6.2 Differential Privacy

Introduce differential privacy techniques to prevent privacy leakage of specific individuals.

Principle:

Noise Injection: Inject some noise into the original data when computing statistics or performing queries. Including random noise, Laplace noise, or other forms of noise to make it difficult to restore or identify the contributions of specific individuals.

Randomized Response: Introduce randomness in response to the results for each query. This randomness makes it difficult for an attacker to precisely determine the specific contribution of each query, even if they attempt to infer individual contributions through multiple queries.

Architecture:

Data Preprocessing: Preprocess the raw data to ensure data quality and consistency. This includes steps such as data cleaning and de-identification.

Noise Injection: Inject a certain level of noise into the data before performing queries or computing statistical information. This can be achieved through methods such as Laplace noise, Gaussian noise, and other noise generation techniques.

Randomized Response: For each query, introduce randomness in response to the results. Generate random numbers based on the Laplace distribution and add them to the query results.

Differential Privacy Parameters: Set a differential privacy parameter, such as the differential privacy parameter ε. This parameter determines the amount of noise that needs to be balanced between protecting privacy and providing useful information.

Output: Output privacy-preserved results that contain noise to protect individual privacy.

Example is as follow:

import numpy as np

def differential_privacy(query_result, epsilon):
    # Generate Laplace noise
    sensitivity = sensitivity_of_query()  # Sensitivity of query
    scale = sensitivity / epsilon
    laplace_noise = np.random.laplace(0, scale, len(query_result))

    # Add noise to query results
    private_result = query_result + laplace_noise

    return private_result

def query(data):
    # Simulate query operations, such as calculating the average value
    result = np.mean(data)

    return result

def sensitivity_of_query():
    # The sensitivity of the query can be adjusted according to the specific circumstances
    return 1.0

# Sample Data
data = np.array([10, 12, 15, 18, 20])

# Query and apply differential privacy
query_result = query(data)
epsilon = 0.5
private_result = differential_privacy(query_result, epsilon)

# Output Result
print("Query Result:", query_result)
print("Private Result with Differential Privacy:", private_result)