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 $10^8$ 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.

翻译：本文提出了一种完全数字化的框架，通过随机置换过程利用系统时序抖动，复现了相干态量子随机数生成（QRNG）的统计行为。我们的方法将硬件和操作系统源的计算时序变化转化为置换动力学，生成泊松分布的数字，精确复现了光学相干态的光子统计特性。该理论基于一致收敛定理建立，该定理在模投影下以严格的误差界提供了指数级收敛至均匀分布的特性。在多个参数体系和高达$10^8$字节的样本量上进行的大量实验验证表明，该方法具有卓越性能：香农熵接近7.999998比特/字节，最小熵超过7.99比特/字节，在大规模下超越了理论界限。该架构通过复合时序分布和自适应置换行为，固有地抵抗侧信道攻击，且无需经典密码学后处理即可运行。我们的研究结果表明，相干态QRNG功能可以完全通过经典计算过程实现，无需量子光子硬件即可提供数学可证明的均匀性和实用的密码学安全性。