Fully Homomorphic Encryption (FHE): A Beginner's Guide

In today's digital age, data privacy is paramount. As we communicate and store information online, our personal and sensitive data must remain secure. Encryption has long been a cornerstone of data protection, ensuring that our emails and databases are safeguarded. However, encryption has traditionally posed a challenge when it comes to processing data. Decrypting data for computation often compromises its privacy. But what if we could perform computations on encrypted data without ever decrypting it?

I. Fully Homomorphic Encryption (FHE)

What is FHE?

Fully Homomorphic Encryption (FHE) is a revolutionary cryptographic technology that enables computation over encrypted data. Unlike traditional encryption methods, FHE allows for complex operations to be performed on encrypted data without ever needing to decrypt it. This means that sensitive data can remain encrypted throughout the entire computation process, significantly enhancing privacy and security.

FHE allows computation over encrypted data

The Significance of FHE

The significance of FHE cannot be overstated. It represents a monumental shift in the way we think about data privacy and security. With FHE, data can be processed and analyzed without ever needing to be decrypted, ensuring that sensitive information remains private and secure. This has far-reaching implications for a wide range of industries, from finance and healthcare to government and beyond.

Historical Context

The concept of FHE has been around for decades, but it wasn't until 2009 that Craig Gentry proposed the first practical FHE scheme. His breakthrough solution addressed the challenge of noise accumulation in encrypted data, paving the way for the development of fully homomorphic encryption as we know it today.

Basic Components and Operations

FHE shares many fundamental components with traditional cryptography, including encryption, decryption, and key generation. However, it also introduces new concepts and operations that enable computation over encrypted data. These operations include arithmetic operations such as addition and multiplication on ciphertexts, as well as more complex operations like bootstrapping, which is used to recursively evaluate the decryption circuit to reduce and manage noise accumulation.

If you interested in FHE. We had an article that express more on Privacy by Design: Programmable Cryptography's Next Steps

II. Categories of Homomorphic Encryption

Homomorphic encryption comes in various categories, each with its own set of capabilities and limitations. Understanding these categories is crucial for selecting the right type of encryption for a given application.

Partially Homomorphic Encryption

Partially homomorphic encryption enables only one type of operation, either addition or multiplication. This means that you can perform either addition or multiplication operations on encrypted data, but not both.

Somewhat Homomorphic Encryption

Somewhat homomorphic encryption is limited for one operation but unlimited for the other. For example, it may be limited in the number of multiplications it can perform but unlimited in the number of additions.

Leveled Homomorphic Encryption

Leveled homomorphic encryption is limited in the number of operations it can perform for both addition and multiplication.

Fully Homomorphic Encryption

Fully homomorphic encryption is the most powerful type of homomorphic encryption, allowing for unlimited operations for both addition and multiplication, as well as other operations. This means that you can perform any computation on encrypted data without ever needing to decrypt it.

Each type of homomorphic encryption has its own set of trade-offs in terms of performance, security, and usability. It is important to carefully consider these trade-offs when selecting the right type of encryption for a given application.

ZKPs

III. Applications and Use Cases of FHE

Fully Homomorphic Encryption (FHE) has a wide range of applications and use cases across various industries. Below are some examples of how FHE can be used to enhance privacy and security in different contexts.

Private Inference & Training

FHE can be used to protect the privacy of both the model and data in machine learning and AI applications. By performing computations on encrypted data, FHE enables private inference and training, ensuring that sensitive information remains private throughout the entire process.

Encrypted Searches (PIR)

FHE can be used to perform encrypted searches, also known as Private Information Retrieval (PIR). This allows users to query an encrypted file and only see the result of their specific query without revealing the entire contents of the database.

Policy Compliance & Identity Management

FHE can be used to enable secure identity management by allowing the processing of identity-related data without exposing sensitive information. This enables organizations to comply with regulators' Know Your Customer (KYC) policies while maintaining data privacy.

Blockchain Use Cases

FHE has significant implications for blockchain technology, offering solutions for private transactions, Maximal Extractable Value (MEV) mitigation, scaling, and private blockchains. For example, FHE can be used to perform encrypted computations within a trustless environment, enabling private transactions and smart contracts while maintaining data privacy.

These are just a few examples of the many applications and use cases of FHE. As research and development in FHE continue to progress, we can expect to see even more innovative applications emerge, reshaping the way we think about data privacy and security in the digital age.

