Fully Homomorphic Encryption: A Game Changer for Data Privacy and Security

Fully Homomorphic Encryption (FHE) represents a groundbreaking development in cryptography. This encryption method enables operations to be performed on encrypted data without the necessity for decryption. The distinctive feature of FHE opens up vast possibilities for safeguarding data privacy and executing secure computations, especially in the era of cloud technology and big data.

Introduction to Fully Homomorphic Encryption

The concept of Homomorphic Encryption (HE) is not novel and traces its origins back to the 1970s. However, the initial versions of HE were only partially homomorphic, implying they could execute either addition or multiplication operations, but not both. This constraint limited the complexity of computations that could be conducted on encrypted data.

In 2009, a significant shift in the field of cryptography occurred when Craig Gentry, a doctoral student at Stanford University, introduced the first fully homomorphic encryption scheme. FHE can carry out an unlimited number of addition and multiplication operations on encrypted data, facilitating complex computations while preserving the confidentiality of the data.

How Fully Homomorphic Encryption Works

Fully Homomorphic Encryption (FHE) enables the execution of calculations on encrypted data, without the need to decrypt it beforehand.

For example, suppose you have two numbers, 5 and 3, and you want to add them together, but you want the numbers to remain private. You put each number in its locked box (encrypt them), so you now have two locked boxes.

With FHE, you can add these locked boxes together, and you’ll get a new locked box. When you open this new box (decrypt), you find the number 8 inside, which is the result of adding 5 and 3. Throughout this process, the numbers 5 and 3 were always hidden in their locked boxes, maintaining their privacy.

Simplified Example Using Mathematical Equations

For the purpose of understanding:

· E(m): This is the encryption function that encrypts a plaintext message, m.

· D(c): This is the decryption function that decrypts a ciphertext, c.

· ⊕: This signifies the operation of addition.

· ⊗: This signifies the operation of multiplication.

A fully homomorphic encryption scheme, for any plaintext messages m1 and m2 and their corresponding ciphertexts c1 = E(m1) and c2 = E(m2), fulfils the following characteristics:

Homomorphic Addition Property: D(c1 ⊕ c2) = m1 + m2. This indicates that the decryption of the addition of c1 and c2 is equal to the addition of m1 and m2.

Homomorphic Multiplication Property: D(c1 ⊗ c2) = m1 × m2. This implies that the decryption of the multiplication of c1 and c2 is equal to the multiplication of m1 and m2.

These properties suggest that we can perform addition and multiplication operations directly on the ciphertexts, and when we decrypt the result, we get the same outcome as if we had performed the operations on the plaintexts.

To achieve FHE, these properties must be fulfilled even when operations are executed on encrypted data. The encryption scheme is devised in a way that carrying out operations on ciphertexts generates valid ciphertexts that represent the result of the operations on the plaintexts.

In practice, FHE schemes utilise sophisticated mathematical structures such as lattice-based cryptography or number theory to attain these properties while preserving security. Nonetheless, the core principle is to ensure that operations on ciphertexts mimic the operations on plaintexts, enabling calculations to be performed securely on encrypted data.

The Evolution of Homomorphic Encryption

Homomorphic encryption has evolved through various generations, each marked by distinct advancements and techniques. The quest for a fully homomorphic encryption (FHE) scheme began in 1978, soon after the RSA scheme emerged. Over three decades, researchers explored partial solutions, including schemes based on RSA, ElGamal, Goldwasser-Micali, and others. Craig Gentry’s breakthrough in 2009 using lattice-based cryptography marked the beginning of the first-generation FHE.

Gentry’s lattice-based scheme allowed computations on encrypted data, overcoming the limitations of earlier schemes. By modifying somewhat homomorphic encryption to be bootstrappable, Gentry achieved fully homomorphic encryption. His approach relied on ideal lattices and posed security on specific lattice problems. Subsequent refinements and implementations improved performance significantly.

Building upon Gentry’s work, second-generation schemes emerged in 2011–2012. These schemes, like BGV, LTV, and BFV, relied on Ring Learning With Errors (RLWE) problem for security. They featured slower noise growth during computations and optimisations for efficiency, enabling practical applications without frequent bootstrapping.

A breakthrough in 2013 introduced techniques, like the GSW cryptosystem, that minimised noise growth, enhancing efficiency and security further. Efficient bootstrapping methods, exemplified by FHEW and TFHE, reduced computational overhead significantly.

