FHE, ZK, and MPC: Similarities and Differences Among Three Encryption Technologies

Encryption technology plays a crucial role in protecting data security and personal privacy. This article will provide a detailed comparison of three advanced encryption technologies: Fully Homomorphic Encryption (FHE), Zero-Knowledge Proof (ZK), and Multi-Party Computation (MPC).

Zero-Knowledge Proof (ZK): Proving without Revealing

Zero-knowledge proof technology aims to address the problem of how to verify the authenticity of information without disclosing specific content. It is based on encryption principles and allows one party to prove to another party the existence of a secret without revealing any specific information about that secret.

For example, if Alice wants to prove her good credit status to Bob, an employee of a car rental company, but is unwilling to provide detailed bank statements, then a "credit score" provided by a bank or payment software can be seen as a form of zero-knowledge proof. Alice can prove her credit rating to Bob without revealing specific account information, under the premise of "zero knowledge."

In the field of blockchain, the application of ZK technology can refer to a certain anonymous encryption currency. When users make transfers, they need to prove that they have the transfer rights while maintaining anonymity. By generating ZK proofs, miners can verify the legitimacy of the transaction without knowing the identity of the transaction initiator and put it on the chain.

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

Multi-party secure computation technology mainly addresses the issue of how to enable multiple participants to perform secure computations without revealing sensitive information. It allows multiple participants to collaboratively complete computational tasks without any party disclosing its input data.

For example, if three people want to calculate their average salary but do not want to disclose the specific amounts to each other, they can use the following method: each person divides their salary into three parts and gives two parts to the other two people respectively. Then, each person sums up the received numbers and shares the results. Finally, the three people sum these three results again and take the average to obtain the average salary, without being able to know each other's specific salary amounts.

In the cryptocurrency field, MPC technology is applied to develop new types of wallets. These wallets no longer require users to remember 12 mnemonic words, but instead use a method similar to 2/2 multi-signature, distributing the private keys across multiple locations such as the user's mobile phone, the cloud, and service providers. Even if the user accidentally loses their phone, they can still restore access through other means.

Fully Homomorphic Encryption (FHE): Encrypted Outsourced Computation

Fully homomorphic encryption technology focuses on solving the problem of how to encrypt sensitive data so that the encrypted data can be computed by an untrusted third party, while the results can still be correctly decrypted by the original data owner.

In practical applications, FHE allows data owners to hand over their raw data, which has noise added (through multiple addition or multiplication operations), to a third party with strong computational capabilities for processing, and then decrypt it themselves to obtain the real results, while the third party knows nothing about the original data content.

This technology is particularly important when handling sensitive data in cloud computing environments. For example, when dealing with medical records or personal financial information, FHE can ensure that the data remains in an encryption state throughout the processing, thus safeguarding data security and complying with privacy regulations.

In the field of blockchain, FHE technology can be applied to improve the PoS (Proof of Stake) consensus mechanism and voting systems. By allowing nodes to complete block verification work without knowing each other's answers, it can prevent plagiarism among nodes, thus addressing the issues of laziness and centralization in small PoS networks. Similarly, in the voting process, FHE can ensure that voters complete their votes without knowing each other's voting intentions, preventing the occurrence of herd voting.

Technical Comparison

Although these three technologies aim to protect data privacy and security, they differ in terms of application scenarios and technical complexity:

1. Application scenario:
   • ZK focuses on "how to prove", applicable in situations where permission or identity verification is required.
   • MPC focuses on "how to compute" and is applicable in situations where multiple parties need to compute together while protecting their respective data privacy.
   • FHE focuses on "how to encryption", suitable for scenarios that require complex computations while keeping data in an encrypted state.

2. Technical Complexity:
   • ZK is theoretically powerful, but designing effective and easy-to-implement protocols is quite complex, requiring a deep understanding of mathematics and programming.
   • MPC needs to address synchronization and communication efficiency issues during implementation, especially in cases of multi-party participation, where coordination costs and computational overhead can be quite high.
   • FHE faces significant challenges in computational efficiency. Although it is theoretically very attractive, the high computational complexity and time cost in practical applications remain major obstacles.

In summary, these three encryption technologies each have their own characteristics and application areas, together forming an important part of modern cryptography, providing strong support for data security and privacy protection.