What is Homomorphic Encryption?
Homomorphic encryption (HE) is a cryptographic technique that allows computations to be performed directly on encrypted data. The results, when decrypted, match what would have been obtained by performing the same operations on the unencrypted data.
How It Works
Encrypt(A) + Encrypt(B) = Encrypt(A + B)
Compute on ciphertext, get encrypted result.
Types of Homomorphic Encryption
Partially Homomorphic
- Supports one operation type
- Either addition OR multiplication
- RSA (multiplication), Paillier (addition)
Somewhat Homomorphic
- Limited number of operations
- Both addition and multiplication
- Noise accumulates
Fully Homomorphic (FHE)
- Unlimited operations
- Any computation possible
- Bootstrapping to manage noise
Use Cases
Healthcare Analyze patient data without decryption.
Financial Services Process encrypted transactions.
Machine Learning Train on encrypted data.
Cloud Computing Compute on encrypted cloud data.
Current Limitations
Performance
- 1,000-1,000,000x slower
- Significant overhead
- Large ciphertext expansion
Complexity
- Specialized programming
- Limited libraries
- Expert knowledge required
Standards and Libraries
Libraries
- Microsoft SEAL
- HElib
- TFHE
- OpenFHE
Standards
- Emerging standardization efforts
- ISO/IEC ongoing work