Comparative Analysis of FHE, ZK, and MPC Cryptography Techniques

In the field of Cryptography, Fully Homomorphic Encryption ( FHE ), Zero-Knowledge Proof ( ZK ), and Multi-Party Computation ( MPC ) are three important privacy protection technologies. Although they all aim to protect data privacy and security, there are some differences in specific application scenarios and technical characteristics. This article will provide a detailed comparison of these three technologies.

Zero-Knowledge Proof ( ZK )

Zero-knowledge proof technology focuses on how to verify the truth of a statement without revealing any specific information. It is based on Cryptography and allows one party, the prover, to prove to another party, the verifier, that they know a certain secret without disclosing any information about that secret.

For example, Alice can prove her good credit to the car rental company employee Bob without having to show specific bank statements. The "credit score" of payment software is similar to a type of zero-knowledge proof, which can demonstrate a user's credit status without revealing specific transaction records.

In the blockchain field, anonymous coins are a typical application of ZK technology. When users make transfers, they need to prove their transfer authority while maintaining anonymity. By generating ZK proofs, miners can verify the legitimacy of transactions and put them on the chain without knowing the identity of the transactors.

Multi-Party Computation ( MPC )

Multi-party secure computation technology mainly addresses how to allow multiple participants to jointly complete computational tasks without disclosing sensitive information from each party. It enables multiple parties to collaborate on computations without revealing their respective input data.

A classic application scenario of MPC is: Alice, Bob, and Carol want to calculate the average salary of the three of them, but do not want to disclose the specific salary amounts to each other. Through MPC technology, they can divide their respective salaries into three parts, exchange two parts with each other, and then sum the received numbers and share the result. Finally, the three of them sum the three results again and average them, which will give them the average salary, but they will not know each other's specific salary amounts.

In the cryptocurrency field, MPC wallets are an important application. They divide the private key into multiple parts, which are jointly held by users, the cloud, and exchanges, enhancing the security of assets. Even if a user loses their phone, they can recover the private key through other parties. Some MPC wallets also support the introduction of more third parties to further enhance security.

Fully Homomorphic Encryption ( FHE )

Homomorphic encryption technology focuses on how to encrypt data so that the encrypted data can be given to untrusted third parties for computation, while the computation results can still be correctly decrypted. This enables the use of external computing resources while protecting data privacy.

A typical application scenario of FHE is: Alice does not have sufficient computational power and needs to rely on Bob for calculations, but she does not want to disclose the real data to Bob. Through FHE, Alice can encrypt the original data and then let Bob process the encrypted data. Finally, Alice can decrypt it to obtain the real result, while Bob cannot know the content of the original data throughout the entire process.

In the blockchain field, FHE can be used to solve some problems in PoS consensus mechanisms. For example, in some small PoS networks, nodes may tend to directly follow the verification results of large nodes rather than verifying themselves, which can lead to centralization issues. Through FHE technology, nodes can complete block verification without knowing the answers of other nodes, avoiding mutual plagiarism.

In addition, FHE can also be applied to scenarios such as decentralized voting to prevent voters from influencing each other. Some projects are exploring the combination of FHE with re-staking ( to provide more secure outsourced node services for small blockchains.

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Technical Comparison

Although these three technologies are all dedicated to protecting data privacy and security, there are some differences in their application scenarios and technical complexity:

1. Application Scenarios:

   • ZK emphasizes "how to prove", applicable to scenarios that require verification of permissions or identity.
   • MPC emphasizes "how to compute", applicable to scenarios where multiple parties need to compute together while protecting their own data privacy.
   • FHE emphasizes "how to encrypt", applicable to scenarios requiring complex calculations while keeping data in an encrypted state.

2. Technical Complexity:

   • The theoretical foundation of ZK is strong, but designing effective and easily implementable protocols is relatively complex, requiring a solid background in mathematics and programming.
   • MPC needs to address synchronization and communication efficiency issues during implementation, especially in cases with multiple parties involved, where coordination costs and computational overhead are relatively high.
   • FHE faces significant challenges in computational efficiency. Although it is theoretically attractive, the high computational complexity and time costs in practical applications remain major obstacles.

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Conclusion

With the development of the digital age, data security and personal privacy protection face unprecedented challenges. FHE, ZK, and MPC are three cryptography technologies that provide us with powerful privacy protection tools, each playing an important role in different scenarios. Understanding the characteristics and application scenarios of these technologies is crucial for building a safer and more private digital world.

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