Why is "Fully Homomorphic Encryption (FHE)" the holy grail of encryption schemes?

What are Homomorphic and Fully Homomorphic Encryption?

If you look directly at Portal Ventures' original text, you might find the complex mathematical descriptions of fully homomorphic encryption (FHE) confusing.

In fact, the world of cryptography is filled with profundity and technicality, but we can explain these concepts in a simple and accessible way. In this section, I will attempt to provide you with some more intuitive and easier-to-understand examples to help you gain a deeper understanding of fully homomorphic encryption.

First, imagine a "secret magic box." You can put any item into this box and lock it. Once locked, you cannot see or touch the contents inside the box. However, surprisingly, this magic box allows you to change the color or shape of the items inside without opening it.

As shown in the image above, fully homomorphic encryption (FHE) can be viewed as a magic box:

Your Envelope: This represents the original data you want to encrypt.
Magic Box Operation: Even without decrypting or opening the envelope, you can perform operations (such as addition, subtraction, etc.) on the data inside the envelope.
New Envelope: After the magic box operation, you will get a new encrypted result.

This is the basic idea of homomorphic encryption: the ability to operate on encrypted data without knowing the data itself.

This simple example helps clarify what "fully homomorphic encryption" is doing. But in reality, the concept itself can still be a bit elusive. So, what do we mean by "fully" and "homomorphic"?

What does "Fully" mean?

In cryptography, encryption schemes can support various operations, such as addition, multiplication, etc. When we say an encryption scheme is "fully homomorphic," we mean that this encryption scheme supports performing any number of basic operations (such as addition and multiplication) on encrypted data without needing to decrypt it. This contrasts with partially homomorphic encryption (such as schemes that only support addition or only support multiplication).

What does "Homomorphic" mean?

"Homomorphic" comes from Greek, meaning "same shape or structure." In cryptography, when we say an encryption scheme is homomorphic, it means that certain operations have the same effect on plaintext as they do on ciphertext. In other words, if you perform a certain operation on encrypted data and then decrypt the result, it is equivalent to first decrypting the data and then performing the same operation on the decrypted data.

For example, consider an encryption scheme that supports homomorphic addition. Suppose you have two numbers: 3 and 4. You can encrypt these two numbers first, and then use this homomorphic encryption scheme to add the two encrypted numbers. Finally, you decrypt the summed result. The decrypted result will be 7, which is the same as the result you would get by directly adding the plaintext 3 and 4.

However, you might ask, how do we perform these addition and subtraction operations on non-numeric data? In fact, we can use specific encoding methods to convert non-numeric data into numerical forms, allowing us to perform operations like addition and multiplication on them. This means that the application of fully homomorphic encryption is not limited to mathematical calculations; it can also be widely applied in other fields.

To explain this concept more intuitively, let’s consider an example involving medical data.

Suppose a hospital has some patient data, such as age and blood sugar levels, but does not want to send it directly to a cloud service provider for analysis due to privacy concerns.
By using fully homomorphic encryption, the hospital can first encrypt this data.
Imagine that the cloud service provider needs to calculate the average age of all patients (which requires addition and division) and the total blood sugar levels multiplied by the number of patients (which involves addition and multiplication).
All these calculations can be performed on the encrypted data without needing to decrypt it. The cloud service provider completes the calculations without decrypting the data and then returns the encrypted results to the hospital. This ensures data privacy while also meeting data processing needs.

This is the charm of fully homomorphic encryption; it provides us with a secure and flexible method for data processing.

Why is FHE Important?

Currently, existing methods for computing on encrypted data are not ideal. They are relatively expensive in terms of resource usage and time consumption.

As a result, the industry standard process is for a third party (i.e., a company) to decrypt the data before performing computations.

For a concrete example, imagine you have a data file containing financial information about some high-profile individuals.

We call this file "M." We need a company to analyze this data.
What is the current process? First, I use an encryption function like RSA or AES to encrypt M. At this point, M becomes E(M), where E is the encryption function.
Next, I send E(M) to the company server. The company now decrypts E(M) to plaintext using the relevant decryption function D, resulting in D(M).
The company directly analyzes the plaintext file M.
After the operation, it encrypts M again, generating E(M').
The company then sends the encrypted M' back to me, and I decrypt it again.

Notice that the key issue here is that when the company decrypts M and stores it on its server for computation, the third party can access sensitive data that should have been protected. If that party is hacked or has malicious intent, it could lead to problems.

Fully homomorphic encryption (FHE) addresses this issue by allowing computations to be performed on encrypted data. The company no longer needs to decrypt E(M). It performs the analysis directly on the encrypted data. There is no need for decryption, nor is there a trust assumption.

In summary, the introduction of fully homomorphic encryption solves a key problem in the current data processing workflow: the privacy risks that may be exposed when third parties handle data. FHE provides us with an effective way to process encrypted data while ensuring data privacy.

How is FHE Applied in Crypto?

Fully homomorphic encryption (FHE) opens a new door in the world of encryption, bringing us many previously unimaginable application scenarios. The original text from Poly Venture describes the scenarios rather simply, so we attempt to present a more organized interpretation in a table.

