Author: Haotian
Vitalik’s article on Fully Homomorphic Encryption (FHE) has once again sparked exploration and imagination in the field of new encryption technologies. In my opinion, FHE offers a larger scope of possibilities compared to Zero-Knowledge Proofs (ZKP), and it can facilitate the implementation of AI+Crypto in various application scenarios. How should we understand FHE fully homomorphic encryption?
1) Definition: FHE enables operations on encrypted data in a specific format without the concern of exposing the data or compromising privacy. In contrast, ZKP can only solve the consistency and transmission of data in an encrypted state, allowing the receiving party to verify the authenticity of the submitted data in a point-to-point encrypted transmission scheme. FHE does not limit the range of entities involved in the operations, making it a multi-to-multi encryption computation scheme.
2) How it works: Traditional computer computations operate on plaintext data. If the data is encrypted, it needs to be decrypted before performing the computation, which inevitably exposes sensitive information. Homomorphic encryption constructs a special encryption scheme that can transform ciphertexts in a “homomorphic” manner, ensuring that the results of the computation on the ciphertexts remain the same as if it were performed on the plaintexts. In a homomorphic encryption system, plaintext addition corresponds to ciphertext multiplication (a certain rule), so performing addition on plaintext data only requires multiplication on ciphertexts (equivalence).
In summary, homomorphic encryption uses a special homomorphic transformation to enable computations on data in an encrypted state, yielding the same results as if it were performed on plaintexts. This is achieved by ensuring the homomorphic correspondence property in the computation rules.
3) Application scenarios: In traditional internet domains, FHE can be widely applied in areas such as cloud storage, biometric identification, healthcare, finance, advertising targeting, and genetic sequencing. Taking biometric identification as an example, personal biometric data such as fingerprints, iris scans, and facial features are sensitive information. Using FHE technology, these data can be compared and verified in an encrypted state on servers. Similarly, in the healthcare sector, FHE can bridge the gap between years of fragmented data, allowing different healthcare institutions to perform joint analysis and modeling without sharing the original data.
In the field of cryptography, FHE can also be applied to various scenarios that require strong privacy, such as gaming, DAO voting governance, MEV protection, private transactions, and regulatory compliance. In a gaming scenario, for instance, the platform can drive the game forward without prying into the players’ cards, making the game more fair. Similarly, in DAO voting, whales participating in governance can generate voting results through computations without exposing their addresses and voting quantities. Additionally, users can submit encrypted transactions to the Mempool, avoiding the exposure of target addresses, transfer amounts, and other private messages. In a regulatory scenario, the government can monitor fund pools and separate assets associated with blacklisted addresses without accessing the privacy data of legitimate transactions.
4) Limitations: It is worth noting that the computational environment for conventional computations on plaintexts is often complex, involving not only addition, subtraction, multiplication, and division but also conditional loops, logical gate judgments, and more. Currently, partially homomorphic encryption and fully homomorphic encryption can only efficiently perform operations on addition and multiplication, with more complex computations requiring combination and superposition, which increases the computational power demand.
Therefore, theoretically, fully homomorphic encryption can support any computation. However, due to performance bottlenecks and algorithm characteristics, the types and complexity of homomorphic computations that can be efficiently executed are currently limited. Complex computations require significant computational power consumption. Thus, the implementation of fully homomorphic encryption is a process of algorithm optimization and control of computational power cost, with particular attention to performance after hardware acceleration and enhanced computational power.
In conclusion, in my view, although it may take time for FHE fully homomorphic encryption to mature and be applied, it serves as a complementary extension to ZKP technology and can provide valuable support for AI privacy computation with large models, AI data collaborative modeling, AI collaborative training, crypto privacy-compliant transactions, and the extension of crypto scenarios.