Fully Homomorphic Encryption (FHE) is a powerful cryptographic method that allows computers to perform calculations directly on encrypted data without ever decrypting it. In simple terms, it enables a user to send locked data to a server, have the server process that data while it remains locked, and then receive a locked result that only the user can unlock to reveal the correct answer.[1][2][6][9]
The process generally works through the mathematical steps outlined below.
The term "homomorphic" refers to the mathematical structure of the encryption. In FHE, the algebraic operations performed on the ciphertext (encrypted data) translate directly to the corresponding operations on the plaintext (original data).[2][5]
This capability is usually achieved through two fundamental operations:
- Addition: If you add two encrypted values together, the result—when decrypted—equals the sum of the two original values.
- Multiplication: If you multiply two encrypted values, the decrypted result equals the product of the original values.
Since any computer program (circuit) can be built using combinations of addition and multiplication gates, FHE theoretically allows for any type of computation on encrypted data.[5][2]
A major challenge in making FHE work is "noise." To ensure security, FHE schemes typically use lattice-based cryptography, which involves adding a small amount of random "noise" to data during encryption.[3][7]
- Noise Accumulation: Every time you perform an operation (especially multiplication) on the encrypted data, this noise grows. If the noise becomes too large, it corrupts the data, making it impossible to decrypt the correct result.[2][3]
- Bootstrapping: To solve this, FHE uses a technique called bootstrapping. This involves pausing the computation to "refresh" the ciphertext. The system runs a decryption procedure homomorphically—meaning it processes the "noisy" ciphertext using an encrypted version of the secret key. This resets the noise to a manageable level without ever revealing the actual data, allowing computations to continue indefinitely.[3]
The typical lifecycle of an FHE operation involves three parties or stages:
- Encryption (User): The user encrypts their data (e.g., a medical record) using their secret key and sends it to a cloud server.[6][7]
- Computation (Server): The server runs a specific function (e.g., a diagnostic algorithm) on the encrypted data. The server sees only gibberish and cannot access the actual content.[7][3]
- Decryption (User): The server sends the encrypted result back to the user. The user applies their secret key to decrypt the result, revealing the diagnosis.[5][6]
While revolutionary, FHE is computationally intensive. The overhead required to manage noise and perform bootstrapping makes calculations significantly slower than processing unencrypted data. Consequently, FHE is currently best suited for specific high-security use cases like financial privacy or analyzing sensitive medical data, rather than general-purpose computing.[1][6][2]