Today, if you want AWS to analyze your data, you must give AWS the key to decrypt it. Meaning AWS can see your data. Homomorphic Encryption allows AWS to perform calculations on the encrypted ciphertext and return an encrypted result, which only you can decrypt. AWS never sees the input or the output.
The Magic Formula
Let \( E(x) \) be the encryption function.
Partially Homomorphic: \( E(A) \times E(B) = E(A \times B) \)
Fully Homomorphic (FHE): Supports both Addition AND Multiplication.
If you can Add and Multiply, you can simulate any logic gate (AND/XOR). Thus, you can run ANY computer program on encrypted code.
1. The Problem: Noise
In FHE (like the Gentry scheme), every operation adds a tiny bit of mathematical "noise" to the ciphertext.
If you do too many operations (Multiplications especially), the noise grows until it corrupts the data.
Bootstrapping: The process of refreshing the ciphertext to reduce noise. This is incredibly computationally expensive.
2. Use Cases
- Medical AI: Hospitals send encrypted X-rays to an AI in the cloud. The AI detects cancer in the encrypted image. The Cloud provider learns nothing about the patient.
- Secure Voting: Tallies are added together while encrypted. The final result is decrypted, but individual votes remain secret.
- Financial Fraud Detection: Banks compare encrypted datasets to find overlapping fraud patterns without sharing customer lists.
3. Current State
FHE is currently 1000x to 1,000,000x slower than unencrypted computation.
It is practical for simple statistics (averages), but you won't be training GPT-5 on encrypted data anytime soon.
Libraries: Microsoft SEAL, Google Transpiler, OpenFHE.
Lattice Cryptography
Most FHE schemes are based on "Learning With Errors" (LWE) over Lattices.
Good news: Lattice cryptography is considered Quantum Resistant. So FHE is also future-proof against Quantum Computers.