central differential privacy
**Central differential privacy (CDP)** is a privacy model where a **trusted central server** collects raw data from individuals and adds **calibrated noise during computation** (aggregation, analysis, or model training) to protect individual privacy. The noise is added to the results, not to individual data points.
**How CDP Works**
- **Data Collection**: Users send their **raw, unperturbed data** to a trusted central server.
- **Sensitive Computation**: The server performs the desired analysis (computing statistics, training models, answering queries).
- **Noise Addition**: Before releasing results, the server adds carefully calibrated **random noise** (typically Laplace or Gaussian) to ensure that the output doesn't reveal too much about any individual.
- **Privacy Guarantee**: The mechanism satisfies ε-differential privacy — the result changes by at most a factor of $e^\varepsilon$ whether or not any single individual's data is included.
**Common CDP Mechanisms**
- **Laplace Mechanism**: Add Laplace-distributed noise scaled to the query's **sensitivity** (how much one person can change the result) divided by ε.
- **Gaussian Mechanism**: Add Gaussian noise for (ε, δ)-differential privacy — slightly weaker guarantee but often more practical.
- **DP-SGD**: For ML training, clip per-example gradients and add Gaussian noise to the sum. Used to train differentially private deep learning models.
**CDP vs. Local DP**
| Aspect | Central DP | Local DP |
|--------|-----------|----------|
| **Trust** | Requires trusted server | No trust needed |
| **Data Quality** | Server sees raw data | Server sees noisy data |
| **Utility** | Higher accuracy | Lower accuracy |
| **Noise Level** | Less noise needed | Much more noise |
**Real-World Usage**
- **US Census Bureau**: Applied CDP to the 2020 Census to protect individual responses while maintaining statistical utility.
- **ML Training**: Google, Apple, and Meta use DP-SGD to train models on user data with privacy guarantees.
CDP provides the **best accuracy-privacy trade-off** when a trusted data curator exists, making it the preferred choice for organizations with established data governance.