I’ve released an updated version (v2.1) of RGE-256, a research-oriented ARX-based pseudorandom number generator. https://zenodo.org/records/17861488

The project investigates structured ARX diffusion, cross-coupled state mixing, and empirical performance across multiple statistical test suites.

Version 2.1 incorporates corrections, independent testing, and new variants addressing limitations in the earlier prototype.

### *Key Highlights (v2.1)*

* *Dieharder:* 96/114 tests passed (≈84%). All three failures occurred only at extreme file-rewind counts (>1700), consistent with dataset exhaustion rather than structural bias.

* *TestU01 BigCrush:* Independent testing (via SmokeRand) confirms the core permutation (RGE256Lite) passes the full BigCrush battery.

* *PractRand ≥ 1 TiB:* Independent multithreaded PractRand runs show stable behavior through at least 1 TiB of input without anomalies.

* *Avalanche performance:* ~15.97 bits flipped per 32-bit output when a single input bit is changed (ideal is 16), indicating near-ideal diffusion.

* *Autocorrelation:* All measured lags satisfied |ρ| < 2×10⁻⁴.

* *Bit-frequency uniformity:* All bit positions within ~0.03% of 0.5.

* *Counter-mode variants:* New RGE256LiteSafe and RGE256ctr variants guarantee a minimum period of 2⁶⁴ and avoid potential short-cycle states.

* *C99 implementation:* Added reference C99 version with a Python wrapper for realistic throughput benchmarking and easier integration into test harnesses.

* *Revised analysis:* Clarified period-analysis limitations of nonlinear ARX constructions and corrected earlier misconceptions about PractRand resource requirements.

The generator is *not intended for cryptographic use*. Its purpose is to explore ARX structure behavior, evaluate diffusion patterns, and provide a reproducible basis for statistical testing.

### *Repositories*

*Core PRNG and preprint materials:* [https://github.com/RRG314/rge256](https://github.com/RRG314/rge256)

*Interactive demonstration / web app:* [https://github.com/RRG314/rge-256-app](https://github.com/RRG314/rge-256-app)

Feedback on ARX construction, test methodology, period analysis, or implementation details is welcome.