FHE: Direct computation on encrypted data

FHE( fully homomorphic encryption) is an advanced encryption technology that allows for computations to be performed directly on encrypted data, thus enabling data processing while protecting privacy. FHE has potential applications in various fields such as finance, healthcare, cloud computing, and machine learning, but due to its enormous computational and memory overhead, commercialization still requires time.

Basic Principles

The core of FHE is to hide the original information through polynomials. The encryption process uses a key polynomial, a random polynomial, and a small "noise" polynomial. Decryption requires knowledge of the key polynomial.

In order to perform computations on encrypted data, FHE converts operations into "circuits". Addition and multiplication form the basic operations and can express any computation. However, each operation increases noise, and multiplication particularly leads to exponential growth of noise, which limits the depth of computation.

To address the noise issue, FHE employs the following techniques:

• Key switch: compress ciphertext size
• Modulus switching: reduce noise budget
• Bootstrap (: Reset the noise to the initial level

Currently, mainstream FHE solutions adopt Bootstrap technology, but the computational overhead is still substantial. Compared to ordinary computation, FHE computation may be 500 million times slower.

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Challenges Faced

The biggest challenge of FHE is the enormous computational overhead. DARPA specifically launched the DPRIVE program, attempting to increase the computation speed of FHE to 1/10 of normal computation, but progress has been slow.

The main areas of improvement include:

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

Although the progress of FHE technology is slow, it is still significant for protecting sensitive data, especially in the post-quantum era.

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

Blockchain Integration

FHE is mainly used in blockchain to protect data privacy, including on-chain privacy, AI training data privacy, on-chain voting privacy, and so on. However, fully encryption transactions can also bring new issues, such as losing the positive effects of MEV bots and significantly increasing node requirements.

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Main Projects

Current major FHE projects include:

• Zama: provides a development framework based on TFHE
• Fhenix: Building a privacy-first Layer 2
• Privasea: used for LLM data operations
• Inco Network: Build FHE Layer 1
• Mind Network: for Restaking
• Octra: Implements FHE using hypergraphs technology

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

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

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

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

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

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Outlook

FHE is still in its early stages and faces many challenges. However, with more investment and talent, as well as the development of dedicated chips, FHE is expected to bring transformation to fields such as finance and healthcare in the future. Its combination with cutting-edge technologies such as quantum computing is also worth looking forward to.