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

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.