IID-Based QPP-RNG: A Random Number Generator Utilizing Random Permutation Sorting Driven by System Jitter

Abstract: We propose a groundbreaking random number generator that achieves truly uniform, independent, and identically distributed (IID) randomness by integrating Quantum Permutation Pads (QPP) with system jitter--derived entropy, herein called IID-based QPP-RNG. Unlike conventional RNGs that use raw timing variations, our design uses system jitter solely to generate ephemeral QPP pads and derives 8-bit outputs directly from permutation counts, eliminating the need for post-processing. This approach leverages the factorial complexity of permutation sorting to systematically accumulate entropy from dynamic hardware interactions, ensuring non-deterministic outputs even from fixed seeds. Notably, IID-based QPP-RNG achieves a min-entropy of 7.85-7.95 bits per byte from IID min-entropy estimate, surpassing ID Quantique's QRNG (7.157042 bits per byte), which marks a breakthrough in randomness quality. Our implementation employs a dynamic seed evolution protocol that continuously refreshes the internal state with unpredictable system jitter, effectively decoupling the QPP sequence from the initial seed. Cross-platform validation on macOS (x86 and ARM) and Windows (x86) confirms uniformly distributed outputs, while evaluations compliant with NIST SP 800-90B show a Shannon entropy of 7.9999 bits per byte. Overall, IID-based QPP-RNG represents a significant advancement in random number generation, offering a scalable, system-based, software-only, post-quantum secure solution for a wide range of cryptographic applications.