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

In today's digital age, encryption technology is essential for protecting data security and personal privacy. This article will delve into three advanced encryption technologies: Fully Homomorphic Encryption (FHE), Zero-Knowledge Proofs (ZK), and Multi-Party Computation (MPC), analyzing their mechanisms, application scenarios, and practical uses in the blockchain field.

Zero-Knowledge Proof (ZK): Proving without Revealing

The core of zero-knowledge proof technology lies in how to verify the authenticity of information without revealing any specific content. It is built on a solid foundation of encryption, allowing one party to prove the existence of a secret to another party without disclosing any information about that secret.

For example, suppose someone wants to prove their good creditworthiness to a car rental company but is unwilling to provide detailed bank statements. In this case, the "credit score" provided by a bank or payment software can serve as a form of zero-knowledge proof. This way, the customer can demonstrate their good credit without disclosing personal financial details.

In the field of blockchain, the application of zero-knowledge proof technology is very extensive. Taking a certain anonymous encryption currency as an example, when users make transfers, they need to prove their right to transfer these coins while maintaining anonymity. By generating a ZK proof, miners can verify the legitimacy of the transaction and put it on the chain without knowing the identity of the transaction initiator.

Multi-Party Computation (MPC): Joint computation without leakage

Multi-party secure computation technology mainly addresses how to enable multiple participants to safely perform joint computations without leaking sensitive information. This technology allows multiple parties to complete a computational task without any party having to reveal its input data.

For example, suppose three people want to calculate their average salary but do not want to disclose the exact salary amounts to each other. By using MPC technology, each person can divide their salary into three parts and exchange two of those parts with the other two individuals. Then, each person sums the numbers they received and shares the summation result. Finally, the three people calculate the total sum of these three summation results to obtain the average, without being able to determine the exact salaries of the others.

In the field of cryptocurrency, MPC technology is widely used for wallet security. Some trading platforms have launched MPC wallets that divide the private key into multiple parts, stored separately on the user's phone, in the cloud, and at the exchange. This method not only enhances security but also increases the possibility of recovering the private key.

Fully Homomorphic Encryption (FHE): Encrypted Computation Does Not Leak

The goal of fully homomorphic encryption technology is to perform computations on encrypted data without the need to decrypt it. This allows users to hand over sensitive data, encrypted, to untrusted third parties for computation while still being able to decrypt the correct results.

In practical applications, FHE allows data to remain in an encrypted state throughout the processing, which not only protects data security but also complies with strict privacy regulatory requirements. For example, FHE technology is particularly important when processing medical records or personal financial information in a cloud computing environment.

In the field of blockchain, FHE technology also has unique applications. For example, a certain project uses FHE technology to solve the problem of nodes being lazy and following large nodes in a small PoS network. By allowing PoS nodes to complete block verification work without knowing each other's answers, it prevents plagiarism among nodes. Similarly, in voting systems, FHE technology can prevent voters from influencing each other, ensuring the authenticity of the voting results.

Summary

Although ZK, MPC, and FHE are all aimed at protecting data privacy and security, there are significant differences in their application scenarios and technical complexity:

• ZK focuses on "how to prove" and is suitable for scenarios that require verification of permissions or identity.
• MPC focuses on "how to compute" and is suitable for situations where multiple parties need to compute jointly while protecting their own data privacy.
• FHE focuses on "how to encrypt", making it possible to perform complex computations while the data remains encrypted.

In terms of technical complexity, ZK requires deep mathematical and programming skills, MPC faces challenges in synchronization and communication efficiency, while FHE has significant obstacles in computational efficiency.

As the challenges to data security and personal privacy protection continue to grow, these advanced encryption technologies will play an increasingly important role in the digital world of the future. Understanding and applying these technologies is crucial for building a secure and trustworthy digital ecosystem.