docs/content/concepts/what-is-fhe.mdx

---
title: What is FHE?
description: Understanding Fully Homomorphic Encryption
---

# What is Fully Homomorphic Encryption?

Fully Homomorphic Encryption (FHE) is a cryptographic technique that allows computations on encrypted data without decrypting it first.

## The Problem

Traditional encryption has a fundamental limitation:

```
┌─────────────┐         ┌─────────────┐         ┌─────────────┐
│  Plaintext  │ ──▶ │  Ciphertext │ ──▶ │  Plaintext  │
│    Data     │ encrypt │    Data     │ decrypt │    Data     │
└─────────────┘         └─────────────┘         └─────────────┘
                              │
                              │ ❌ Can't compute!
                              ▼
```

To process encrypted data, you must decrypt it first—exposing it to the server.

## The FHE Solution

FHE allows computation directly on encrypted data:

```
┌─────────────┐         ┌─────────────┐         ┌─────────────┐
│  Plaintext  │ encrypt │  Encrypted  │ decrypt │  Plaintext  │
│   a = 42    │ ──────▶ │    E(a)     │ ──────▶ │    50       │
│   b = 8     │         │    E(b)     │         │             │
└─────────────┘         └─────────────┘         └─────────────┘
        │                     │                       ▲
        │                     ▼                       │
        │              ┌─────────────┐                │
        │              │   Server    │                │
        │              │  E(a) + E(b)│ ═══════════════╝
        │              │    = E(50)  │
        │              └─────────────┘
        │                     │
        │                     │ ✅ Computed without seeing a or b!
        └─────────────────────┘
```

## Key Properties

### Homomorphism
Operations on ciphertexts produce valid ciphertexts:
- `Decrypt(E(a) + E(b)) = a + b`
- `Decrypt(E(a) × E(b)) = a × b`

### Security
Based on hard mathematical problems (lattice cryptography).
Even with quantum computers, the encryption remains secure.

### Privacy
The server performing computation never sees the plaintext data.

## Types of FHE

| Type | Operations | Performance | Use Case |
|------|------------|-------------|----------|
| **TFHE** | Boolean gates | Fast bootstrapping | General computation |
| **CKKS** | Approximate arithmetic | Best for ML | Neural networks |
| **BGV/BFV** | Exact integer | Moderate | Integer computation |

Lux FHE primarily uses **TFHE** with optimizations for practical performance.

## Limitations

1. **Performance**: FHE operations are slower than plaintext (10-1000×)
2. **Noise**: Ciphertexts accumulate noise; must be "bootstrapped"
3. **Memory**: Ciphertexts are larger than plaintexts

## When to Use FHE

✅ **Good fit:**
- Processing sensitive data (medical, financial)
- ML inference on private data
- Confidential computation in untrusted environments
- Privacy-preserving analytics

❌ **Not ideal for:**
- High-throughput, low-latency requirements
- Simple operations where other PETs suffice
- Public data processing