What is FHE

Fully Homomorphic Encryption (FHE) was first discussed in the 1970s, but has been difficult to achieve. The basic idea is to encrypt data and perform calculations on it without decrypting it. Initially, only simple operations such as addition or multiplication could be performed on encrypted data, known as partially homomorphic encryption. A breakthrough occurred in 2009 when Craig Gentry demonstrated that any computation could be performed on encrypted data, leading to the development of fully homomorphic encryption.

FHE is an advanced form of encryption that allows calculations to be performed on encrypted data without the need for decryption. This means that operations can be performed on ciphertext (encrypted data) to generate encrypted results, which are consistent with the results of operations on plaintext (unencrypted data) when decrypted.

Key Features of Fully Homomorphic Encryption

Homomorphism

• Addition: Performing addition operations on ciphertext is equivalent to performing addition operations on plaintext.

?(?+?)=?(?)+?(?)

• Multiplication: Performing multiplication operations on ciphertext is equivalent to performing multiplication operations on plaintext.

?(?×?)=?(?)×?(?)

• Noise Management: When using FHE to encrypt data, noise is added to the ciphertext to ensure security. However, this noise increases after each operation. Managing and minimizing noise is crucial because if the noise becomes too large, computations may become inaccurate or fail.
• Unlimited Operations: Unlike partially homomorphic encryption (PHE), which supports only one type of operation (addition or multiplication) and a limited number of operations, and some homomorphic encryption (SHE) that supports addition and multiplication but with a limited number of times, FHE supports an unlimited number of additions and multiplications. This allows any type of computation to be performed on encrypted data.

Strictly speaking, fully homomorphic encryption is a special case of homomorphic encryption. Homomorphic encryption means that performing addition or multiplication operations on ciphertext is equivalent to performing the same operations on plaintext, i.e.:

?(?+?)=?(?)+?(?)

?(?×?)=?(?)×?(?)

In this context, a and E(a), b and E(b) can be considered equivalent. However, two important challenges need to be noted:

1. The equivalence between plaintext and ciphertext involves adding some noise to the plaintext before performing operations to obtain the ciphertext. If the noise leads to significant bias, computations may fail. Therefore, controlling noise is crucial for various algorithms.
2. The cost of addition and multiplication is enormous. Ciphertext computations may be 10,000 to 1,000,000 times more expensive than plaintext computations. Only when an unlimited number of additions and multiplications can be performed on ciphertext does fully homomorphic encryption become achievable.

Different types of homomorphic encryption have unique value in their respective fields and can be classified based on their implementation level:

• Partially Homomorphic Encryption (PHE): Supports one type of operation (addition or multiplication) for an unlimited number of operations. For example, RSA is partially homomorphic in terms of multiplication.
• Some Homomorphic Encryption (SHE): Supports addition and multiplication, but with a limited number of times. This is useful for specific applications that require only a small number of operations.
• Fully Homomorphic Encryption (FHE): Supports an unlimited number of additions and multiplications, allowing arbitrary computations on encrypted data. This makes FHE extremely powerful but also computationally intensive.

The main advantage of FHE is its ability to perform any type of computation on encrypted data, ensuring privacy and security throughout the entire computation process.

Applications of FHE in Blockchain

Vitalik pointed out that FHE could be a key technology for blockchain scalability and privacy protection. Current blockchains are transparent by default, with every transaction and smart contract variable being public. FHE can transform fully transparent blockchains into partially encrypted forms while still being controlled by smart contracts.

For example, Zama is developing an FHE virtual machine that allows programmers to write Solidity code that operates on FHE primitives. This approach can address privacy issues on today's blockchains, making use cases such as encrypted payments, slot machines, and casinos possible while retaining transaction graphs, making it more regulatory-friendly compared to solutions like Tornado Cash.

Another key application of FHE is to improve the usability of privacy projects. Projects like Zcash, Aztec, and Tornado Cash face significant usability issues such as long retrieval times for balance information and synchronization delays. FHE provides a solution through Oblivious Message Retrieval (OMR), allowing wallet clients to synchronize without exposing the content being accessed.

However, FHE cannot directly address blockchain scalability issues like Rollup technology. Combining FHE with zero-knowledge proofs (ZKP) may address some scalability challenges. Verifiable FHE can ensure correct execution of computations, similar to ZK Rollups, providing a trusted computation mechanism for the blockchain environment.

