FHE: The "invisibility cloak" of Cryptography

FHE( Fully Homomorphic Encryption) is an advanced encryption technology that allows computation to be performed directly on encrypted data, thus enabling data processing while protecting privacy. This technology has potential applications in various fields such as finance, healthcare, cloud computing, and machine learning, but due to its significant computational and memory overhead, commercialization is still a work in progress.

Basic Principles

The core idea of FHE is to use polynomials to hide the original information. A simplified encryption process may be as follows:

1. Choose a key polynomial s(x)
2. Generate a random polynomial a(x)
3. Generate a small "noise" polynomial e(x)
4. Encrypt plaintext m: c(x) = m + a(x)*s(x) + e(x)

During decryption, as long as the key s(x) is known, the plaintext m can be recovered from c(x).

To achieve arbitrary depth computation, FHE employs the following techniques:

• Key Switching: Compressing Ciphertext Size
• Modulus switching: control noise growth
• Bootstrap (: Reset noise level

Currently, mainstream FHE schemes are based on bootstrapping techniques, such as BGV, BFV, CKKS, etc.

![Gate Ventures Research Institute: FHE, Wearing Harry Potter's Invisibility Cloak])https://img-cdn.gateio.im/webp-social/moments-4a7670767b0963cded31da66c52ad97e.webp(

Challenges Faced

The biggest problem with FHE is the huge computational overhead. Compared to ordinary computation, the FHE version may be billions of times slower. To accelerate FHE, the U.S. DARPA has launched the DPRIVE program, aiming to increase the speed of FHE to 1/10 of ordinary computation. The program mainly focuses on the following aspects:

1. Increase processor word length
2. Develop dedicated ASIC chips
3. Build MIMD Parallel Architecture

Although progress is slow, FHE technology still has significant importance in the long term, especially in handling sensitive data.

![Gate Ventures Research Institute: FHE, wearing Harry Potter's invisibility cloak])https://img-cdn.gateio.im/webp-social/moments-186e4abe7434e22b3daf0389cf199699.webp(

Applications in Blockchain

FHE is mainly used in the blockchain field to protect data privacy, including:

• On-chain privacy protection
• AI training data privacy
• On-chain voting privacy
• On-chain privacy transaction review
• Potential MEV Solutions

However, the performance of FHE currently limits its large-scale application.

![Gate Ventures Research Institute: FHE, wearing Harry Potter's invisibility cloak])https://img-cdn.gateio.im/webp-social/moments-673ae606fcd3769523e1a330f991464d.webp(

![Gate Ventures Research Institute: FHE, wrapped in Harry Potter's invisibility cloak])https://img-cdn.gateio.im/webp-social/moments-22d66cabb8f0a526bb728b7b4ced159b.webp(

![Gate Ventures Research Institute: FHE, wearing Harry Potter's invisibility cloak])https://img-cdn.gateio.im/webp-social/moments-d745afb65d7c110a6e6333a6d73b60b5.webp(

Main Projects

Currently, FHE-related projects are mainly based on the technology provided by Zama:

• Fhenix: Privacy-first Optimism Layer 2
• Privasea: LLM Data Computation
• Inco Network: Building Layer 1
• Arcium: Integrates FHE, MPC, and ZK technologies
• Mind Network: Provides a subnet architecture based on FHE

In addition, Octra adopts its self-developed hypergraphs technology to implement FHE.

![Gate Ventures Research Institute: FHE, wearing Harry Potter's invisibility cloak])https://img-cdn.gateio.im/webp-social/moments-99ea73218c9e569a2de152d8a37338f4.webp(

![Gate Ventures Research Institute: FHE, wearing Harry Potter's invisibility cloak])https://img-cdn.gateio.im/webp-social/moments-74c86e1ff0ef22f5aef9b5cc441d60eb.webp(

![Gate Ventures Research Institute: FHE, wearing Harry Potter's invisibility cloak])https://img-cdn.gateio.im/webp-social/moments-93dd078bf652201018797c88a14203f9.webp(

![Gate Ventures Research Institute: FHE, wearing Harry Potter's invisibility cloak])https://img-cdn.gateio.im/webp-social/moments-ed3a576f24107d796df96ed44068e43f.webp(

Outlook

FHE is still in its early stages, facing many challenges:

• High cost
• The engineering difficulty is high
• The commercial prospects are unclear.

However, with the increase in investment and the deployment of dedicated chips, FHE is expected to bring about transformation in fields such as defense, finance, and healthcare. In the future, the combination of FHE with cutting-edge technologies such as quantum computing may lead to explosive growth.