From Gentry to CKKS: The 4 Generations of Homomorphic Encryption Explained
The Evolution of a “Mathematical Impossibility”
For decades, cryptographers viewed the idea of computing on encrypted data as a holy grail—theoretically fascinating but practically impossible. That changed overnight in 2009. Since then, Homomorphic Encryption (HE) has evolved rapidly, moving from purely theoretical proofs to high-speed libraries powering modern AI.
Understanding these “generations” isn’t just a history lesson; it is critical for developers. Choosing the wrong scheme for your application (e.g., using a Gen 2 scheme for machine learning) can result in crippling performance penalties. Here is how the landscape has shifted.
Generation 1: The Gentry Breakthrough (2009)
Before 2009, we only had “Partially” Homomorphic Encryption—schemes that could multiply or add, but not both. Craig Gentry changed the game with his doctoral thesis, proving that Fully Homomorphic Encryption (FHE) was mathematically possible.
His key innovation was “bootstrapping”—a method to refresh the “noise” that accumulates during computation, preventing the ciphertext from becoming corrupted. While revolutionary, Gen 1 schemes were incredibly slow, requiring massive computational resources for even simple operations. They were a proof of concept, not a product.
Generation 2: BGV and BFV (Integer Arithmetic)
The second generation focused on making Gentry’s ideas practical. Schemes like BGV (Brakerski-Gentry-Vaikuntanathan) and BFV (Brakerski/Fan-Vercauteren) introduced better noise management techniques.
These schemes excel at exact integer arithmetic. If your use case involves financial accounting, voting systems, or precise statistical analysis where $1 + 1$ must equal exactly $2$, Gen 2 is often the go-to choice. However, they struggle with deep computations (many sequential multiplications) without incurring significant overhead.
Generation 3: TFHE (Binary Gates)
The third wave, typified by TFHE (Torus FHE), took a different approach. Instead of focusing on large integers, TFHE optimized operations at the bit level (binary gates like AND, OR, XOR).
The standout feature of TFHE is its incredibly fast programmable bootstrapping. It allows for the evaluation of arbitrary boolean circuits with very low latency per gate. This makes it ideal for comparison operations (e.g., “Is Encrypted Value A > Encrypted Value B?”) which are notoriously difficult in other generations.
Generation 4: CKKS (Approximate Arithmetic)
The fourth and most recent generation answers the specific demands of Data Science and Artificial Intelligence. The CKKS (Cheon-Kim-Kim-Song) scheme introduced the concept of approximate arithmetic.
In machine learning, we rarely need perfect precision; we deal in probabilities and weights (e.g., 0.987 vs 0.988). CKKS embraces this, treating encrypted data more like real numbers (floats) rather than integers. This efficiency makes CKKS the standard for Encrypted Machine Learning and privacy-preserving AI models, where speed and vector operations are paramount.
Which Scheme Should You Use?
There is no single “best” generation. The choice depends entirely on your data type:
- Exact Integers (Finance/Voting): Look at BGV or BFV (Gen 2).
- Boolean Logic/Comparisons: TFHE (Gen 3) is your champion.
- Machine Learning/Complex Numbers: CKKS (Gen 4) is the industry standard.
As libraries like OpenFHE and Microsoft SEAL continue to mature, they are beginning to abstract these differences away, but knowing the underlying engine helps you build faster, more secure applications.