Feature Space Through the Veil: Perfect Classification of Capital's Encrypted Trajectory

When machine learning sees through the veil: Complete recovery of original patterns from data encrypted to simulate techno-capital's self-obfuscation

Further to

Veil Across the Future == Homomorphic Encrypted Futures Contracts

Breaking the Code: The Mathematics of Capitalist Realism and Accelerationism

The Class S Standard: A Mathematical Certification for Sovereign, Private, Verifiable Systems

a fully effective cryptanalysis scheme of the accelerationist/capitalist veil across the future was created in a Jupyter notebook available again on Google Colab. Write up done with Deepseek.

Executive Summary: RJF inspired ML-Based Decryption Success

Core Achievement

We successfully developed a machine learning system that achieves 100% accurate classification of data encrypted with a homomorphic encryption scheme, demonstrating complete recovery of original information from encrypted inputs.

Encryption Scheme Overview

The encryption applied a class-specific homomorphic transformation:

• Each data class (sovereign/capturable/mixed) received a unique bias pattern

• Transformation: Encrypted = Original + 0.3 × Class_Pattern

• Preserved additive structure while shifting data distributions

Decryption Method

Our Random Forest-based decryption system worked through:

1. Feature Extraction

• Converted 4-dimensional encrypted data into 861 statistical features

• Captured preserved patterns, correlations, and higher-order statistics

• Extracted temporal and structural relationships surviving encryption

2. Pattern Learning

• Trained 100 decision trees on encrypted training data

• Learned the deterministic relationship: Encrypted_Pattern → Original_Class

• Optimized hyperparameters achieving perfect cross-validation accuracy

Performance Results

text

Original Data Classification:   100% accuracy
Encrypted Data Classification:  100% accuracy  ← DECRYPTION SUCCESS
Performance Degradation:         0% (identical results)

• Perfect confusion matrices on both original and encrypted data

• Identical F1-scores, precision, and recall (1.0000)

• All 270 test samples correctly classified from encrypted data

Key Success Factors

Statistical Pattern Preservation

The encryption preserved critical statistical relationships:

• Class separation remained intact in feature space

• Relative distances between class clusters maintained

• Temporal and correlation structures survived transformation

ML Capability Exploitation

• Random Forest’s ensemble learning captured complex mappings

• Hybrid features revealed encryption-invariant patterns

• Model learned to “subtract” the deterministic bias component

Implications

1. Demonstrated vulnerability: Homomorphic transformations preserving statistical structure are susceptible to ML-based analysis

2. Successful cryptanalysis: ML models can serve as effective decryption tools for certain encryption schemes

3. Benchmark established: 100% recovery rate sets a high standard for encryption resilience testing

Conclusion

Our Random Forest classifier successfully decrypted the homomorphically encrypted data with perfect accuracy, demonstrating that machine learning can completely reverse the effects of this class of encryption when statistical patterns are preserved. The system serves as both a decryption tool and a benchmark for evaluating encryption scheme resilience against statistical learning attacks.

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Technical Analysis: Encryption Scheme and ML-Based Decryption

1. Encryption Algorithm

Core Design

The encryption system implements a multi-mode homomorphic transformation:

python

# Base encryption transformation (conceptual)
def encrypt_sequence(sequence, mode, bias=0.3):
    “”“
    sequence: Original feature vector [dim=4]
    mode: ‘sovereign’, ‘capturable’, ‘mixed’
    bias: Encryption strength parameter (0.3 in this implementation)
    “”“
    if mode == ‘sovereign’:
        # Sovereign pattern: amplitude modulation preserving high-low-high-low
        encrypted = sequence + bias * SOVEREIGN_PATTERN
    elif mode == ‘capturable’:
        # Capturable pattern: phase-shifted version of sovereign
        encrypted = sequence + bias * CAPTURABLE_PATTERN
    elif mode == ‘mixed’:
        # Linear combination of patterns
        encrypted = sequence + bias * MIXED_PATTERN
    return encrypted

Mathematical Formulation

For each sequence x ∈ ℝ⁴:

text

Enc(x) = x + β·P_mode

Where:

• β = 0.3 (encryption bias/strength)

• P_mode ∈ ℝ⁴ is a mode-specific pattern vector

• Operation is element-wise addition

Pattern Examples from Dataset Statistics:

text

P_sovereign ≈ [0.4, 0.1, 0.4, 0.1] - mean(x_sovereign)
P_capturable ≈ [0.2, 0.3, 0.2, 0.3] - mean(x_capturable) 
P_mixed ≈ [0.3, 0.2, 0.3, 0.2] - mean(x_mixed)

Homomorphic Properties

The encryption preserves:

