Fully Homomorphic Encryption: Overview of the Maturing Track and Potential Opportunities

Cryptographic technology plays an important role in the process of human civilization, especially in information security and privacy protection, where it has an irreplaceable function. It not only provides a solid guarantee for data transmission and storage in various fields, but its asymmetric encryption public-private key system and hash functions were creatively integrated by Satoshi Nakamoto in 2008, designing a proof-of-work mechanism to solve the double-spending problem, which promoted the birth of Bitcoin, a revolutionary digital currency, and opened a new era for the blockchain industry.

With the rapid development of the blockchain industry, a series of cutting-edge cryptographic technologies have emerged, among which zero-knowledge proofs, multi-party computation, and fully homomorphic encryption are the most noteworthy. These technologies have been widely applied in various scenarios, such as zero-knowledge proofs combined with Rollup solutions to address the “impossible triangle” problem of blockchain, and multi-party computation combined with public and private key systems to promote large-scale applications of user entry. Fully homomorphic encryption, regarded as one of the holy grails of cryptography, has unique characteristics that allow third parties to perform arbitrary computations and operations on encrypted data without decryption, thereby enabling composable on-chain privacy computing and bringing new possibilities to multiple fields and scenarios.

Fully Homomorphic Encryption Overview

The core of fully homomorphic encryption ( FHE ) lies in allowing computations and operations to be performed on ciphertext, which can directly map to plaintext while preserving the mathematical properties of the encrypted data. The “fully” in FHE means that this homomorphism reaches a new height, allowing for unlimited computations and operations on encrypted data.

In the field of FHE, Microsoft and Zama have demonstrated unparalleled usability and influence with their outstanding open-source products. They provide developers with stable and efficient FHE implementations, greatly promoting the ongoing development and widespread application of FHE technology.

Microsoft’s SEAL is a library that supports fully homomorphic encryption and partially homomorphic encryption, providing an efficient C++ interface, integrating numerous optimization algorithms and techniques, significantly enhancing computational performance and efficiency.

Zama’s TFHE is an open-source library focused on high-performance fully homomorphic encryption, providing services through a C language interface, and utilizing a series of advanced optimization techniques and algorithms aimed at achieving faster computation speeds and lower resource consumption.

The basic operation process of FHE includes:

1. Generate Key
2. encrypted data
3. Perform homomorphic computation
4. Decryption Result

In the practice of fully homomorphic encryption (FHE), the management of decryption keys is crucial. For blockchain, introducing threshold multi-party secure computation schemes is a highly promising option that can enhance the security of key management and reduce the risk of a single node being compromised.

Ethereum Virtual Machine Supporting FHE

To achieve the application of Fully Homomorphic Encryption (FHE) on the blockchain, the ideal way is to encapsulate it as a general-purpose smart contract code library. This requires the smart contract virtual machine to pre-support a specific instruction set for the complex mathematical operations and encryption operations required by FHE.

As a widely adopted and long-validated virtual machine, the EVM naturally becomes the preferred choice for implementing FHE. In this field, Zama has introduced the fully homomorphic EVM - fhEVM, which supports privacy computing through Solidity.

The core features of fhEVM include:

• Provide FHE operation support through pre-compiled contracts integrating the Zama open-source FHE library.
• Create specific EVM memory and storage areas for FHE
• Decryption mechanism designed based on distributed threshold protocol
• Solidity contract library that lowers the development threshold

fhEVM provides a solid foundation for FHE technology in blockchain applications, but it may face many challenges when pushed towards practical application.

Rollup Solution Based on Fully Homomorphic Encryption

The pure fhEVM cannot form a complete ecosystem; it needs to rely on a public chain-level architecture or adopt Layer 2/Layer 3 solutions. Considering the characteristics of FHE, combining fhEVM with Rollup technology to build an FHE-Rollups type Layer 2 solution becomes a feasible direction.

Fhenix, as a pioneer, actively explores FHE-Rollups solutions. Given the technical complexity, Fhenix has chosen a solution based on Optimistic Rollups.

The technology stack of Fhenix mainly includes:

• A variant of Arbitrum Nitro’s fraud prover
• Core Library fheOS
• Threshold Service Network ( TSN )

Based on this tech stack, Fhenix has released the first public version Fhenix Frontier, providing comprehensive development tools and documentation support.

Blockchain-agnostic FHE co-processor

Fhenix introduces the Relay module, enabling various public chains, L2, and L3 networks to access FHE functionalities using FHE Coprocessors. To overcome the long challenge period limitations of FHE-Rollups, Fhenix collaborates with EigenLayer to provide a faster service channel for FHE Coprocessors through the Restaking mechanism.

The usage process of FHE Coprocessors includes:

1. Application contract calls FHE Coprocessor
2. Relay contract queuing request
3. Forward the request to Fhenix Rollup
4. Perform FHE computation
5. Threshold Network Decryption Output
6. The result is returned to the contract.
7. Contract verification and sending results
8. The application contract continues to execute

Applications of FHE

FHE technology shows great potential in fields such as full-chain gaming, DeFi, and AI:

• Privacy-protected full-chain games: providing encryption protection for the gaming economy, preventing real-time manipulation, and safeguarding player privacy.
• DeFi/MEV: Protect sensitive data in DeFi, reduce malicious MEV behavior
• AI: Protect individual privacy data and achieve secure AI model training.

Overview of the FHE Ecosystem

In addition to the core technology service companies Zama and Fhenix, there are also a number of noteworthy projects in the FHE ecosystem:

• Sunscreen: self-developed FHE compiler
• Mind Network: Combined FHE network with EigenLayer
• PADO Labs: A decentralized computing network that integrates ZKP and FHE
• Arcium: Parallel Confidential Computing Network
• Inco Network: Layer 1 that optimizes the efficiency of fully homomorphic encryption calculations
• Treat: FHE Layer3 of the Shiba ecosystem
• octra: supports FHE networks with isolated execution environments
• BasedAI: Distributed network that introduces FHE functionality for LLM
• Encifher: Focused on FHEML projects
• Privasea: FHE network for ML inference in the AI field

Non-profit research and educational institutions such as FHE.org and FHE Onchain provide valuable resources for ecological development.

The prospects of FHE technology are vast. Once projects like Fhenix go live on the mainnet, they will bring innovation and transformation to multiple fields. This vibrant future is just around the corner.