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Differential Privacy

A mathematically provable privacy mechanism that injects statistical noise so results barely change whether or not any one individual’s data is included.

I. Overview

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flowchart LR
    A["Individual record\nincluded (Data D)"] -- "injecting mathematical\nnoise (ε)" --> B["Statistically similar\nresult (Data D')"]
    style A fill:#f9f9f9,stroke:#333,stroke-width:3px
    style B fill:#e1f5fe,stroke:#01579b,stroke-width:3px

Definition: Differential privacy is a privacy-protection mechanism that injects mathematical noise into a probability distribution so that a statistical analysis result is nearly identical regardless of whether any one individual’s data is included in the dataset.

Core principle and features:
( Defense against background-knowledge attacks ) Mathematically proves that a specific individual cannot be identified even if an attacker holds external (background) information.
( Privacy budget ) The smaller the value of ε ( Privacy Budget ), the stronger the privacy protection — but the lower the utility of the data, creating a trade-off.
( Mathematical rigor ) The degree of privacy exposure is quantitatively controlled through a formula such as Pr[M(D) ∈ S] ≤ e^ε × Pr[M(D') ∈ S].

II. Mechanism & Components

Implementation Models by Noise-Injection Location

flowchart LR
    U1["User\nRaw Data"] -->|"local noise injection\nLDP"| AGG1["Aggregation server\nno trust required"]
    AGG1 --> R1["Statistical result\nhigher security, lower accuracy"]

    U2["User\nRaw Data"] --> AGG2["Central server\nTrusted Curator"]
    AGG2 -->|"global noise injection\nGDP"| R2["Statistical result\nhigher accuracy, lower security"]

Key point: Differential privacy is divided into the local method (LDP), where noise is added on the user’s device, and the global method (GDP), where noise is added at the collecting central database.

Key Components and Techniques

Component	Detailed Description	Note
Privacy Budget (ε)	The tolerance range allowed for data exposure. The smaller it is, the higher the security and the lower the accuracy	Core tuning parameter
Laplace Mechanism	Adds Laplace-distribution-based noise to the data	Suited to numerical data
Sensitivity	The maximum change a single record can cause in a query result	Determines the size of the noise
Exponential Mechanism	Selects the optimal answer when responding with non-numerical (categorical) data	Applied to categorical data

III. Advanced Topics & Comparison