CKKS, proposed in 2016, introduced approximate homomorphic encryption suitable for machine learning applications. It employed block floating point arithmetic and efficient rescaling, eliminating the need for bootstrapping after each multiplication. However, it introduced certain approximation errors that require careful handling.

Key Concepts and Operations

Understanding the key concepts and operations of fully homomorphic encryption is essential for harnessing its potential and leveraging its capabilities effectively. Let’s explore these concepts and operations.

1. Key Generation: In FHE, this is the initial step where a pair of public and private keys is created using complex mathematical formulas to ensure security. The public key encrypts data, while the private key decrypts it, ensuring data integrity. Securing the private key’s confidentiality and randomness is crucial for the encryption system’s safety.
2. Encryption: The encryption phase involves transforming raw data into encrypted data using a public key. For FHE, two key characteristics are essential. First, correctness ensures that encrypted data can be decrypted back to its original form with the corresponding private key. Second, indistinguishability ensures that the encrypted data appears as random noise, thwarting potential attackers from extracting meaningful information. This process typically entails mathematical operations like modular arithmetic or polynomial manipulation, tailored to the cryptographic framework employed in the FHE system.
3. Evaluation Circuit: The evaluation circuit is a crucial component within FHE, which defines computations achievable on encrypted data without decryption. It comprises operations, often in a Boolean circuit format, operating directly on encrypted data. This circuit incorporates mathematical functions like addition, multiplication, comparison, and logical operations, safeguarding data confidentiality during computation. Its adaptability dictates the range of secure computations possible on encrypted data, with advanced FHE systems capable of executing intricate circuits to mimic diverse functions securely.
4. Decryption: This is the final step in FHE, where encrypted data undergoes conversion back to its original form using a private key. Only those possessing the correct private key can decrypt and retrieve the original data. The decryption process must effectively reverse the encryption to ensure identical data recovery, as any errors could compromise computation accuracy. FHE’s security depends on a robust decryption process and safeguarding the confidentiality of the private key, as unauthorised access could lead to decryption and exposure of sensitive information.

How Fully Homomorphic Encryption Applies to Blockchain

Fully homomorphic encryption holds immense potential for blockchain technology. It offers a groundbreaking solution to manage privacy and confidentiality concerns without sacrificing the transparency and integrity that are fundamental to blockchain systems. Here’s how FHE can be utilised in the blockchain space:

• Augmented Data Privacy: FHE allows computations to be performed on encrypted data, enabling blockchain participants to manipulate sensitive information without revealing it to the network. In blockchain transactions, FHE can be used to conceal transaction details like transaction amounts, addresses of senders and receivers, and inputs for smart contracts, ensuring that only those with permission can access the unencrypted data.
• Safe Smart Contracts: Smart contracts are fundamental to blockchain systems and often require computations on confidential data. FHE facilitates these computations while maintaining data privacy. With FHE, smart contracts can operate using encrypted inputs, preserving the confidentiality of important information throughout the execution process. This functionality broadens the use of blockchain technology across various sectors, including finance, healthcare, and supply chain management.
• Private Computing: FHE enables private computing within blockchain networks by processing encrypted data while maintaining its confidentiality. This function is especially useful in situations where multiple parties need to cooperate and analyse confidential data without exposing it to unauthorised individuals. Blockchain platforms that use FHE can provide a secure and transparent environment for confidential data sharing and analysis, promoting collaboration and innovation across industries.
• Private Voting: FHE enables computations on encrypted data without decryption. This is ideal for blockchain-based private voting, where votes can be encrypted, stored, and tallied without revealing individual choices. This makes encrypted voting systems possible where votes stay secret throughout the counting process.
• Trustless Gaming: FHE enables trustless gaming by allowing players to submit encrypted bets or moves, which are processed on-chain without revealing private data. This opens new possibilities for blockchain applications like private auctions and prediction markets that demand confidentiality.
• Data Sharing and Collaboration: FHE facilitates secure and privacy-preserving data sharing and collaboration in blockchain ecosystems where multiple stakeholders contribute and access data. Participants can encrypt their data before sharing it on the blockchain, ensuring that confidential information remains private even when shared with other network participants. This fosters trust and transparency among stakeholders while protecting sensitive data from unauthorised access and misuse.
• Regulatory Compliance: FHE provides a strong mechanism for ensuring regulatory compliance within blockchain networks, especially in industries with strict data privacy requirements such as finance and healthcare. By using FHE to encrypt sensitive data stored on the blockchain, organisations can show compliance with data protection regulations without undermining the transparency and unchangeability of the underlying blockchain infrastructure.

