Homomorphic Encryption
A cryptographic scheme that enables direct computation on encrypted data without ever decrypting it.
I. Overview
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A["Encrypted\ndata"] -- "Direct computation without decryption" --> B["Privacy-preserving\nanalysis"]
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Definition: A cryptographic system in which the result of performing an operation on ciphertext Enc(m) of plaintext m remains equivalent to the result of performing the operation on the plaintext and then encrypting it.
Core Value:
( Privacy Preservation ) Computation can be performed on data while it remains encrypted, without ever decrypting it to plaintext
( Maximized Data Utility ) Enables data analysis using external resources such as the cloud while protecting sensitive information
( Mathematical Safety ) Can simultaneously achieve quantum-resistant security by relying on techniques such as lattice-based cryptography
II. Mechanism & Components
A. Stages of Development by Computational Scope
| Category | Generation | Features & Limitations |
|---|---|---|
| Partially Homomorphic (PHE) | 1st generation | Supports only one operation — either addition or multiplication (RSA, ElGamal) |
| Somewhat Homomorphic (SHE) | 2nd generation | Supports both addition and multiplication, but with a limit on the number of operations |
| Fully Homomorphic (FHE) | 3rd generation | Supports unlimited logical/arithmetic operations with no count restriction (Gentry, 2009) |
B. Core Technologies of Fully Homomorphic Encryption (FHE)
| Core Technology | Description | Note |
|---|---|---|
| Lattice-based cryptography | Encryption based on the mathematical hardness of lattice structures (e.g., LWE) | Provides quantum resistance (PQC) |
| Bootstrapping | Removes accumulated noise during computation so that operations can continue | The key technology enabling FHE |
| Packing | Places multiple pieces of data into a single ciphertext for parallel processing | Improves computational efficiency |
III. Advanced Topics & Comparison
| Comparison Item | Homomorphic Encryption | Differential Privacy (DP) |
|---|---|---|
| Security Mechanism | Mathematical encryption (access control) | Mathematical noise injection (data perturbation) |
| Data Form | Ciphertext (results also remain encrypted) | Statistical values (results are plaintext but contain error) |
| Computational Accuracy | 100% accurate (identical to plaintext once decrypted) | Approximate (error introduced by noise) |
| Key Limitation | High computational load (CPU/memory consumption) | Loss of data utility (privacy budget management) |
Last updated 18 Aug 2026, 00:00 UTC.