvesting. Empirical results across platforms demonstrate entropy convergence toward 8 bits and near-ideal uniformity, validating the hybrid QSQS framework as a practical approach for post-quantum cryptographic randomness. The work lays a foundation for integrating physics-inspired randomness into cryptographic modules, reducing reliance on external TRNG/QRNG hardware while maintaining strong statistical and unpredictability properties.

Abstract

We propose and experimentally demonstrate the \emph{Quasi-Superposition Quantum-inspired System (QSQS)} -- a conceptual quantum system for randomness generation built on measuring two conjugate observables of a permutation sorting process: the deterministic permutation count $n_p$ and the fundamentally non-deterministic sorting time $t$. By analogy with quantum systems, these observables are linked by an uncertainty-like constraint: algorithmic determinism ensures structural uniformity, while system-level fluctuations introduce irreducible unpredictability. We realize this framework concretely as \emph{QPP-RNG}, a system-embedded, software-based true random number generator (TRNG). In QPP-RNG, real-time measurements of sorting time $t$ -- shaped by CPU pipeline jitter, cache latency, and OS scheduling -- dynamically reseed the PRNG driving the permutation sequence. Crucially, QSQS transforms initially right-skewed raw distributions of $n_p$ and $t$ into nearly uniform outputs after modulo reduction, thanks to internal degeneracies that collapse many distinct states into the same output symbol. Empirical results show that as the repetition factor $m$ increases, output entropy converges toward theoretical maxima: Shannon and min-entropy values approach 8 bits, chi-squared statistics stabilize near ideal uniformity, and bell curves visually confirm the flattening from skewed to uniform distributions. Beyond practical implications, QSQS unifies deterministic algorithmic processes with non-deterministic physical fluctuations, offering a physics-based perspective for engineering true randomness in post-quantum cryptographic systems.

Figures (11)

• Figure 1: Raw distributions of random permutation counts and elapsed times per sorting cycle, with corresponding modulo 16 reductions. Panels (a) and (c): right-skewed distributions of raw permutation counts $\hat{N}_p$ and elapsed times $\hat{T}_i$. Panels (b) and (d): nearly uniform distributions after modulo 16, producing 4-bit random outputs.
• Figure 2: Byte-level frequency distribution from dQRNG with $N=4, m=1$. The wide spread ($\sigma=1097.80$) indicates significant deviation from uniformity.
• Figure 3: Byte-level frequency distribution from qQRNG with $N=4, m=1$. Even larger spread ($\sigma=2046.28$) shows higher initial non-uniformity due to system-level jitter.
• Figure 4: For $N=4, m=2$, dQRNG frequencies become substantially flatter ($\sigma=115.77$), indicating rapid convergence toward uniform distribution.
• Figure 5: For $N=4, m=2$, qQRNG shows notable improvement ($\sigma=379.08$), though still higher variance than dQRNG.