GGH-crypto

GGH-crypto is a Python package implementing the Goldreich-Goldwasser-Halevi (GGH) public key cryptosystem and its optimization, GGH-HNF by Micciancio. This package is designed for educational and research purposes, offering insights into lattice-based cryptography. This project was developed as part of a 3-year degree program at the Università degli Studi di Milano (University of Milan). It explores the resilience of lattice-based cryptography against quantum threats and introduces an hybrid variant.

Features

• Implementation of the original GGH cryptosystem (1997)
• Implementation of the GGH-HNF optimization (2002)
• Utility functions for lattice-based cryptography
• Algorithms for solving the Closest Vector Problem (CVP)
• Lattice reduction algorithms

Usage and details

For detailed installation, usage, examples and documentation, please visit the GitHub repository.

Note

Both the original GGH cryptosystem and its GGH-HNF optimization have known security vulnerabilities. This implementation is not intended for production use.

Changelog

1.0.5

• Added nguyen_fix parameter to GGHCryptosystem (default False). When enabled, implements the Mandangan et al. (2020) countermeasure against Nguyen's attack: error entries are drawn from {σ-2, σ-1, σ, σ+1} instead of {-σ, +σ}, preserving ||e|| = σ√n while breaking the elimination stage of the attack.
• Key generation with nguyen_fix=True automatically retries until a basis yielding σ > 2 is found (required by the countermeasure). Raises ValueError after 100 failed attempts with a suggestion to increase the dimension.

1.0.4

• Initial stable release.