FHE is the holy grail of computation, and the value and computation are transitioning to open and permissionless networks. FHE will support most of the required infrastructure and applications.

As the market remains quiet in the bear market, investors and project parties will always start looking for new growth points.

In the absence of sustained hotspots, it is an excellent opportunity to explore and understand new technologies in depth, as new technologies may become the core of the next market narrative.

Last month, the well-known crypto venture capital firm Portal Ventures published a detailed article on the technology of Fully Homomorphic Encryption (FHE) on its official blog. However, this in-depth technical article does not seem to have attracted widespread attention.

The authors at Portal Ventures said: "Fully Homomorphic Encryption is the holy grail of encryption schemes."

Understanding the technologies that VCs are focusing on is crucial for investors, as it can help us predict and understand potential trends in the next market cycle. In fact, technologies such as homomorphic encryption, zero-knowledge proofs, and secure multiparty computation have profound implications in the field of cryptography, especially fully homomorphic encryption, which may have huge potential applications in the cryptocurrency and web3 domains.

However, the problem is that most people know very little about the true meaning of fully homomorphic encryption, how it works, and how it differs from other technologies. In a sluggish market with low investment sentiment, it is undoubtedly a wise choice to step out of the hype and delve into the research and understanding of these cutting-edge technologies.

Coincidentally, several years ago, I had the opportunity to work with FHE-related technology solutions. Therefore, I decided to provide an in-depth interpretation of this article by Portal Ventures, hoping to offer some new perspectives and insights to everyone.

What are Homomorphic and Fully Homomorphic Encryption?

If you were to read the original article by Portal Ventures directly, you might find the complex mathematical descriptions of Fully Homomorphic Encryption (FHE) confusing.

In fact, the world of cryptography is full of profound and technical aspects, but we can completely explain these concepts in a simple and popular way. In this section, I will try to provide you with some more intuitive and easy-to-understand examples to help you understand fully homomorphic encryption.

First, imagine a "magic box." You can put any item into this box and lock it. Once locked, you cannot see or touch the contents of 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 above image, Fully Homomorphic Encryption (FHE) can be seen as a magic box:

1. Your Envelope: This represents the original data you want to encrypt.
2. 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.
3. New Envelope: After the magic box operation, you will get a new encrypted result.

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

This popular example helps to understand what "fully homomorphic encryption" is doing. However, in reality, this concept itself is still a bit hard to grasp with just one explanation. So, what does "fully" and "homomorphic" mean?

1. 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 any number of basic operations (such as addition and multiplication) on encrypted data without the need for decryption. This contrasts with partially homomorphic encryption (such as schemes that only support addition or only support multiplication).

1. What does "homomorphic" mean?

• "Homomorphic" comes from Greek, meaning "the same shape or structure." In cryptography, when we say an encryption scheme is homomorphic, it means that some operations on plaintext have the same effect as on ciphertext. In other words, if you perform a certain operation on encrypted data and then decrypt the result, it is equivalent to 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, then use this homomorphic encryption scheme to add the two encrypted numbers. Finally, you decrypt the result of the addition. The decrypted result will be 7, which is the same as the result you would get by directly adding the plaintext 3 and 4.

But you may ask, how do we perform these addition, subtraction, multiplication, and division operations on non-numeric data? In fact, we can use specific encoding methods to convert non-numeric data into numeric form, allowing us to perform addition, multiplication, and other operations 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 of medical data.

1. Suppose a hospital has some patient data, such as age and blood sugar levels, but for privacy reasons, they do not want to send this data directly to a cloud service provider for analysis.
2. By using fully homomorphic encryption, the hospital can first encrypt this data.
3. Imagine that the cloud service provider needs to calculate the average age of all patients (which requires addition and division) and the sum of blood sugar levels multiplied by the number of patients (involving addition and multiplication).
4. All these calculations can be performed on the encrypted data without the need for decryption. The cloud service provider completes the calculations without decrypting the data, then returns the encrypted results to the hospital. This ensures data privacy while meeting the data processing needs.

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

Why is FHE Important?

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

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

To illustrate with a specific example, imagine you have a data file containing financial information of 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's server. The company then decrypts E(M) to plaintext using the relevant decryption function D, resulting in D(M).
• The company directly performs analysis operations on file M in plaintext.
• After the operations, M is encrypted again, generating E(M').
• The company sends the encrypted M' back to me, and then I decrypt it again.

Do you notice the key problem here? When the company decrypts M and stores it on its server for computation, a third party can access the originally protected sensitive data. If this person is subject to a hack or has malicious intent, it can lead to problems.

