As the market becomes quiet in a bear market, investors and project owners will always start looking for new growth points.

The window period when there is a lack of sustained hot spots is an excellent opportunity to explore and gain a deeper understanding of new technologies, as they may become the core of the next market narrative.

Last month, Portal Ventures, a well-known crypto venture capital firm, published an article on its official blog that discussed fully homomorphic encryption (FHE) technology in detail. However, this in-depth technical article did not seem to attract widespread attention from the public.

The authors at Portal Ventures put it this way:“Fully homomorphic encryption is the holy grail of encryption".

Understanding the technologies that VCs focus on is crucial for investors because it can help us predict and understand the potential trends of the next market cycle.Zero knowledge proofand multiple partiesSafetyComputing and other technologies have a profound impact on the field of cryptography, especially fully homomorphic encryption, which iscryptocurrencyandweb3There may be huge application potential in various fields.

But the problem is that most people know very little about what fully homomorphic encryption really means, how it works, and how it differs from other technologies. In a down market and when investment sentiment is low, it is undoubtedly a wise choice to jump out of the hype and delve into these cutting-edge technologies.

Somewhat coincidentally, I had the opportunity to come across FHE-related technical solutions at work a few years ago. Therefore, I decided to conduct an in-depth interpretation of this article by Portal Ventures, hoping to provide some new perspectives and thoughts for everyone.

Homomorphic and fully homomorphic encryption, what exactly are they?

If you read the original paper from Portal Ventures directly, you might be confused by the complex mathematical description of fully homomorphic encryption (FHE).

In fact, the world of cryptography is full of abstruse and technicalities, but we can explain these concepts in a simple and popular way. In this section, I try 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 box". You can put any object into this box and lock it. Once locked, you cannot see or touch the contents of the box. But, surprisingly, this box allows you to change the color or shape of the object inside without opening it.

As shown in the figure above, Fully Homomorphic Encryption can be thought of 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 still perform operations on the data in the envelope (such as addition, subtraction, etc.).

3. New Envelope: After the magic box operation, you will get a new encryption result.

This is the basic idea of homomorphic encryption:Encrypted data can be operated without understanding the data itself.

This simple example helps to clarify what "fully homomorphic encryption" is doing. But in fact, the concept itself is still a bit confusing. So, what are "full" and "homomorphic"?

1. What does "Fully" mean?

• In cryptography, an encryption scheme can support multiple operations, such as addition, multiplication, etc. When we say that an encryption scheme is "fully homomorphic", we mean that the encryption scheme supports any number of basic operations (such as addition and multiplication) on the encrypted data without decryption. This is in contrast to partially homomorphic encryption (such as schemes that only support addition or only support multiplication).

2. What is "Homomorphism”(Homomorphic)?

• "Homomorphic" comes from the Greek word for "same shape or structure". In cryptography, when we say that an encryption scheme is homomorphic, we mean that some operation has the same effect on the plaintext as it does on the ciphertext. In other words, if you perform a certain operation on the 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.

3. For example, consider an encryption scheme that supports homomorphic addition. Suppose you have two numbers: 3 and 4. You can first encrypt these two numbers, and 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 get by adding the plaintext 3 and 4 directly.

However, you may ask, how can we perform these addition, subtraction, multiplication and division operations on non-digital data? In fact, we can use a specific encoding method to convert non-digital data into digital form, so as to perform operations such as 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 used in other fields.

To explain this concept more intuitively, let us consider the example of medical data.

1. 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.

2. By using fully homomorphic encryption, hospitals can encrypt this data first.

3. Imagine that a cloud service provider needs to calculate the average age of all patients (which requires addition and division) and the sum of blood sugar values multiplied by the number of patients (which involves addition and multiplication).

4. All of these calculations can be done on encrypted data without decryption. The cloud service provider completes the calculation without decrypting the data and then returns the encrypted results to the hospital. This ensures the privacy of the data while also meeting the needs of data processing.

This is the charm of fully homomorphic encryption, which provides us with aSafetyAnd flexible data processing method.

Why is FHE important?

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

Therefore, the industry standard process is for the data to be decrypted by a third party (i.e. the company) before being computed.

As a concrete example, imagine you have a data file containing financial information on a number of high-profile individuals.

• We call this file "M". We need a company to analyze this data.

• What is the current process? First, I encrypt M using an encryption function such as RSA or AES. 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) into plaintext through the relevant decryption function D, that is, D(M).

• The company directly performs plain text analysis on file M.

• After the operation, M is encrypted again to generate E(M').

• The company then encrypts M' and sends it back to me, and I decrypt it again.

Did you notice that the key problem here is that when the company decrypts M and stores it on its servers for calculation,A third party can access sensitive data that is supposed to be protected. This can cause problems if that person is hacked or has malicious intent.

Fully homomorphic encryption (FHE) solves this problem by allowing computation to be performed on encrypted data. Companies no longer need to decrypt E(M). It performs analysis directly on the encrypted data. There is no need for decryption and no trust assumptions.

