Digital Coherent-State QRNG Using System-Jitter Entropy via Random Permutation

We present a fully digital framework that replicates the statistical behavior of coherent-state quantum random number generation (QRNG) by harnessing system timing jitter through random permutation processes. Our approach transforms computational timing variations from hardware and operating system sources into permutation dynamics that generate Poisson-distributed numbers, accurately reproducing the photon statistics of optical coherent states. The theoretical foundation is established by the Uniform Convergence Theorem, which provides exponential convergence to uniformity under modular projection with rigorous error bounds. Extensive experimental validation across multiple parameter regimes and sample sizes up to 10⁸ bytes demonstrates exceptional performance: Shannon entropy approaching 7.999998 bits/byte and min-entropy exceeding 7.99 bits/byte, outperforming theoretical bounds at scale. The architecture inherently resists side-channel attacks through compound timing distributions and adaptive permutation behavior, while operating without classical cryptographic post-processing. Our results establish that coherent-state QRNG functionality can be entirely realized through classical computational processes, delivering mathematically provable uniformity and practical cryptographic security without quantum photonic hardware.