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

We present IID-Based QPP-RNG, 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. Unlike conventional RNGs that rely directly on raw timing variations, IID-Based QPP-RNG uses system jitter solely to generate ephemeral QPP pads and derives its final 8-bit outputs from permutation counts -- without the post-processing module. This design leverages the factorial complexity of random permutation-based sorting to systematically accumulate entropy from dynamic hardware interactions, ensuring non-deterministic outputs even when starting from fixed seeds. Our implementation employs a dynamic seed evolution protocol that continuously refreshes the internal state using unpredictable system jitter, decoupling the deterministic QPP sequence from the initial seed. Rigorous cross-platform validation on macOS (x86 and ARM) and Windows (x86) confirms that the generator produces uniformly distributed 8-bit outputs. Evaluations compliant with NIST SP 800-90B demonstrate exceptional statistical quality, with a Shannon entropy of 7.9999 bits per byte and a min-entropy of 7.18 bits per byte. IID-Based QPP-RNG represents a significant advancement in random number generation by bridging algorithmic complexity with system-level entropy, offering a scalable, software-only, post-quantum-secure solution for cryptographic applications in environments lacking dedicated hardware entropy sources.