FHE vs ZK vs MPC, What's the Difference?

After understanding fully homomorphic encryption (FHE), it is easy to compare it with other familiar technologies, such as zero-knowledge proofs (ZK) and secure multi-party computation (MPC). At first glance, they all seem to address similar privacy and computation issues. But what are the actual connections and differences among these three?

First, let’s understand the basic definitions of these three technologies:

FHE: Allows computations to be performed on encrypted data without decryption.
ZK: Allows one party to prove to another that a statement is true without revealing any specific information about that statement.
MPC: Enables multiple parties to jointly compute on their private data without revealing their input data to other participants.

Now, let’s look at their similarities and differences from multiple dimensions:

Purpose:

The main purpose of FHE is to perform computations without decryption.
The goal of ZK is to prove the correctness of a fact without disclosing any information about that fact.
The aim of MPC is to allow multiple parties to compute securely together without revealing their respective inputs.

Privacy and Computation:

In ZK, computations are not necessarily private. For example, while you can use ZK to verify whether a bank account balance exceeds $100,000, the computation involved in such verification is not necessarily private.
In contrast, FHE ensures the privacy of computations since all computations are performed on encrypted data.

Limitations and Challenges:

MPC requires at least one honest server and may be susceptible to DDoS attacks, silent collusion attacks, and communication overhead.
ZK is primarily used for proving correctness rather than as a privacy technology.
FHE, while providing strong privacy, has lower computational efficiency and higher resource demands.

Applications in the Crypto Space:

FHE can be used to build more private smart contracts and other blockchain applications.
ZK is used to create scalable blockchain solutions, such as zk-rollups.
MPC is mainly used for private key management and custody.

Cross-Usage:

MPC can be combined with FHE to form threshold FHE by splitting an FHE encryption key into multiple parts and giving each participant one to enhance security.
zkFHE is a combination of zero-knowledge proofs and fully homomorphic encryption, which is being researched to achieve zk-rollups on FHE smart contracts.

Overall, while FHE, ZK, and MPC overlap in some areas, each has its unique advantages and application scenarios. In the world of encryption, these three technologies offer tremendous potential for enhancing privacy and security, but their combination and further research remain an active area in the crypto community.

Finally, we can also provide a streamlined comparison table to help everyone understand these technologies more intuitively.

Future Prospects of FHE

From the above text, it is clear that fully homomorphic encryption (FHE) is undoubtedly a powerful technology.

But why has it not been widely adopted, and why is it rarely mentioned even in crypto CT? On one hand, there is a certain threshold to understanding the technology itself; on the other hand, FHE currently faces some challenges that make it difficult to easily enter the public eye in a commercial form.

The challenges may include:

Computationally Intensive: When our ciphertexts interact, more noise is added to maintain security. FHE schemes use "bootstrapping" techniques to reduce noise, but this is very computationally intensive and resource-consuming.
Limited Functionality: FHE computations are limited to addition, multiplication, and their variants/combinations. For example, if statements cannot be used in FHE because the content is encrypted. Additionally, constructing relatively complex operations, such as comparisons and divisions, requires careful planning of basic logic, leading to more complex programming skills and lower computational efficiency.
Compatibility/Integrability Issues: Existing applications and service providers are not built to compute on encrypted data. This limits the integration of FHE with existing technologies and increases the inertia required to develop FHE-compatible applications.

Possible solutions:

Hardware Accelerators: Some FHE schemes, such as nuFHE and cuFHE, can use GPU acceleration, but major breakthroughs will come from faster FPGAs and ASICs. Other technologies, such as photonic technology, are also being researched to accelerate FHE hardware use cases.
New Programming Paradigms: Just as packages like pandas and numpy are used for complex mathematics in Python, FHE libraries will also be built. Currently, Zama and Sunscreen are two projects building such libraries and SDKs for FHE. Additionally, dedicated compilers need to be developed to enable developers to unify FHE, ZKP, and MPC.
Integration between FHE and Existing Solutions: Solutions will be built to make existing tools compatible with FHE, serving as an intermediary layer between tools and FHE encrypted data.

Finally, Portal Ventures reiterates in the conclusion of the original text:

"FHE is the holy grail of computation, and we are approaching its commercialization. Value and computation are transitioning to an open, permissionless network, and we believe FHE will support most of the necessary infrastructure and applications."

Moreover, they expressed interest in projects currently researching FHE. Therefore, we can see that VCs are interested in FHE, or rather, VCs tend to be the first to show interest in hardcore technologies that have not yet entered the public eye.

History shows that crypto projects based on new technologies often carry a shiny halo and high valuations, attracting attention from various capital sources.

Before the next feast begins, we should indeed spend more time researching the identities of the guests in advance so that we can respond smoothly when the banquet starts.

FHE Ecosystem News and Research

FHE is a hot topic in the encryption community recently. FHE has ideal privacy protection capabilities, but its performance still has gaps. With the entry of Crypto capital, it will greatly accelerate the development and maturity of the technology, just like the rapid development of ZK in recent years.

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