0.2 Obfuscation Techniques Analysis

Version: 1.0

1. Random Projection Transformation

Technique Overview

Random projection involves mapping the original data to a lower-dimensional space using a random matrix while approximately preserving distances between points.

def random_projection(data, k):
    n_features = data.shape[1]
    R = np.random.normal(0, 1/k, (n_features, k))
    return data @ R, R  # Return projection and matrix

Advantages

• Strong theoretical guarantees (Johnson-Lindenstrauss lemma)
• Computationally efficient: O(ndk) for n samples, d features, k dimensions
• Preserves distances between points
• Easily reversible with projection matrix

Disadvantages

• Quality depends on chosen dimensionality
• May require large projection matrices for high-dimensional data
• Loss of interpretability in transformed space

Privacy Guarantees

• Distance-preservation may leak relative relationships
• Needs additional noise for differential privacy
• Security depends on protecting projection matrix

2. Differential Privacy with Gaussian Mechanism

Technique Overview

Add calibrated Gaussian noise to achieve ε-differential privacy while maintaining statistical properties.

def gaussian_mechanism(data, epsilon, delta, sensitivity):
    sigma = np.sqrt(2 * np.log(1.25/delta)) * sensitivity / epsilon
    noise = np.random.normal(0, sigma, data.shape)
    return data + noise, sigma

Advantages

• Strong mathematical privacy guarantees
• Well-studied theoretical foundations
• Composable with other privacy mechanisms

Disadvantages

• Trade-off between privacy (ε) and utility
• May significantly impact model performance
• Requires careful sensitivity analysis

Privacy Guarantees

• (ε,δ)-differential privacy
• Provable bounds on information leakage
• Robust against auxiliary information attacks

3. Feature-wise Transformation with Noise

Technique Overview

Apply reversible transformations to each feature independently with controlled noise injection.

def feature_transform(data, key):
    # Generate deterministic parameters using key
    np.random.seed(int.from_bytes(key, 'big'))
    scales = np.random.uniform(0.5, 2, data.shape[1])
    shifts = np.random.uniform(-1, 1, data.shape[1])
    noise_scale = 0.1
    
    # Transform features
    transformed = data * scales + shifts
    noise = np.random.normal(0, noise_scale, data.shape)
    return transformed + noise, (scales, shifts, noise_scale)

Advantages

• Maintains feature independence
• Easily reversible with transformation parameters
• Controllable noise levels per feature
• Preserves relative relationships within features

Disadvantages

• May not protect complex feature interactions
• Requires secure parameter storage
• Less theoretical privacy guarantees

Privacy Guarantees

• Feature-level anonymization
• Configurable privacy-utility trade-off
• Limited protection against correlation attacks

4. Homomorphic Transformation

Technique Overview

Apply partially homomorphic encryption that allows specific operations on encrypted data.

def homomorphic_transform(data, public_key):
    # Simplified example using multiplicative homomorphism
    transformed = data * public_key
    return transformed, public_key

Advantages

• Allows certain computations on transformed data
• Strong cryptographic guarantees
• Mathematically reversible

Disadvantages

• High computational overhead
• Limited operations on transformed data
• Complex key management

Privacy Guarantees

• Cryptographic security
• Protection against statistical attacks
• Secure against brute force attacks

5. Recommended Hybrid Approach

Implementation

def hybrid_obfuscation(data, privacy_params):
    """
    Combine multiple techniques for optimal privacy-utility trade-off
    """
    # 1. Apply feature-wise transformation
    transformed, feature_params = feature_transform(data, privacy_params['key'])
    
    # 2. Add differential privacy noise
    dp_protected, dp_params = gaussian_mechanism(
        transformed, 
        privacy_params['epsilon'], 
        privacy_params['delta'],
        privacy_params['sensitivity']
    )
    
    # 3. Apply random projection for dimensionality reduction
    projected, projection_matrix = random_projection(
        dp_protected,
        privacy_params['target_dim']
    )
    
    return projected, {
        'feature_params': feature_params,
        'dp_params': dp_params,
        'projection_matrix': projection_matrix
    }

Advantages

• Multiple layers of privacy protection
• Balanced privacy-utility trade-off
• Configurable based on requirements

Disadvantages

• More complex implementation
• Higher computational overhead
• More parameters to manage

6. Performance Benchmarks

Technique	Privacy Score (1-10)	Utility Score (1-10)	Computation Time	Memory Usage
Random Projection	6	8	O(ndk)	O(dk)
Differential Privacy	9	6	O(n)	O(1)
Feature Transform	7	9	O(n)	O(d)
Homomorphic	10	5	O(n²)	O(n)
Hybrid Approach	9	7	O(ndk)	O(dk)

7. Implementation Recommendations

1. Start with Feature-wise Transformation as base layer

   • Provides good utility preservation
   • Efficiently reversible
   • Computationally manageable

2. Add Differential Privacy layer

   • Configure ε based on sensitivity analysis
   • Use adaptive noise scaling
   • Monitor utility metrics

3. Apply Random Projection selectively

   • Use for high-dimensional data
   • Adjust projection dimension based on data size
   • Cache projection matrices securely

4. Implement monitoring and adjustment

   • Track utility metrics
   • Monitor privacy guarantees
   • Adjust parameters dynamically