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https://github.com/cpscript/qrcryptography

Experimental post-quantum cryptographic framework implementing hybrid lattice-based encryption with hash based signatures. Combining Ring-LWE, standard LWE, and Merkle trees for defense against classical and quantum attacks.
https://github.com/cpscript/qrcryptography

cryptographic-research cryptography experimental hash-based-signatures python quantum-resistant ring-lwe

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Experimental post-quantum cryptographic framework implementing hybrid lattice-based encryption with hash based signatures. Combining Ring-LWE, standard LWE, and Merkle trees for defense against classical and quantum attacks.

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README 

          
> QRCs is an experimental post-quantum cryptographic framework implementing hybrid lattice-based encryption with hash-based digital signatures. The system combines Ring Learning With Errors, standard Learning With Errors, and Merkle signature schemes to provide defense against both classical and quantum cryptanalytic attacks.



## Architecture



The system implements a multi-layer cryptographic approach using:



Ring-LWE encryption for structured lattice problems

Standard LWE encryption for unstructured lattice security  

Hash-based signatures using Merkle trees and Winternitz one-time signatures

Advanced Reed-Solomon error correction with Berlekamp-Massey decoding

Constant-time operations for side-channel resistance

Military-grade entropy collection from multiple hardware sources

Key switching and bootstrapping for homomorphic operations

Authenticated encryption with HMAC-SHA3-512



## Security Levels



CLASSICAL_128 - 128-bit classical security equivalent

CLASSICAL_192 - 192-bit classical security equivalent

CLASSICAL_256 - 256-bit classical security equivalent

QUANTUM_128 - 128-bit post-quantum security

QUANTUM_192 - 192-bit post-quantum security  

QUANTUM_256 - 256-bit post-quantum security

FORTRESS - Maximum security configuration



## Installation



Python 3.8 or higher required with numpy dependency.



```

pip install numpy

```



No additional dependencies required. System uses only Python standard library and numpy.



## Basic Usage



```python

from QRCs import QRCs, SecurityLevel



# Initialize system

system = QRCs(SecurityLevel.QUANTUM_256)



# Generate keypair

public_key, private_key = system.generate_keypair()



# Encrypt data

plaintext = b"confidential message"

associated_data = b"authentication context"

ciphertext = system.encrypt(plaintext, public_key, associated_data)



# Decrypt data

decrypted = system.decrypt(ciphertext, private_key, associated_data)



# Digital signatures

signature = system.sign(plaintext, private_key)

is_valid = system.verify(plaintext, signature, public_key)

```



## Technical Specifications



Ring dimension: 1024 to 4096 coefficients depending on security level

Lattice dimension: 512 to 2048 vectors

Coefficient modulus: Multiple prime moduli up to 30 bits

Gaussian parameter: 3.2 to 6.0 standard deviation

Error correction: Reed-Solomon with 16 to 64 error correction capacity

Hash function: SHA3-512 for all cryptographic hashing

Signature tree height: 16 to 32 levels supporting 65536 to 4 billion signatures



## Performance Characteristics



Key generation: 50-500ms depending on security level

Encryption: 5-50ms per kilobyte

Decryption: 3-30ms per kilobyte  

Signature generation: 10-100ms

Signature verification: 5-50ms

Memory usage: 1-16MB depending on security parameters



Performance scales with security level. FORTRESS configuration provides maximum security at cost of reduced performance.



## Implementation Details



All arithmetic operations use constant-time implementations to prevent timing attacks. Random number generation combines multiple entropy sources including hardware performance counters, system entropy pools, and cryptographic random generators.



Error correction uses advanced Reed-Solomon codes with polynomial-time Berlekamp-Massey algorithm for optimal error locator computation. The system can correct up to t errors per codeword where t is configurable.



Key switching enables homomorphic operations while maintaining security properties. Bootstrapping allows noise reduction in ciphertext without exposing secret information.



## Cryptographic Primitives



Ring-LWE problem hardness based on shortest vector problem in ideal lattices

Standard LWE problem hardness based on shortest vector problem in general lattices

Hash-based signatures provide information-theoretic security

Number theoretic transforms enable efficient polynomial arithmetic

Discrete Gaussian sampling for lattice noise generation

Modular arithmetic with precomputed primitive roots



## Research Applications



This implementation is suitable for:



Post-quantum cryptography research

Lattice-based cryptanalysis studies

Hybrid cryptographic system analysis

Performance benchmarking of post-quantum algorithms

Educational purposes in advanced cryptography



## Limitations



The system has not undergone formal security analysis or peer review. Parameter selection is based on current research but may require adjustment as cryptanalytic techniques advance.



Signature keys support limited number of signatures before requiring regeneration. Performance decreases significantly at maximum security levels.



Implementation focuses on correctness and research utility rather than production optimization. Side-channel protections may be incomplete against sophisticated physical attacks.



## Compliance



This software implements cryptographic algorithms that may be subject to export restrictions in some jurisdictions. Users are responsible for compliance with applicable laws and regulations.



## Disclaimer



This software is provided for research only. No warranties are made regarding security, correctness, or fitness for any particular purpose. The implementation has not been audited or certified for production use.



Users assume all risks associated with the use of this cryptographic software. The authors disclaim all liability for any damages resulting from use of this system.



This is experimental research software and should not be used to protect sensitive or critical information without extensive additional testing and validation.



## References



Implementation based on current research in post-quantum cryptography including but not limited to lattice-based encryption schemes, hash-based signature systems, and error correction algorithms as published in peer-reviewed cryptographic literature.