FHE, ZK, and MPC: A Depth 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 advanced technologies that have garnered significant attention. Each of them targets different application scenarios, providing unique solutions for data privacy and security. This article will compare the characteristics, working principles, and applications of these three technologies in the blockchain domain in detail.

Zero-Knowledge Proof (ZK): Proving without Revealing

The core problem solved by zero-knowledge proof technology is: how to verify the authenticity of certain information without disclosing any specific details. ZK is built on a rigorous basis of encryption, allowing one party (the prover) to prove to another party (the verifier) the authenticity of a statement without revealing any information other than the validity of the statement.

For example, suppose someone needs to prove their good credit status to a car rental company but does not want to provide detailed bank statements. In this case, the "credit score" provided by the bank or payment platform can be seen as a type of zero-knowledge proof. The customer can prove that their credit score meets the standards without showing specific financial information.

In blockchain applications, a typical case of ZK technology is anonymous encryption currencies. For example, when users make a transfer, they need to prove that they have enough balance to complete the transaction while remaining anonymous. By generating ZK proofs, users can demonstrate the validity of the transaction to the network, while miners or validators can confirm the legality of the transaction without needing to know the identities of the parties involved or the specific amounts.

Multi-Party Computation (MPC): Collaborative computing without leakage

Multi-party secure computation technology is primarily used to solve how to allow multiple participants to perform joint computations securely while protecting each party's sensitive information. MPC enables multiple parties to collaborate on a computational task, but each participant cannot learn the input data of others.

A classic MPC application scenario is to calculate the average salary of multiple people without revealing each individual's specific salary. Participants can split their salary data into multiple parts and exchange portions of the data with others. By summing the received data and sharing the results, the average can ultimately be calculated, but no one can know the exact salary of others.

In the cryptocurrency field, MPC technology is widely used for wallet security. For example, some trading platforms have launched MPC wallets that split private keys into multiple parts, which are separately stored by the user's device, cloud storage, and the platform. This method not only enhances security but also provides users with a more convenient asset recovery solution.

Fully Homomorphic Encryption (FHE): Encrypted Outsourced Computation

The problem that fully homomorphic encryption technology solves is: how to encrypt sensitive data so that a third party can perform computational processing on the data without decrypting it, while the result can still be correctly decrypted by the original data owner. FHE allows for arbitrary computation operations to be performed on encrypted data without affecting the correctness of the result after decryption.

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

In the blockchain field, FHE technology is expected to solve some issues present in PoS (Proof of Stake) networks. For instance, in some small PoS networks, validating nodes may tend to directly adopt the validation results of larger nodes rather than independently verifying transactions, which may lead to network centralization. By using FHE technology, nodes can complete block validation without knowing the validation results of other nodes, thereby maintaining the decentralized nature of the network.

In addition, FHE can also be applied to decentralized voting systems to prevent voters from influencing each other or voting along with the crowd, ensuring that the voting results better reflect the true public opinion.

Technical Comparison

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

1. Application Focus:

   • ZK focuses on "how to prove" and is applicable in 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 encryption", suitable for scenarios that require complex computations while keeping the data in an encrypted state.

2. Technical Complexity:

   • The implementation of ZK requires a deep understanding of mathematics and programming skills, and designing effective and easy-to-implement protocols is challenging.
   • MPC needs to address synchronization and communication efficiency issues during implementation, especially in cases with many participants.
   • FHE faces significant challenges in computational efficiency. Although it is theoretically attractive, its practical application is still limited by high computational complexity and time costs.

These three technologies are continuously evolving, providing powerful tools for data security and personal privacy protection. With advancements in technology and the expansion of application scenarios, they will play an increasingly important role in the future digital world.