RCLP

Post-quantum. Lattice-hard. Self-inverse.

A post-quantum cryptographic framework built from the Golay code, Leech lattice, and two-sided surfaces.

Launch Page · GitHub · LumenHelix

---

RCLP (Reversibility-Constrained Lattice Problem) defines a new hardness assumption using two-sided surface flips constrained by the Golay code and embedded in the Leech lattice. RCLP-KEM achieves 100 percent decryption correctness and ciphertexts/secret keys roughly 5-6 times smaller than ML-KEM-768.

Why RCLP

• Compact keys. 192-byte ciphertexts and 388-byte secret keys at the 128-bit security level.
• Self-inverse decryption. The flip operation is an involution: applying it twice returns the original state.
• Mathematically transparent. Every foundational claim is backed by exact-computation verification scripts.

Quick start

macOS / Linux

git clone https://github.com/lumenhelixlab/RCLP.git
cd RCLP
git clone https://github.com/LumenHelixLab/RCLP.git
cd RCLP
python3 -m venv .venv
.venv/bin/pip install -r requirements.txt
.venv/bin/pip install -e .
.venv/bin/python -m pytest tests/

Windows (PowerShell)

git clone https://github.com/lumenhelixlab/RCLP.git
Set-Location RCLP
git clone https://github.com/LumenHelixLab/RCLP.git
Set-Location RCLP
python -m venv .venv
.venv\Scripts\pip install -r requirements.txt
.venv\Scripts\pip install -e .
.venv\Scripts\python -m pytest tests/

Windows (Git Bash / WSL)

git clone https://github.com/lumenhelixlab/RCLP.git
cd RCLP
git clone https://github.com/LumenHelixLab/RCLP.git
cd RCLP
python3 -m venv .venv
.venv/bin/pip install -r requirements.txt
.venv/bin/pip install -e .
.venv/bin/python -m pytest tests/

Tested on Windows 11, macOS Sonoma, Ubuntu 22.04/24.04, and modern mobile browsers.

Features

Feature	What it gives you
Golay constraint structure	The [24,12,8] extended binary Golay code enforces valid flip patterns and corrects up to 3 errors.
Leech lattice substrate	The unique 24-dimensional even unimodular lattice with 196,560 minimal vectors provides the geometric hardness.
Conway automorphisms	Sign-change automorphisms indexed by Golay codewords embed the monomial subgroup 2^12.M24 in Co0.
Verified by computation	All mathematical foundations — Golay weight distribution, Leech minimal vectors, KEM correctness — are computationally verified.

Architecture

Golay Code  ->  Valid Flip Pattern  ->  Leech Lattice Vector  ->  Two-Sided Surface  ->  RCLP-KEM Ciphertext
       ^                                                                            |
       └─────────────── Babai + Nearest-Codeword Decoder ───────────────────────────┘

Development

# Verify mathematical foundations
python verify_golay.py
python verify_leech.py
python benchmark.py

# Run full test suite
python -m pytest tests/

Roadmap

• Formal hardness reduction from RCLP to standard lattice problems
• Quantum security analysis and independent cryptanalytic review
• Optimized C/C++ reference implementation for fair benchmarking

License

Released under the MIT License.

---

_{RCLP is a LumenHelix project — Applied Symbolic Dynamics & Reversible Computation.}