SD-ARX: State-Dependent Addition-Rotation-XOR Networks

A novel closed-loop architecture for ARX primitives that replaces static rotation constants with state-dependent values, fundamentally accelerating diffusion convergence.

v1.0 (Community Edition) — DONE

• Scalar + SIMD reference implementations
• Benchmark harness & diffusion analytics (SAC/SADM)
• TestU01 BigCrush runs and logs
• Apache‑2.0 licensing; citation metadata

Status: Community Edition (Apache‑2.0). Available under commercial terms—see Enterprise Edition below.

Overview

SD-ARX introduces a new architectural principle for Addition-Rotation-XOR (ARX) networks: entropy-dependent routing. Rather than applying fixed rotation schedules, SD-ARX derives rotation magnitudes dynamically from the evolving internal state, creating a feedback mechanism that eliminates geometric dead zones and dramatically accelerates diffusion.

This repository contains the reference implementation instantiated as SD-ChaCha8, an 8-round PRNG demonstrating the SD-ARX principle.

The SD-ARX Architecture

Core Innovation

Traditional ARX designs use static rotation constants:

d[i+1] = (d[i] XOR a[i+1]) <<< R_static

SD-ARX couples rotation to state entropy:

r = R(state)                              // Derive rotation from state
d[i+1] = (d[i] XOR a[i+1]) <<< r         // Apply state-dependent rotation

Architectural Advantages

• Eliminates dead zones: Static schedules create geometric isolation; state-dependent rotations eliminate fixed unreachable positions
• Accelerates diffusion: ~14.3% improvement in first-pass Hamming weight diffusion
• Maintains bijectivity: Proven invertible when R depends only on unchanged state words
• Generalizable: Applies to any ARX primitive (ChaCha, Salsa20, NORX, BLAKE)

Performance (Apple M3, ARM64)

Generator	Cycles/Byte	vs ChaCha20	SAC Convergence
SD-ChaCha8 Barrett	1.681	1.67x faster	2 double-rounds
SD-ChaCha8 (modulo)	2.649	1.06x faster	2 double-rounds
ChaCha20	2.810	1.00x (baseline)	2 double-rounds
ChaCha12	2.077	1.35x faster	3-4 double-rounds
ChaCha8	1.914	1.47x faster	Incomplete

Platform: Apple M3 (ARM64), Clang -O3 -march=native, clock_gettime

Statistical Validation

TestU01 BigCrush

• Status: All 160 tests passed
• Data processed: ~10 TB per variant
• Variants tested: Original (modulo) and Barrett (optimized)
• Complete results in /results

Additional Validation

• Strict Avalanche Criterion: Achieved by round 2
• Topological uniformity: Vietoris-Rips persistent homology matches true-random baselines
• Spectral statistics: Eigenvalue spacing follows Wigner-Dyson GOE distribution

When to Use SD-ChaCha8

Use when:

• Pipeline requires ARX non-linearity to eliminate GF(2) hyperplane artifacts
• ChaCha20 is a throughput bottleneck
• Naively truncating to ChaCha8 degrades statistical quality
• SAC compliance needed at reduced round count

Do NOT use when:

• Raw throughput is paramount (use xoshiro256++, PCG64 instead)
• Cryptographic security required (SD-ARX has data-dependent timing)
• Linear generators suffice for your application

Implementation Variants

1. Barrett Scalar (Recommended for most users)

// 1.681 cycles/byte on ARM64
// Uses Barrett reduction: (x mod 31) via multiply-shift

2. Original (Modulo-based)

// 2.649 cycles/byte on ARM64
// Direct modulo operation, portable but slower

3. SIMD (Advanced)

// ARM NEON / x86 AVX2 vectorization
// Requires careful handling of per-lane variable rotations

Building

# Scalar implementation
gcc -O3 -march=native sd_chacha8_barrett.c -o sd_chacha8

# With benchmarks
make benchmark

# Run full test suite
make test

Usage Example

#include "sd_chacha8.h"

// Initialize state
sd_chacha8_state state;
sd_chacha8_init(&state, key, nonce);

// Generate random bytes
uint8_t output[64];
sd_chacha8_generate(&state, output, 64);

Repository Structure

/src/           - Core implementations (Barrett, original, SIMD)
/tests/         - TestU01, validation scripts, statistical tests
/benchmarks/    - Performance measurement tools
/analysis/      - Diffusion analysis, TDA, spectral statistics
/docs/          - Paper, supplementary materials

Citation

If you use SD-ChaCha8 in your research, please cite:

@article{dsouza2026sdarx,
  author = {D'Souza, Meldon},
  title = {SD-ARX: A Closed-Loop Architecture for Accelerated Diffusion in ARX Networks},
  journal = {[Under Review]},
  year = {2026}
}

Important Disclaimers

Not for cryptographic use: Data-dependent timing of dynamic rotations introduces side-channel vulnerabilities. SD-ARX is designed for non-cryptographic random number generation in simulation and stochastic optimization.

Platform-specific performance: Throughput values are measured on Apple M3 (ARM64). x86-64 performance may differ due to different instruction latencies and SIMD widths.

Architectural niche: SD-ChaCha8 targets ARX-committed pipelines. For throughput-critical workloads without ARX requirements, linear generators (xoshiro256++, PCG64) are significantly faster.

License

License

This project uses a dual-licensing model.

• Community Edition — Apache License 2.0 (see LICENSE.md)
• Enterprise Edition — commercial license (see LICENSE-ENTERPRISE.md)

For Research Queries, Contact

Meldon D'Souza
Department of Statistics and Data Science
Christ (Deemed-to-be) University, Bengaluru, India
Email: meldon.dsouza@mscsai.christuniversity.in

Acknowledgments

Based on ChaCha20 by D. J. Bernstein. TestU01 validation framework by P. L'Ecuyer and R. Simard.

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Last updated: March 2026
Status: Research implementation, validation complete, paper under review