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Also known as: Goldreich–Goldwasser–Halevi
An early lattice-based public-key encryption scheme proposed by Goldreich, Goldwasser, and Halevi.
DESCRIPTION
The GGH encryption scheme constructs public keys from lattices and relies on the hardness of lattice problems like CVP and SVP. It was significant in demonstrating practical lattice-based public-key encryption. However, cryptanalysis revealed vulnerabilities under certain parameter choices and schemes derived from it. GGH influenced later designs but is generally considered superseded by more robust lattice constructions. Today, NTRU and module/RLWE-based schemes are preferred for practical deployment.
ALTERNATIVE DEFINITIONS
Wikipedia
The GGH encryption scheme is an early asymmetric key cryptosystem based on lattice problems, proposed by Oded Goldreich, Shafi Goldwasser and Shai Halevi.
Highlights authorship and lattice-problem basis as defining characteristics.
Springer
We present a public-key cryptosystem and a signature scheme based on the computational difficulty of lattice reduction problems.
Original publication emphasizes security reductions to lattice problems.
RELATED TERMS
Lattice-Based Cryptography Shortest Vector Problem Closest Vector Problem Post-Quantum Cryptography GGH Signature Scheme Lattice Reduction
COMPETING TERMS
KNOWLEDGE AREAS
TARGET AUDIENCE
Security Architect Cybersecurity Engineer Software Developer
EXTERNAL SOURCES
- Wikipedia - GGH encryption scheme
- IACR ePrint - Preprint on lattice-based public-key cryptosystems
- IACR ePrint - Cryptanalysis and discussions of GGH variants
TOP QUESTIONS
What is GGH in lattice cryptography?
GGH is an early lattice-based public-key encryption scheme relying on hard lattice problems such as SVP and CVP.
Category: Basics
Why is GGH historically important?
It demonstrated practical feasibility of lattice-based public-key cryptography and influenced subsequent designs.
Category: Relevancy
Is GGH still recommended today?
No, it’s largely superseded by more robust schemes like NTRU and module/RLWE-based constructions.
Category: Alternatives
What weaknesses affected GGH?
Certain parameter choices and structural aspects enabled cryptanalysis, reducing its practical security.
Category: Risks
What is the main difference between GGH and NTRU?
NTRU uses polynomial rings and different algebraic structures enabling better performance and security trade-offs in practice.
Category: Comparison
What problems underpin GGH security?
Closest Vector Problem and Shortest Vector Problem in lattices are central to its security arguments.
Category: Mathematics
When was GGH introduced?
The scheme appeared in the late 1990s in work by Goldreich, Goldwasser, and Halevi.
Category: History
What is a lesson learned from GGH?
Parameterization and structure matter greatly; rigorous analysis is needed before wide deployment.
Category: Lessons
What modern schemes evolved after GGH?
NTRU, Kyber, and other module-lattice approaches are considered more viable today.
Category: Evolution