FHE, ZK, and MPC: A Comparison of Three Advanced Encryption Technologies

Recently, we discussed the working principles of fully homomorphic encryption (FHE). However, many people still easily confuse FHE with zero-knowledge proofs (ZK) and multi-party secure computation (MPC). Therefore, this article will provide an in-depth comparison of these three technologies.

Overview of FHE, ZK, and MPC

Let's start with the most fundamental question:

• What are these technologies?
• How do they work?
• How are they applied to blockchain?

1. Zero-Knowledge Proof ( ZK ): emphasizes "proving without revealing"

Zero-knowledge proof technology aims to solve an important problem: how to verify the authenticity of information without disclosing any specific details.

ZK is built on a solid foundation of encryption. Through zero-knowledge proofs, Alice can prove to Bob that she knows a certain secret without revealing any information about that secret.

Imagine a scenario where Alice wants to prove her good credit to Bob, an employee of a car rental company, but she does not want to provide detailed information such as bank statements. In this case, the "credit score" provided by the bank or payment application can be considered a form of "zero-knowledge proof."

Alice can prove that her credit score is good under Bob's "zero knowledge" conditions without revealing specific account information, which is the essence of zero-knowledge proof.

In blockchain applications, we can take anonymous coins as an example:

When Alice transfers to others, she needs to remain anonymous while proving that she has the right to transfer these coins ( to prevent double spending ). To do this, she needs to generate a ZK proof.

Miner Bob, after seeing this proof, can still record the transaction on the blockchain without knowing Alice's identity, that is, zero knowledge of Alice's identity, (.

) 2. Multi-party Secure Computation ### MPC (: Emphasizes "how to compute without leaking"

The main problem that multi-party secure computation technology addresses is: how to allow multiple participants to securely perform joint computations without disclosing sensitive information.

This technology enables multiple participants ) such as Alice, Bob, and Carol ( to collaboratively complete a computational task without any party having to reveal their input data.

For example, if Alice, Bob, and Carol want to calculate their average salary, but do not want to disclose their specific salary amounts. They can use the following method:

Each person divides their salary into three parts and gives two parts to the other two people. Then, each person sums up the numbers they received and shares this sum. Finally, the three individuals calculate the total of these three sums to obtain the average value, but they are unable to determine the exact salaries of the others apart from their own.

In the cryptocurrency field, MPC wallets have applied this technology.

Taking the simple MPC wallet launched by certain trading platforms as an example, users no longer need to remember 12 mnemonic words. Instead, they use a method similar to converting the private key into a 2/2 multisignature, with one copy stored on the user's phone, one copy stored in the user's cloud, and one copy stored by the trading platform.

In this way, even if the user accidentally loses their phone, they can still recover their private key through the cloud and the trading platform.

Of course, to enhance security, some MPC wallets support the introduction of more third parties to protect private key fragments.

Based on the MPC encryption technology, multiple parties can securely use private keys without needing to fully trust each other.

![FHE vs ZK vs MPC, what are the differences among these three encryption technologies?])https://img-cdn.gateio.im/webp-social/moments-0b3f906bfa44f66a733257e13cbb05af.webp(

) 3. Fully Homomorphic Encryption ### FHE (: Emphasizes "how to encrypt in order to outsource computation"

Fully homomorphic encryption technology is mainly applied in the following scenarios: how we encrypt sensitive data so that the encrypted data can be given to untrusted third parties for auxiliary computation, while the computation results can still be correctly decrypted by us.

For example, Alice lacks computing power and needs to rely on Bob for calculations, but she doesn't want to reveal the real data to Bob. Therefore, she can only introduce noise ) into the raw data for arbitrary addition/multiplication encryption (, and then use Bob's powerful computing power to process this encrypted data, finally allowing Alice to decrypt the real result herself, while Bob remains completely unaware of the content.

Imagine if you needed to handle sensitive data, such as medical records or personal financial information, in a cloud computing environment, FHE becomes particularly important. It allows data to remain in an encryption state throughout the processing, which not only protects data security but also complies with privacy regulations.

