FHE: The Cloak of Invisibility in the Field of Cryptography

FHE( Fully Homomorphic Encryption) is an advanced encryption technology that allows for computation on data while it is in an encrypted state. This means that data can be analyzed and processed while maintaining privacy. FHE has potential application scenarios in various fields such as finance, healthcare, cloud computing, and machine learning. However, due to its enormous computational and memory overhead, commercial applications still face challenges.

The Basic Principles of FHE

The core of FHE is to hide the original information through polynomials. A simplified FHE encryption process is 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. Encrypted message m: c(x) = m + a(x)*s(x) + e(x)

During decryption, as long as you know the key s(x), you can recover the original information m from c(x).

Introducing noise e(x) is to enhance security, but it also brings the issue of noise accumulation. To address this problem, FHE employs the following techniques:

• Key switching: Compressing ciphertext size
• Modulus Switching: Reduce Noise
• Bootstrap: Reset noise to initial level

Currently, mainstream FHE solutions all adopt Bootstrap technology, but the computational overhead is still quite large.

Challenges Facing FHE

The biggest challenge of FHE is computational efficiency. Compared to ordinary computation, the computational overhead of FHE is several orders of magnitude higher. The U.S. DARPA's Dprive program aims to solve this problem, with the goal of increasing the FHE computation speed to 1/10 of ordinary computation.

The main optimization directions include:

• Increase processor word length
• Develop dedicated ASIC processors
• Adopting MIMD parallel architecture

Although progress is slow, FHE still has unique value in protecting sensitive data in the long term, especially in the post-quantum era.

The Application of FHE 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 transaction privacy audit
• Potential MEV Solutions

But it also faces challenges such as increased efficiency and node requirements.

Major FHE Projects

The main FHE projects currently include:

• Zama: provides development tools based on TFHE
• Fhenix: Build a privacy-first L2 network
• Privasea: FHE Applications for LLM
• Inco Network: Building an L1 network for FHE
• Arcium: Integrating FHE, MPC, and ZK technologies
• Mind Network: FHE-based Restaking Solution
• Octra: Implementing FHE using hypergraphs technology

Future Outlook

FHE technology is still in its early stages and faces many challenges:

• Inefficient, high cost
• The difficulty of engineering implementation is high.
• The commercial prospects are unclear.
• Lack of capital investment

However, with the emergence of dedicated chips and an influx of more funds, FHE is expected to bring about transformation in fields such as defense, finance, and healthcare. It will unlock the potential of combining private data with future quantum algorithms, ushering in new development opportunities.