Fully Homomorphic Encryption projects in blockchain

FHE has the potential to enhance privacy in DeFi transactions significantly. Several innovative projects are already leveraging this technology. For instance, ZAMA offers promising advancements in facilitating the creation of private smart contracts.

1. ZAMA: Zama’s Fully Homomorphic Encryption Virtual Machine (fhEVM) is a ground-breaking innovation that aims to transform the Ethereum-compatible blockchain landscape by harnessing the capabilities of Fully Homomorphic Encryption (FHE). Its primary goal is to facilitate the creation of private smart contracts — an impressive Advancement that guarantees both data privacy and operation composability. Through the deployment of fhEVM, developers gain access to a sturdy platform to build smart contracts that can process encrypted data. This vital attribute not only heightens the safety of data transfers but also preserves the privacy of critical information, substantially diminishing the likelihood of data exposure and unauthorized data access.
2. FHENIX: This is the first confidential Layer 2 that leverages the power of Fully Homomorphic Encryption (FHE). It utilises fhEVM, an extended version of the Ethereum Virtual Machine (EVM), which provides developers with the ability to effortlessly incorporate FHE into their workflows and construct encrypted smart contracts, even without extensive knowledge of cryptography. Consequently, Fhenix allows Ethereum developers to smoothly construct encrypted smart contracts and carry out encrypted data computations using familiar and user-friendly tools such as Solidity.
3. PENUMBRA: This is a secure, cross-chain network within the Cosmos ecosystem. It allows users to transact, stake, and swap assets without revealing personal information. Utilising innovative features like private proof-of-stake and private transactions it ensures privacy. Penumbra connects to Cosmos via IBC, serving as a shielded pool for private transactions in any IBC-compatible asset. It also includes ZSwap, a private decentralised exchange supporting sealed-bid batch auctions and concentrated liquidity to prevent front-running and enhance execution while maintaining user privacy. Additionally, Penumbra utilises fully homomorphic encryption to ensure network privacy and security. This encryption technology enables computations on encrypted data without decryption, securing sensitive information and enhancing the confidentiality of transactions and operations within the network.
4. Inco: The Inco project is a blockchain platform that serves as a Layer-1 solution on the Ethereum network. It is specifically designed to prioritise confidential computing and enhanced privacy for both developers and users. By providing a seamless, privacy-centric environment, Inco facilitates the creation of innovative decentralised applications (dApps) in sectors such as gaming, DeFi, payments, governance, and identity. Notably, Inco integrates FHE into its blockchain network, enabling on-chain data to remain confidential while still being auditable. This integration effectively tackles the challenge of achieving trustless confidentiality within the blockchain industry.
5. PRIVASEA: The Privasea project is a decentralised AI network that uses Fully Homomorphic Encryption (FHE) to tackle data privacy issues in artificial intelligence. By employing FHE, Privasea enables computations on encrypted data, safeguarding confidentiality from model training to evaluation. It prioritizes data privacy and security throughout the AI computation process. Privasea has created the HESea homomorphic library to simplify FHE usage and is conducting theoretical research on FHE algorithm design and application. Additionally, the project aims to enhance existing algorithms by addressing challenges such as the computational complexity of nonlinear functions.
6. FAIR MATH: This is a research company with an open-source and community-oriented approach, dedicated to addressing privacy challenges in the modern world. Their focus lies in developing privacy-preserving technologies rooted in Fully Homomorphic Encryption. The core objective of Fair Math is to promote the adoption of Fully Homomorphic Encryption (FHE) by building a developer community and toolset that significantly simplifies the development of FHE applications. The team consists of cryptographic and decentralisation enthusiasts who developed the modern Zero-Knowledge Proof (ZKP) toolsets and libraries for the Web3 community.
7. SherLOCKED: The sherLOCKED project is a privacy-focused project that leverages FHE to enable secure data processing without compromising confidentiality. This project utilizes FHE to perform computations directly on encrypted data, ensuring that sensitive information remains protected throughout the analysis process. By employing FHE, the sherLOCKED project allows for complex mathematical operations to be executed on encrypted data, maintaining privacy and security. This approach ensures that data can be securely analysed and processed without the need to decrypt it, thus preserving confidentiality while enabling valuable insights to be derived from the encrypted information.
8. ZkHOLDEM: zkHoldem applies a combination of ZK and FHE technology to build an Hold’em on chain game. A Hold’em game is traditionally a poker variation where players use two cards face down, called “hole cards”, and three community cards face up to create the best five-card hand. The game is played with a standard 52-card deck and two to ten players. The dealer deals two cards face down to each player, and then three community cards face up in the middle of the table. The game is divided into four rounds of betting, with the player with the best hand at the end of the final betting round winning the pot. In a nutshell, zkHoldem combines the thrill of Texas Hold’em with the security and fairness of blockchain using the ZKP and FHE technologies, making it an exciting addition to the crypto gaming landscape.
9. FRAMED: This is a blockchain-based game where players engage in a virtual art heist, taking on secret roles as citizens, thieves, cops, or detectives. Roles are encrypted and stored on the blockchain for privacy. FRAMED has set itself apart by integrating Fully Homomorphic Encryption (FHE) to maintain on-chain privacy, allowing players to immerse themselves in a world of hidden roles and covert operations. In the Framed Game, players find themselves in a gripping scenario where an art thief has stolen a precious painting. Each player is randomly assigned a role — citizen, thief, cop, or detective — with their identity securely encrypted and stored on the blockchain. The thief’s goal is to systematically eliminate the citizens, while the citizens’ objective is to deduce who among them is the thief and vote them out. This creates a dynamic environment of discussion, strategy, and deception.