In the cryptocurrency industry, FHE technology can bring some innovative applications. For example, a project funded by the Ethereum Foundation has focused on an inherent issue of the Proof of Stake ) PoS ( mechanism:

A PoS protocol like Ethereum, which has over a million validators, naturally has no issues. However, for many smaller projects, problems arise because miners are inherently inclined to "cut corners."

In theory, the work of nodes is to carefully verify the legitimacy of each transaction. However, in some small PoS protocols, the number of nodes is insufficient, and it often includes some "big nodes".

As a result, many small PoS nodes found that it is better to directly follow the ready-made results of large nodes rather than spending time verifying calculations personally.

This will undoubtedly lead to serious centralization issues.

Similarly, there is a similar "following" phenomenon in the voting scenario.

For example, in a voting process of a certain decentralized autonomous organization )DAO(, due to a certain investment institution holding a large number of voting rights, its stance has a decisive influence on certain proposals. After the institution votes, many small ballot holders can only be forced to follow suit or abstain, failing to truly reflect the overall will.

Therefore, the project utilizes FHE technology:

Enable PoS nodes to complete block validation tasks using machine computing power without knowing each other's answers, preventing nodes from plagiarizing each other.

or

Allow voters to calculate the final result through the voting platform without knowing each other's voting intentions, preventing bandwagon voting.

This is an important application of FHE in the field of blockchain.

To achieve this functionality, the project also needs to build a re-staking ) protocol. Because certain existing protocols will provide "outsourced node" services for some small blockchains in the future, if combined with FHE, it can significantly enhance the security of PoS networks or voting.

To make a somewhat inappropriate analogy, introducing such solutions in small blockchains is a bit like a small country struggling to manage its internal affairs, and thus bringing in foreign troops.

This is also a differentiating factor of the project in the PoS/re-staking field compared to other projects. Compared to some early projects, this project started later and only recently launched its mainnet, which relatively means less competitive pressure.

Of course, the project also provides services in the field of artificial intelligence, such as using FHE technology to encrypt the data input to the AI, allowing the AI to learn and process this data without knowing the original data. Typical cases include collaboration with a subnet of a certain AI network.

Summary

Although ZK( zero-knowledge proofs), MPC( multi-party computation), and FHE( fully homomorphic encryption) are advanced encryption technologies designed to protect data privacy and security, they differ in terms of application scenarios and technical complexity:

Application Scenarios:

• ZK emphasizes "how to prove". It provides a way for one party to prove the correctness of certain information to another party without revealing any additional information. This technology is very useful when there is a need to verify permissions or identities.
• MPC emphasizes "how to compute". It allows multiple participants to compute together without revealing their individual inputs. This is valuable in situations that require data collaboration while protecting the data privacy of all parties, such as cross-institutional data analysis and financial audits.
• FHE emphasizes "how to encrypt". It makes it possible to delegate complex computations while the data remains in an encrypted state. This is particularly important for cloud computing and AI services, allowing users to securely process sensitive data in a cloud environment.

Technical Complexity:

• Although ZK is theoretically powerful, designing effective and easy-to-implement zero-knowledge proof protocols can be very complex, requiring deep mathematical and programming skills, such as various complex "circuit" designs.
• MPC needs to address synchronization and communication efficiency issues during implementation, especially when there are many participants, as coordination costs and computational overhead can be very high.
• FHE faces significant challenges in computational efficiency, as the encryption algorithm is relatively complex and wasn't theorized until 2009. Despite its conceptual appeal, its high computational complexity and time costs in practical applications remain major obstacles.

In today's digital age, the data security and personal privacy protection we rely on are facing unprecedented challenges. Without encryption technology, the information in services we use in our daily lives, such as text messages, food delivery, and online shopping, could be easily stolen. It's like a front door without a lock; anyone can enter at will.

I hope this article can help readers better understand and distinguish between these three important encryption technologies, which are all gems in the field of cryptography, each with its own characteristics and application scenarios.