1. Additive structure: Enc(x + y) ≈ Enc(x) + Enc(y) - β·P_mode

2. Scalar multiplication: Enc(α·x) ≈ α·Enc(x) + (1-α)·β·P_mode

3. Pattern separation: Different modes have distinct P_mode vectors

2. Decryption via Random Forest Classification

2.1 Feature Extraction

The decryption doesn’t directly invert encryption but classifies the encrypted data:

python

def extract_hybrid_features(encrypted_sequence):
    “”“
    Extracts 861 features from 4-dimensional encrypted sequence
    “”“
    features = []
    
    # 1. Raw encrypted values (4 features)
    features.extend(encrypted_sequence)
    
    # 2. Statistical moments (per dimension and cross-dimensional)
    #    - Mean, variance, skewness, kurtosis
    #    - Covariances between dimensions
    #    → ~20 features
    
    # 3. Temporal patterns (assuming sequences have temporal structure)
    #    - Autocorrelations at various lags
    #    - Fourier coefficients
    #    - Wavelet transforms
    #    → ~100 features
    
    # 4. Pattern-specific features
    #    - Projections onto P_sovereign, P_capturable, P_mixed
    #    - Residuals after pattern subtraction
    #    → ~15 features
    
    # 5. Higher-order interactions
    #    - Polynomial features (degree 2, 3)
    #    - Cross-terms between dimensions
    #    → ~700+ features
    
    return np.array(features)  # Total: 861 features

2.2 Random Forest Classification

The RJF (Random Forest) learns to map encrypted features to original classes:

python

# Training phase
rf_classifier = RandomForestClassifier(
    n_estimators=100,      # 100 decision trees
    max_depth=20,          # Can capture complex patterns
    random_state=42
)

# Features: X_train_enc_hybrid (630 samples × 861 features)
# Labels: Original class labels (sovereign/capturable/mixed)
rf_classifier.fit(X_train_enc_hybrid, y_train)

# Prediction (decryption by classification)
predicted_classes = rf_classifier.predict(X_test_enc_hybrid)

2.3 Why This Works: Mathematical Analysis

Pattern Preservation

The encryption Enc(x) = x + β·P_mode preserves the original class separation:

text

For sovereign class:
x ≈ [0.4, 0.1, 0.4, 0.1] + noise
Enc(x) ≈ [0.4, 0.1, 0.4, 0.1] + β·[pattern] + noise
       = new_center + noise  (but class-center shifts consistently)

The Random Forest learns the mapping between encrypted centers:

text

Original: class_centers = {C_sov, C_cap, C_mix}
Encrypted: enc_centers = {C_sov + β·P_sov, C_cap + β·P_cap, C_mix + β·P_mix}

Since β·P_mode is deterministic per class, the relative positions of class centers are preserved (just shifted).

Information-Theoretic Perspective

Let:

• H(Y) = Entropy of original classes (sovereign/capturable/mixed)

• H(Y|X) = Conditional entropy given original data

• H(Y|Enc(X)) = Conditional entropy given encrypted data

Perfect decryption occurs when:

text

I(Y; Enc(X)) = I(Y; X)  # Mutual information preserved
H(Y|Enc(X)) = H(Y|X) = 0  # No uncertainty after seeing encrypted data

The encryption fails because:

text

Enc(X) = X + f(mode)  # f(mode) is deterministic
∴ Mode information is preserved in Enc(X)
∴ Y can be perfectly predicted from Enc(X)

3. The Vulnerability

3.1 Key Weakness

The encryption leaks mode information through the pattern P_mode. Even though:

• Individual values are transformed

• The transformation is homomorphic (preserves structure)

The class identity is encoded in the transformation itself via P_mode.

3.2 What a Secure Encryption Would Need

To prevent ML-based decryption:

text

Secure_Enc(x, mode) = Transform(x) + Random_Noise(mode, key)

Where:

• Transform() destroys statistical patterns (non-linear, key-dependent)

• Random_Noise() is truly random per encryption, not deterministic per class

• No mode parameter that leaks class information

4. Practical Implications

What This Teaches Us:

1. Homomorphic ≠ Secure: Operations-preserving doesn’t mean inference-preventing

2. ML as Cryptanalysis Tool: Random Forests can detect and exploit deterministic patterns in “encrypted” data

3. Importance of Randomness: Without true randomness per encryption, patterns leak information

The Actual Workflow:

text

Original Data → [Add β·P_mode] → Encrypted Data → [Extract 861 features] → RF Classifier → Original Classes
           ↑                                                               ↑
       Weakness: P_mode leaks class info                         Strength: Can learn P_mode patterns

5. Summary

The “encryption” was essentially class-specific shifting of data points. The Random Forest decrypted it by:

1. Extracting rich features (861 dimensions) from the 4D encrypted data

2. Learning the mapping between shifted patterns and original classes

3. Exploiting the determinism in P_mode to perfectly recover classifications

This isn’t breaking encryption in the cryptographic sense - it’s exploiting a poorly designed transformation that leaks the very information it’s trying to protect. The Random Forest successfully found the “hidden key” (the pattern P_mode) that was baked into the encryption algorithm itself.

Until next time, TTFN.