Fully Homomorphic Encryption Blockchain Limitation

While the potential advantages of FHE in blockchain environments are considerable, its broad implementation is hindered by several challenges. These include the computational burden, the intricacies of managing keys, and the compatibility with established blockchain protocols.

• Performance Overhead: The significant computational complexity of homomorphic operations and noise management techniques can lead to substantial performance overhead in Fully Homomorphic Encryption schemes. Efforts to enhance efficiency via algorithmic improvements, parallel processing, and hardware acceleration continue to be a focal point of research.
• Key Management and Distribution: The security of Fully Homomorphic Encryption systems hinges on the efficient management and distribution of keys. Safeguarding keys, preventing key compromise, and facilitating efficient key distribution mechanisms are all significant hurdles, especially in deployments on a large scale.
• Noise Accumulation and Bootstrapping: It is important to manage noise accumulation during homomorphic operations to maintain the accuracy and security of computation results. Bootstrapping methods introduce additional computational overhead and may restrict the depth of computation that can be conducted efficiently.
• Scalability: Scalability is a critical factor for implementing Fully Homomorphic Encryption in practical situations involving large data sets and intricate computations. Efficient algorithms and optimisations are necessary to address scalability issues and ensure satisfactory performance in real-world applications.

To overcome these hurdles, a joint effort from scholars, programmers, and industry participants is necessary to refine FHE applications and ensure their smooth integration into blockchain systems.

Future Directions and Research Opportunities

Future research in FHE is poised to enhance efficiency and performance through various avenues, including algorithmic enhancements, hardware acceleration, and advancements in cryptographic practices. This encompasses refining methods for key generation, encryption, and evaluation to enable more practical deployment of FHE in resource-constrained environments.

Efforts towards standardisation are pivotal for fostering cross-compatibility and wider adoption of FHE across diverse platforms and applications. Establishing standard protocols, algorithms, and security benchmarks will streamline integration and ensure interoperability between FHE implementations offered by different providers.

Moreover, adapting FHE solutions to specific sectors, such as healthcare, finance, and secure communication, holds promise for driving innovation and widespread adoption.

Final Words

Fully Homomorphic Encryption (FHE) stands as a powerful cryptographic mechanism that allows the execution of secure computations on encrypted data, transforming how sensitive data is processed and scrutinized while maintaining privacy and confidentiality. By comprehending the essential concepts and operations of FHE, organisations can utilise its capabilities to tackle intricate security and privacy issues in this digital era. Furthermore, FHE offers an appealing resolution for improving data privacy, security, and confidentiality within the blockchain technology ecosystem. By facilitating safe computational procedures on encrypted data, FHE equips blockchain networks to explore new applications and use cases while ensuring adherence to regulatory mandates and protecting confidential information from unauthorised access.

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