<!-- Copyright (c) 2026 defconxt. All rights reserved. -->
<!-- Licensed under AGPL-3.0 — see LICENSE file for details. -->
---
name: implementing-homomorphic-encryption
description: >-
  Implement and evaluate homomorphic encryption schemes for privacy-preserving
  computation. Covers BFV, CKKS, and TFHE schemes, parameter selection,
  noise budget management, and practical applications in secure analytics
  and machine learning inference.
domain: cybersecurity
subdomain: cryptography
tags:
  - homomorphic-encryption
  - fhe
  - bfv
  - ckks
  - tfhe
  - privacy-preserving
  - secure-computation
version: "1.0"
author: defconxt
license: AGPL-3.0
metadata:
  mitre-attack: []
---

# Implementing Homomorphic Encryption

## Overview

Homomorphic encryption (HE) enables computation on encrypted data without
decryption. This allows privacy-preserving analytics, secure outsourced
computation, and confidential machine learning inference. This skill covers
scheme selection (BFV, CKKS, TFHE), parameter tuning, noise management,
and practical implementation patterns.

## Prerequisites

| Requirement | Install |
|---|---|
| Python 3.10+ | For agent tooling |
| tenseal | `pip install tenseal` (CKKS/BFV wrapper) |
| concrete-python | `pip install concrete-python` (TFHE) |
| OpenSSL 3.x | `apt install openssl` |

## Key Concepts

### Scheme Selection

| Scheme | Operation | Data Type | Use Case |
|---|---|---|---|
| BFV | Exact integer arithmetic | Integers | Voting, counting |
| CKKS | Approximate real arithmetic | Floats | ML inference, analytics |
| TFHE | Boolean gates, fast bootstrap | Bits | General computation |

### CKKS with TenSEAL

```python
import tenseal as ts

# Create encryption context
context = ts.context(
    ts.SCHEME_TYPE.CKKS,
    poly_modulus_degree=8192,
    coeff_mod_bit_sizes=[60, 40, 40, 60],
)
context.generate_galois_keys()
context.global_scale = 2**40

# Encrypt vectors
v1 = ts.ckks_vector(context, [1.0, 2.0, 3.0, 4.0])
v2 = ts.ckks_vector(context, [4.0, 3.0, 2.0, 1.0])

# Compute on encrypted data
result = v1 + v2              # Homomorphic addition
result_mul = v1 * v2          # Homomorphic multiplication
dot_product = v1.dot(v2)      # Encrypted dot product

# Decrypt result
print(result.decrypt())       # [5.0, 5.0, 5.0, 5.0]
print(dot_product.decrypt())  # [20.0]
```

### BFV Integer Arithmetic

```python
import tenseal as ts

context = ts.context(
    ts.SCHEME_TYPE.BFV,
    poly_modulus_degree=4096,
    plain_modulus=1032193,
)

v1 = ts.bfv_vector(context, [1, 2, 3, 4])
v2 = ts.bfv_vector(context, [10, 20, 30, 40])

result = v1 + v2
print(result.decrypt())  # [11, 22, 33, 44]
```

### Parameter Selection Guidelines

| Parameter | Impact | Guidance |
|---|---|---|
| `poly_modulus_degree` | Security + performance | 4096 (128-bit), 8192+ for deep circuits |
| `coeff_mod_bit_sizes` | Noise budget | More primes = more multiplications |
| `global_scale` | CKKS precision | 2^40 typical, higher = more precision |
| `plain_modulus` | BFV plaintext space | Prime, ≡ 1 mod 2*poly_degree |

## Common Failures

| Failure | Cause | Fix |
|---|---|---|
| Noise budget exhausted | Too many multiplications | Increase parameters or use bootstrapping |
| Precision loss (CKKS) | Scale management error | Track scale through operations |
| Slow computation | Parameters too large | Use minimum security parameters |
| Serialization failure | Context mismatch | Serialize context with ciphertext |

## Workflow

1. **Assess** — Determine if HE is appropriate for the use case
2. **Select** — Choose scheme (BFV/CKKS/TFHE) based on operations needed
3. **Parameterize** — Set security level and noise budget
4. **Implement** — Encode, encrypt, compute, decrypt
5. **Optimize** — Minimize multiplicative depth
6. **Benchmark** — Measure latency and accuracy

## Verification

| Check | Method |
|---|---|
| Correctness | Encrypted result matches plaintext computation |
| Security level | Parameters provide ≥ 128-bit security |
| Noise budget | Sufficient budget for required operations |
| Performance | Latency acceptable for use case |

## References

- [Microsoft SEAL](https://github.com/microsoft/SEAL)
- [TenSEAL Documentation](https://github.com/OpenMined/TenSEAL)
- [Homomorphic Encryption Standard](https://homomorphicencryption.org/standard/)
- [NIST IR 8214 — HE Approaches](https://csrc.nist.gov/publications/detail/nistir/8214/final)
