FHE Schemes – The Road to Practical Adoption
In our Fully Homomorphic Encryption (FHE) journey so far, we’ve looked at the history of FHE and introduced its immense potential for cloud computing and privacy. We subsequently touched on the key mathematical foundations of FHE, and most recently took a considered look at the computational toll this technology currently demands. Now, it’s time to zoom in on the core cryptographic schemes that bring FHE to life: BGV, BFV, CKKS, and TFHE.
It may be helpful to think of each of these schemes as different ‘languages’ that FHE systems use and understand to compute on encrypted data. Each has its own vocabulary, grammar, and specialties — making them suitable for different applications. In this post, we’ll break them down in a friendly and intuitive way, and include a summary table for readers who prefer to jump straight to the conclusions.
Why Different FHE Schemes Exist
Before we dive into acronyms, let’s understand why we even have multiple FHE schemes. Imagine trying to design a tool that lets you perform computations without ever seeing the actual data. You’d quickly run into complex trade-offs between efficiency, precision, the types of data supported, and security.
No single FHE scheme can excel in every area, so different schemes have emerged, each optimizing for specific needs. Some are better for working with numbers, others for logic circuits, and some shine in machine learning tasks. Now, let’s explore schemes.
BGV: The Versatile Classic
BGV stands for Brakerski-Gentry-Vaikuntanathan, after the researchers who introduced it in 2011. We discussed Gentry’s particularly pivotal role in the origin story of FHE, and in BGV, in the introductory post. BGV was one of the first practical FHE schemes and remains widely studied and used today.
Key Characteristics:
- Supports modular integer arithmetic on encrypted data, enabling operations like adding and multiplying directly on ciphertexts representing whole numbers.
- Uses leveled FHE, meaning you can perform a fixed number of computations before needing to refresh or “bootstrap” the ciphertext.
- Employs modulus switching to control noise growth, a clever trick that helps keep encrypted data manageable as operations accumulate.
- Single Instruction, Multiple Data (SIMD) support.
When to Use It:
BGV is great for applications that need precise calculations on integers, like encrypted statistics, private database queries, or secure voting systems.
BFV: The Balanced Workhorse
BFV, short for Brakerski-Fan-Vercauteren, is similar to BGV but with some key differences under the hood. It’s designed for exact arithmetic over integers, just like BGV, but it handles ciphertext and noise in a slightly different way.
Key Characteristics:
- Supports exact modular integer computation, which is a must when approximation isn’t acceptable.
- Easier to implement in some scenarios due to its plaintext modulus design.
- Also uses leveled computation, with optional bootstrapping for deeper operations.
- SIMD support
When to Use It:
Similar to BGV, BFV is designed for applications that demand precise integer computations. Typical use cases range from financial analysis to private identity verification and secure government workflows.
CKKS: The Approximate Mathematician
Now we move into a different territory: approximate arithmetic. The CKKS scheme (named after Cheon-Kim-Kim-Song) was built specifically for real numbers, allowing it to perform operations on decimal values, though with some loss in precision, liker rounding in everyday math.
Key Characteristics
- Ideal for approximate computations on real or complex numbers.
- Especially useful in machine learning, where small errors are tolerable.
- Efficient at vectorized operations, meaning it can process many numbers in parallel.
- Offers the highest throughput among FHE schemes, making it well-suited for processing large volumes of data efficiently.
- SIMD-support.
When to use it
CKKS is the go-to scheme for privacy-preserving AI, such as encrypted neural networks, homomorphic inference, and private data analytics. It’s also useful in healthcare or finance, where averages, trends, and predictions matter more than exact values.
Did You Know?
One of the strongest validations of CKKS is that the most advanced implementation of BFV bootstrapping converts to CKKS, performs bootstrapping using CKKS, and then converts back. This approach takes advantage of CKKS’s efficiency even when working with other schemes.
TFHE: The Speed Demon for Binary Logic
TFHE (short for “Fast Fully Homomorphic Encryption over the Torus”) is different from the previous three schemes. Instead of focusing on numbers, TFHE excels at bit-level operations. Think of it as a secure digital logic processor.
Key Characteristics:
- Fast bootstrapping, allowing arbitrary-depth computation without noise buildup.
- Works with binary data, making it perfect for implementing encrypted logic gates and circuits.
- Suitable for real-time applications thanks to its low-latency design.
- Very fast for bootstrapping, but has low throughput.
When to use it
TFHE is best suited for applications involving simple logic circuits, such as blockchain, smart contracts, and private condition checking (like password verification or access control).
A Quick Comparison Table
| Scheme | Data Type | Precision | Strengths | Common Uses |
| BGV | Integers | Exact | Mature ecosystem | Stats, Voting, Finance, ID verification |
| BFV | Integers | Exact | Simpler noise handling | |
| CKKS | Reals / complex | Approximate | Scalable and high throughput | ML, analytics |
| TFHE | Bits | Exact | Fast bootstrapping | Logic, access control |
Wrapping Up
Each FHE scheme is like a different type of secret calculator. Some are better with exact values, others work faster when a bit of approximation is okay, and some thrive in logical decision-making.
The future of FHE isn’t about picking a single winner — it’s about choosing the right tool for the job. As this field evolves, we may even see hybrid models that combine the best features of each. However, newer generation FHE schemes can offer advancements in efficiency, scalability, and usability. Moreover, they are usually better suited to modern applications.
With a solid grasp of FHE schemes and bootstrapping, you’re ready for the next step: exploring FHE tools. In the upcoming posts, we’ll dive into libraries and compilers. Stay tuned!