Relationship between FHE and Zero-Knowledge Proofs (ZKP)

FHE and ZKP are complementary technologies serving different purposes. ZKP allows for verifiable computation and zero-knowledge properties, providing privacy for private states. However, ZKP does not provide privacy for shared states, which is crucial for permissionless smart contract platforms like Uniswap. This is where FHE and multi-party computation (MPC) come into play, allowing computations on encrypted data without exposing the data itself.

Combining ZKP and FHE would significantly increase computational complexity and is impractical unless specific use cases require it.

Current Stage and Future Prospects of FHE

FHE is approximately three to four years behind ZKP in terms of development but is catching up rapidly. The first generation of FHE projects is launching testnets, with the mainnet expected to be released later this year. Although FHE still has higher computational overhead than ZKP, its potential for widespread adoption is imminent. Once FHE enters production and scales, it is expected to grow rapidly, similar to ZK Rollups.

Challenges and Bottlenecks

The adoption of FHE faces several challenges, including computational efficiency and key management. Bootstrapping operations in FHE are computationally intensive, but progress in algorithms and engineering optimizations is improving this. Alternative approaches that do not use bootstrapping operations may be more efficient for specific use cases such as machine learning (ML).

Key management also presents challenges. Projects like Zama's fhEVM, Inco, or Phoenix require threshold key management, involving a set of validators with decryption capabilities. This approach needs further development to overcome single point of failure issues.

Use Cases:

Current State of the FHE Market

Cryptocurrency venture capital firms like 1kx have been actively investing in the FHE field, recognizing its potential. 1kx led the investment in the Inco project, built on Zama, focusing on use cases for fhEVM. Inco is collaborating with partners to develop applications such as slot machines, casinos, commercial payments, and games.

Threshold FHE (TFHE) combines FHE with MPC and blockchain, opening up new use cases and showing great promise. The developer-friendly nature of FHE, allowing programming in Solidity, makes it practical and feasible for application development.

Competitive Landscape: Arcium (formerly Elusiv)

Arcium is a DePIN network on Solana for parallel confidential computation. Founded by Yannik Schrade, Julian Deschler, Nicolas Schapeler, and Lukas Steiner, it was renamed from the zk-based compliant privacy protocol Elusiv to Arcium on May 8, 2024.

Arcium supports developers and applications in DeFi, DePIN, AI, etc., providing flexible, trustless, verifiable, high-performance confidential computation capabilities through the DA layer and consensus layer of the underlying blockchain. It is not a blockchain but allows developers to deploy confidential smart contracts on different blockchains and provides the ability to configure trust models for non-blockchain users on demand.

In May 2024, Arcium completed a strategic financing round of $5.5 million, led by Greenfield Capital, with participation from Coinbase Ventures, Heartcore Capital, Longhash VC, L2 Iterative Ventures, Stake Facilities, Smape Capital, Everstake, Solana co-founder Anatoly Yakovenko, and Monad co-founder Keone Han.

Cysic

Cysic is a hardware acceleration company focused on real-time generation and verification of zero-knowledge (ZK) proofs. They offer ZK Computation as a Service (ZK-CaaS) based on proprietary ASIC, FPGA, and GPU chips. Cysic has developed FPGA hardware and plans to launch ZK DePIN chips/devices called ZK Air and ZK Pro, forming the Prover Network for DePIN.

In February 2023, Cysic completed a $6 million seed financing round led by Polychain Capital, with participation from HashKey, SNZ Holding, ABCDE, A&T Capital, and Web3.com Foundation.

Zama

Zama is an open-source cryptography company developing FHE solutions for blockchain and AI. Co-founded by Hindi and renowned cryptographer and one of the inventors of FHE, Pascal Paillier, in early 2020, Zama provides FHE solutions for Web3 projects, such as the TFHE-re library, TFHE compiler Concrete, privacy-preserving machine learning Concrete ML, and confidential smart contract fhEVM.

Zama focuses on Threshold Fully Homomorphic Encryption (TFHE), with TFHE-re implemented in pure Rust for encrypted boolean and integer computations, allowing developers and researchers fine-grained control over TFHE for advanced functionality. fhEVM integrates TFHE-re into the EVM, enabling homomorphic operations as precompiled contracts without modifying the compilation tool.

On March 7, 2024, Zama completed a $73 million Series A financing round led by Multicoin Capital and Protocol Labs, with participation from Metaplanet, Blockchange Ventures, Vsquared Ventures, Stake Capital, Filecoin founder Juan Benet, Solana co-founder Anatoly Yakovenko, and Ethereum co-founder Gavin Wood. The funding will be used to continue research and development of their FHE tools.

