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

In the field of encryption, Fully Homomorphic Encryption ( FHE ), Zero-Knowledge Proof ( ZK ), and Multi-Party Computation ( MPC ) are three important encryption technologies. Although they all aim to protect data privacy and security, there are significant differences in application scenarios and technical complexity. Let's take a closer look at the characteristics and applications of these three technologies.

Zero-Knowledge Proof ( ZK )

The core of ZK technology lies in "proving without revealing." It allows one party (, the prover ), to prove the validity of a statement to another party (, the verifier ), without disclosing any specific information about the statement.

For example, suppose Alice needs to prove her good credit to Bob, an employee of a car rental company, but does not want to provide detailed bank statements. In this case, the "credit score" provided by a bank or payment software can be regarded as a form of zero-knowledge proof. Alice can prove that her credit score meets the standards without having to show specific account information.

In the field of blockchain, the application of ZK technology is very widespread. Taking the anonymous encryption currency Zcash as an example: when users make a transfer, they need to prove that they have enough coins to complete the transaction while maintaining anonymity. By generating ZK proofs, miners can verify the legitimacy of the transaction without knowing the identities of the parties involved, and add it to the blockchain.

Multi-Party Secure Computation ( MPC )

MPC technology focuses on "how to compute without revealing". It enables multiple parties to collaboratively complete computational tasks without requiring any party to disclose their input data.

A typical application scenario of MPC is to calculate the average salary of multiple people without revealing each person's specific salary. Participants can divide their salary into several parts and exchange some data with others. By summing up the received data and exchanging it again, the average value can ultimately be obtained, but no one can know each other's exact salary.

In the field of cryptocurrency, MPC technology is used to develop more secure wallet solutions. For example, the MPC wallets launched by certain trading platforms split the private key into multiple parts, which are stored separately on the user's phone, in the cloud, and at the exchange. This method enhances asset security, allowing users to recover access even if they lose their phone through other channels.

Fully Homomorphic encryption(FHE)

FHE technology focuses on solving the problem of "how to encrypt so that outsourcing is possible." It allows computations on encrypted data without needing to decrypt first. This means that sensitive data can be processed by a third party while still in an encrypted state, and the results can still be correctly decrypted.

In practical applications, FHE allows one party without sufficient computing power, such as Alice(, to hand over encrypted data to a third party with powerful computing capabilities, such as Bob), for processing. Bob completes the computation without knowing the original data content, and finally, Alice can decrypt to obtain the real result.

FHE has important applications in cloud computing and artificial intelligence. For example, when handling sensitive data such as medical records or personal financial information, FHE can ensure that the data remains in an encryption state throughout the processing, thus protecting data security and complying with privacy regulations.

In the blockchain field, FHE technology can be used to address some issues in PoS( proof of stake) mechanisms. For example, in some small PoS networks, nodes may tend to directly follow the verification results of large nodes rather than independently verifying each transaction. By using FHE, nodes can complete block verification without knowing the answers of other nodes, thereby preventing plagiarism and enhancing the level of decentralization in the network.

Similarly, in the voting system, FHE can prevent the "vote buying" phenomenon, ensuring that each voter's choice remains unknown to others while still allowing for an accurate calculation of the final result.

Technical Comparison

Although these three technologies are all aimed at protecting data privacy and security, they differ in terms of application scenarios and technical complexity:

1. Application Scenarios:

   • ZK focuses on proving the truth of a statement without revealing specific information.
   • MPC allows multiple parties to compute together without revealing their respective inputs.
   • FHE makes it possible to perform complex computations while keeping the data in an encrypted state.

2. Technical Complexity:

   • The implementation of ZK can be very complex, requiring deep mathematical and programming skills.
   • MPC needs to address synchronization and communication efficiency issues, especially in cases with multiple parties involved.
   • Although FHE is theoretically attractive, it faces significant challenges in computational efficiency in practical applications.

These three encryption technologies together form an important cornerstone of modern data security and privacy protection. With the continuous development of technology and the expansion of application scenarios, they will play an increasingly important role in protecting personal privacy and promoting secure data collaboration.