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

In today's digital age, data security and privacy protection have become increasingly important. Fully Homomorphic Encryption (FHE), Zero-Knowledge Proofs (ZK), and Multi-Party Computation (MPC) are three advanced encryption technologies that address these challenges. This article will provide a detailed comparison of these three technologies, exploring their working principles, application scenarios, and potential in the blockchain field.

1. Zero-Knowledge Proof (ZK): A method of proof that does not disclose information

Zero-knowledge proof technology aims to address the issue of how to verify the authenticity of information without disclosing specific content. It is based on encryption and allows one party (the prover) to prove the truth of a statement to another party (the verifier) without revealing any information other than the truth of that statement.

For example, suppose Alice needs to prove her good credit status to Bob, an employee of a car rental company, but does not want to provide detailed bank statements. In this case, a "credit score" similar to those provided by banks or payment software can serve as a form of zero-knowledge proof. Alice can prove that her credit score meets the requirements, while Bob does not need to know Alice's specific financial situation.

In the field of blockchain, the application of ZK technology can refer to the anonymous encryption currency Zcash. When users make transfers, they need to prove that they have enough coins for the transaction while maintaining anonymity. By generating ZK proofs, miners can verify the legitimacy of the transaction without knowing the identities of both parties and add it to the blockchain.

2. Multi-Party Computation (MPC): A Method for Secure Collaborative Computing

Secure Multi-Party Computation technology is mainly used to address how to perform collaborative computations without disclosing sensitive information from any party involved. It allows multiple participants to jointly complete a computational task without any party revealing its input data.

For example, suppose three people want to calculate their average salary but do not want to disclose their individual salary amounts. Using MPC technology, each person can divide their salary into three parts and exchange two of those parts with the other two. Then, each person sums the received numbers and shares this sum. Finally, the three individuals sum the three results again and calculate the average, thus obtaining the average salary while being unable to know the specific salaries of others.

In the cryptocurrency field, MPC technology is applied in the design of certain wallets. These wallets divide the private keys into multiple parts, stored separately on user devices, in the cloud, and by the platform, enhancing the security of assets and the convenience of recovery. Some MPC wallets also support the introduction of more third parties to protect the private key shards, further enhancing security.

3. Fully Homomorphic Encryption (FHE): Outsourcing Computation on Encrypted Data

Fully homomorphic encryption technology addresses the issue of how to allow third parties to compute while protecting data privacy. It allows various operations on encrypted data without decryption, and the final encrypted result can be decrypted by authorized parties to obtain the correct computation result.

In practical applications, FHE allows users to hand over encrypted sensitive data to untrusted third parties for processing without worrying about data leakage. For example, when handling medical records or personal financial information in a cloud computing environment, FHE can ensure that the data remains encrypted throughout the processing, thereby protecting data security and complying with privacy regulations.

In the blockchain field, FHE technology can be used to address certain issues present in Proof of Stake (PoS) networks. For example, in some small PoS networks, validating nodes may simply follow the results of larger nodes without conducting independent verification, which can lead to centralization of the network. By using FHE technology, validating nodes can complete block verification without knowing the answers of other nodes, thereby preventing plagiarism between nodes.

Similarly, in a decentralized voting system, FHE can prevent the "vote buying" phenomenon, ensuring that each voter makes decisions independently without knowing others' voting tendencies, thereby better reflecting the true public opinion.

Summary

Although ZK, MPC, and FHE are all designed to protect data privacy and security, they differ in 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 together while protecting their own data privacy.
• FHE focuses on "how to encrypt", making it possible to perform complex computations while keeping the data in an encrypted state.

These technologies each have challenges in implementation: ZK requires deep mathematical and programming skills; MPC faces synchronization and communication efficiency issues; FHE has significant challenges in computational efficiency.

As the digitalization process deepens, these encryption technologies will play an increasingly important role in protecting personal privacy and data security, providing strong technical support for building a safer and more trustworthy digital world.