IV. FHE in Context: ZKP, MPC, & FHE

In the realm of programmable cryptography, Fully Homomorphic Encryption (FHE) stands alongside Zero-Knowledge Proofs (ZKPs) and Multi-Party Computation (MPC) as a crucial tool in the quest for data privacy and security. Here, we explore how these three cryptographic primitives interrelate and their respective roles in securing digital transactions and communications.

Overview and Comparison of ZKPs, MPC, and FHE

- Zero-Knowledge Proofs (ZKPs): These are cryptographic methods that allow one party (the prover) to prove to another party (the verifier) that they know a certain piece of information without revealing the actual information itself. This is done by providing a proof that the information satisfies a certain property, without revealing the information itself.

- Multi-Party Computation (MPC): This is a cryptographic technique that allows a group of mutually distrusting parties to compute a joint function over their inputs while keeping their individual inputs private from each other. This is achieved by dividing the computation into smaller pieces, each of which is performed by a different party, and then combining the results to obtain the final result.

- Fully Homomorphic Encryption (FHE): This is a cryptographic technique that allows computations to be performed on encrypted data without needing to decrypt the data first. This allows for secure and private processing of sensitive data, even when the data is stored in an encrypted form.

ZKPs, MPC, FHE, computation costs and interactiveness

Real-World Applications and Use Cases

In Web 3.0 applications, the integration of ZKPs alongside FHE becomes crucial for constructing private and secure systems. ZKPs are vital because they can be used to generate proofs of correctly constructed FHE ciphertexts. Otherwise, users can encrypt any unverified gibberish, corrupting the entire FHE circuit evaluation.

Connection to Blockchain Technology

FHE has significant implications for blockchain technology, offering solutions for private transactions, MEV mitigation, scaling, and private blockchains. For example, FHE can be used to perform encrypted computations within a trustless environment, enabling private transactions and smart contracts while maintaining data privacy.

These cryptographic primitives, when used together, can create powerful and secure systems that protect the privacy and security of digital transactions and communications. As research and development in these areas continue to progress, we can expect to see even more innovative applications emerge, reshaping the way we think about data privacy and security in the digital age.

V. The State of FHE Today and Future Prospects

Fully Homomorphic Encryption (FHE) has come a long way since its inception, but it still faces various challenges and limitations. Here, we delve into the current state of FHE, its ongoing research and development efforts, and the future prospects of this revolutionary technology.

Historical Development and Breakthroughs

Early concepts of FHE in the 1970s-90s laid the theoretical groundwork for homomorphic encryption. However, the real breakthrough came with Craig Gentry's solution in 2009. His scheme was the first practical FHE implementation that addressed the challenge of noise accumulation in encrypted data, making FHE a practical reality.

Performance Improvements and Challenges

Performance improvements have been focused on refining schemes, reducing computation complexity, faster bootstrapping, and hardware acceleration. However, there are still challenges, such as the size of ciphertexts and the cost of computation on-chain. For example, operations on encrypted integers are much more difficult to perform than on plaintext integers.

Implementation Examples

Several projects are actively working on FHE implementations. Zama's fhEVM, Sunscreen, and Fhenix are some examples. However, there are still limitations and challenges with these implementations, such as limited transaction throughput and the difficulty of operating on encrypted values.

Limitations and Future Prospects

There are limitations to FHE, such as network and computation costs, as well as the difficulty of operating on encrypted values. However, with ongoing research and development, FHE is expected to become more usable and scalable in the future. For example, FHE is not yet possible with Ethereum due to the size of ciphertexts and the cost of computation on-chain. However, with the current rate of hardware acceleration, we may see applications in production by 2025.

Conclusion

Fully Homomorphic Encryption (FHE) is a revolutionary technology that promises to transform data privacy. With its ability to perform computations on encrypted data, FHE opens up new possibilities for secure and private data processing. As research and development in FHE continue to progress, we can expect to see even more innovative applications and use cases emerge, reshaping the way we think about data privacy in the digital age.

This article is refer to and simplify concepts from a variety of sources, including from [Zero to Start: Applied Fully Homomorphic Encryption (FHE) Part 1, Part 2] from original author [0xZoey]. If there are objections to this article, please contact the Orochi Network team

About Orochi Network

Orochi Network is a cutting-edge zkOS (An operating system based on zero-knowledge proof) designed to tackle the challenges of computation limitation, data correctness, and data availability in the Web3 industry. With the well-rounded solutions for Web3 Applications, Orochi Network omits the current performance-related barriers and makes ways for more comprehensive dApps hence, becoming the backbone of Web3's infrastructure landscape.

Blog