Sunscreen

Sunscreen is a privacy startup helping engineers build and deploy private applications using encryption technologies such as FHE. They have open-sourced an FHE compiler, a Web3-native compiler that converts standard Rust functions into equivalent private FHE functions, providing arithmetic operations with optimal performance without hardware acceleration. The compiler also supports the BFV FHE scheme and is developing a compiler compatible with ZKP to ensure computational integrity when combined with FHE.

In July 2022, Sunscreen completed a $4.65 million seed financing round led by Polychain Capital, with participation from Northzone, Coinbase Ventures, dao5, Naval Ravikan, Tux Pacific, and others.

Octra

Octra is an FHE blockchain network supporting isolated execution environments, proposing a new type of FHE called Homomorphic Fully Homomorphic Encryption (HFHE), running on hypergraphs. According to official documentation, HFHE can be compatible with and operate independently with any project. Most of Octra's codebase is developed in OCaml, AST, ReasonML (for smart contracts and applications interacting with Octra), and C++. This approach is relatively new, with limited academic discussion. The security of the solution has not been verified and requires further validation.

Fhenix

Fhenix is an Ethereum Layer 2 (L2) supported by FHE Rollups and FHE Coprocessors, fully compatible with EVM and Solidity, using FHE to implement on-chain confidential smart contracts. Fhenix does not use zkFHE but adopts Optimistic Rollup and Zama's FHE to achieve on-chain confidentiality, focusing on TFHE (Threshold FHE).

In September 2023, Fhenix completed a $7 million seed financing round led by Sora Ventures, Multicoin Capital, and Collider Ventures, with participation from Node Capital, Bankless, HackVC, TaneLabs, and Metaplanet. The public testnet is expected to be released in early 2024, supporting ecosystem application development.

Mind Network

Mind Network is an FHE staking layer for DePIN and AI, supported by Zama, aiming to achieve "HTTPZ" (end-to-end encrypted internet). The products include the FHE staking solution MindLayer, the FHE-authorized stealth address protocol MindSAP, and the FHE DataLake MindLake built through the FHE verification network of MindLayer. Users can stake BTC and ETH LST tokens in Mind Network, introducing FHE-enhanced validators to ensure end-to-end encryption in AI and DePIN network verification and computation processes. The intelligent Proof of Intelligence (PoI) consensus mechanism for AI machine learning tasks ensures fair and secure allocation among FHE validators. FHE computations can be hardware-accelerated. MindLake is a data storage Rollup for on-chain encrypted data computation.

In June 2023, Mind Network completed a $2.5 million seed financing round, with participation from Binance Labs, Comma3 Ventures, SevenX Ventures, HashKey Capital, Big Brain Holdings, Arweave SCP Ventures, Mandala Capital, and others.

Inco

Inco Network is a modular confidential computation Layer 1 blockchain and Web3 general privacy layer, providing privacy protection for on-chain applications. It combines Ethereum EVM and FHE, protected by EigenLayer, allowing programs to operate and compute on encrypted data without decryption, using on-chain native randomness. Inco has launched the Gentry testnet to address Web3 privacy challenges, supporting applications such as gaming, DeFi (including dark pools, private lending, and blind auctions), and enterprise solutions (such as confidential stablecoins, private RWAs, and private voting).

In February 2024, Inco Network completed a $4.5 million seed financing round led by 1kx, with participation from Circle Ventures, Robot Ventures, Portal VC, Alliance DAO, Big Brain Holdings, Symbolic, GSR, Polygon Ventures, Daedalus, Matter Labs, and Fenbushi.

Regulatory Environment for Privacy Technologies like FHE

The regulatory environment for privacy technologies like FHE varies in different regions. While data privacy is widely supported, financial privacy remains a gray area. FHE has the potential to enhance data privacy, allowing users to retain ownership of data and potentially benefit from it while maintaining societal benefits such as targeted advertising.

Looking ahead, gradual improvements in theory, software, hardware, and algorithms are expected to make FHE increasingly practical. The development of FHE is currently transitioning from theoretical research to practical applications, with significant progress expected in the next three to five years.

Conclusion

Fully Homomorphic Encryption (FHE) is on the cusp of revolutionary change in the encryption field, providing advanced privacy and security solutions. With ongoing advancements and increasing attention from venture capital, FHE is poised for widespread adoption, addressing key issues of blockchain scalability and privacy protection. As the technology matures, it is expected to unlock new possibilities and drive innovation in various applications within the crypto ecosystem.

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