In summary, the introduction of fully homomorphic encryption solves a key problem in the current data processing process, namely the privacy risk that may be exposed when a third party processes the data. FHE provides us with a method to efficiently process encrypted data while ensuring data privacy.

How is FHE used in Crypto?

Fully homomorphic encryption (FHE) has opened a new door to the world of encryption, bringing us many application scenarios that were previously unimaginable. The original text of Poly Ventures describes the scenarios in a relatively simple way. We try to make a more organized interpretation with a table.

FHE vs ZK vs MPC, can’t tell the difference?

After learning about fully homomorphic encryption (FHE), it's easy to compare it to other familiar technologies, such as zero-knowledge proofs (ZK) and multi-party computation (MPC). At first glance, they all seem to address similar privacy and computational issues. But what are the actual connections and differences between the three?

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

• FHE: Allows computations to be performed on encrypted data without decrypting it.

• ZK:Allows one party to prove to another that a statement is true without revealing any specific information about the statement.

• MPC:Enables multiple parties to jointly perform computations on their private data without revealing the input data to other participants.

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

1. Purpose:

• The main purpose of FHE is toWithout decryptionPerform calculations.
• The goal of ZK isProve the correctness of a factwithout revealing any information about that fact.
• The goal of MPC is允许多方安全地共同计算, without leaking their respective inputs.

2. Privacy and Computing:

• In ZK, computations are not necessarily private. For example, although you can use ZK to verify that a bank account balance exceeds $100,000, the computation to perform such a verification is not necessarily private.
• In contrast, FHE ensures privacy of computations because all computations are performed on encrypted data.

3. Limitations and Challenges:

• MPC requires at least one honest server and can be vulnerable to DDoS attacks, silent collusion attacks, and communication overhead.
• ZK is primarily used for proving correctness, not as a privacy technology.
• Although FHE provides strong privacy, it is computationally inefficient and resource-intensive.

4. Application in the field of encryption:

• FHE can be used to build more private smartphonescontractand otherBlockchainapplication.
• ZK is used to create scalableBlockchainSolutions such as zk-rollups.
• MPC is mainly used for private key management and custody.

5. Cross-use:

• MPC can be combined with FHE to form threshold FHE, which enhances security by splitting a single FHE encryption key into multiple ones and giving one to each participant.
• zkFHE is a combination of zero-knowledge proofs and fully homomorphic encryption, and is being studied to implement zk-rollups on FHE smart contracts.

In general, although FHE, ZK, and MPC overlap in some aspects, they all have their own unique advantages and application scenarios. In the crypto world, all three technologies offer great potential for enhancing privacy and security, but their combination and further research remain cryptographicCommunityan active area.

Finally, we can also provide a flow-saving table to compare the above technologies together to help everyone understand more intuitively.

Future prospects of FHE

From the above, we can feel that fully homomorphic encryption (FHE) is obviously a powerful technology.

But why has it not been widely adopted, and is even rarely mentioned in cryptographic CT? On the one hand, it is because there is a certain threshold to understand the technology itself, and on the other hand, FHE technology is still facing some challenges, making it difficult to easily enter the public eye in a commercial form.

Challenges may include:

1. Computationally intensive: When our ciphertexts interact, more noise is added to maintain security. The FHE scheme uses a “bootstrapping” technique to reduce the noise, but this is very computationally intensive and resource intensive.

2. 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. In addition, building relatively complex operations such as comparison and division requires careful planning of the basic logic, which leads to more complex programming techniques and lower computational efficiency.

3. compatibility/Combination Problem: Existing applications and service providers are not built to perform computations on encrypted data. This limits the integration of FHE into existing technologies and increases the inertia required to develop FHE-compatible applications.

Possible solutions:

1. hardwareaccelerator: Certain FHE schemes, such as nuFHE and cuFHE, can be accelerated using GPUs, but the major breakthroughs will come from faster FPGAs and ASICs. Other technologies, such as photonics, are also being studied to accelerate hardware use cases for FHE.

2. New programming paradigm: Just like packages like pandas and numpy for complex mathematics on Python, FHE libraries will also be built. Currently, Zama and Sunscreen are two projects building such libraries and SDKs for FHE. In addition, specialized compilers need to be built to enable developers to unify FHE, ZKP, and MPC.

3. Integration of FHE with existing solutions: Solutions will be built to make existing tools compatible with FHE, acting as an intermediary layer between the tools and FHE-encrypted data.

Finally, Portal Ventures reiterated in the conclusion of the original article:

“FHE is the holy grail of computing, and we are getting closer to its commercialization. Value and computation are migrating to open, permissionless networks, and we believe FHE will underpin much of the required infrastructure and applications.”

In addition, they also expressed interest in projects that are currently researching FHE. Therefore, we can see that VCs are interested in FHE, or that VCs will be the first to be interested in hardcore technologies that have not yet entered the public eye.

History shows that crypto projects based on new technologies often have a shining halo and high valuations, and are sought after by various capitals.

Before the next banquet begins, we should indeed spend more time researching the identities of the guests entering in advance so that we can be ready when the banquet begins.

The article comes from the Internet:Research on fully homomorphic encryption: Calculation without decryption, what changes will it bring to Web3?