Fully Homomorphic Encryption (FHE) solves this problem by allowing computations on encrypted data. The company no longer needs to decrypt E(M). It can directly analyze the encrypted data. There is no need for decryption, and no need for trust assumptions.

In summary, the introduction of fully homomorphic encryption addresses a key problem in the current data processing process, which is the privacy risk that may be exposed when a third party processes the 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) has opened a new door for the encrypted world, bringing us many previously unimaginable application scenarios. The original article by Poly Venture provides a simple description of the scenarios, and I have tried to make a more organized interpretation in the following table.

FHE vs ZK vs MPC: Can't Tell 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 Multiparty Computation (MPC). At first glance, they all seem to be dedicated to solving similar privacy and computation problems. But what are the actual connections and differences between these three?

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

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

Then, let's look at their similarities, differences, and intersections from multiple dimensions.

1. Purpose:

   1. The main purpose of FHE is to perform computations without decryption.

   2. The goal of ZK is to prove the correctness of a fact without revealing any information about that fact.

   3. MPC aims to allow multiple parties to securely compute together without revealing their respective inputs.

2. Privacy and Computation:

   1. In ZK, the computations are not necessarily private. For example, while you can use ZK to verify if a bank account balance exceeds $100,000, the computation for such verification is not necessarily private.

   2. In contrast, FHE ensures the privacy of computations because all computations are performed on encrypted data.

3. Limitations and Challenges:

   1. MPC requires at least one honest server and may be susceptible to DDoS attacks, collusion attacks, and communication overhead.

   2. ZK is primarily used for proving correctness rather than privacy techniques.

   3. FHE, despite providing strong privacy, has low computational efficiency and high resource requirements.

4. Applications in the Cryptographic Field:

   1. FHE can be used to build more private smart contracts and other blockchain applications.

   2. ZK is used to create scalable blockchain solutions, such as zk-rollups.

   3. MPC is mainly used for private key management and custody.

5. Cross-Usage:

   1. MPC can be combined with FHE to form threshold FHE, enhancing security by splitting an FHE encrypted key into multiple parts and giving each participant one part.

   2. zkFHE is a combination of zero-knowledge proofs and fully homomorphic encryption, being researched to achieve zk-rollups on FHE smart contracts.

Overall, while FHE, ZK, and MPC overlap in some aspects, they each have unique advantages and applications. In the world of cryptography, 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 simplified comparison table to help everyone better understand these technologies.

Future Prospects of FHE

From the above, it is clear that Fully Homomorphic Encryption (FHE) is a powerful technology.

But why hasn't it been widely adopted, and why is it rarely mentioned in the field of encrypted CT? On the one hand, this is due to the inherent complexity of understanding the technology itself, and on the other hand, FHE technology currently faces some challenges, making it difficult to easily enter the public eye in a commercialized form.

The challenges it faces may include:

1. Computationally Intensive: When our ciphertexts interact with each other, more noise is added to maintain security. FHE schemes use "bootstrapping" to reduce noise, but this is very computationally intensive and resource-consuming.

2. Limited Functionality: FHE computations are limited to addition, multiplication, and their variations/combinations. For example, if statements cannot be used in FHE because the content is encrypted. Additionally, building relatively complex operations, such as comparisons and divisions, requires careful planning of basic logic, leading to more complex programming skills and lower computational efficiency.

3. Compatibility/Integration Issues: Existing applications and service providers are not built to perform computations on encrypted data. This limits the integration of FHE with existing technologies and adds inertia to developing FHE-compatible applications.

Possible solutions may include:

1. Hardware Accelerators: Some FHE schemes, such as nuFHE and cuFHE, can use GPU acceleration, but the major breakthrough will come from faster FPGAs and ASICs. Other technologies, such as photonics, are also being researched to accelerate hardware use cases for FHE.

2. New Programming Paradigms: Just as 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 built to enable developers to unify FHE, ZKP, and MPC.

3. Integration with Existing Solutions: Solutions will be built to make existing tools compatible with FHE, serving as an intermediate layer between tools and FHE-encrypted data.

Finally, in the conclusion section of the original article, Portal Ventures once again emphasizes:

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

Furthermore, they also express interest in projects currently researching FHE. Therefore, it can be seen that VCs are interested in FHE, or VCs are interested in hardcore technologies that have not yet entered the public eye.

History has shown that encryption projects based on new technologies often have a bright halo and high valuations, and are sought after by various capital sources.

Before the next feast begins, we should indeed spend more time researching the identities of the guests who will enter, in order to be able to handle them with ease when the feast begins.

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