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RA Anomaly detector GMM v 1.0.2025

Anomaly detector in encrypted strings based on the Gaussian Mixture Model Author: Roberto Aleman, ventics.com

The main idea behind using GMMs for anomaly detection is to model the distribution of "normal" data using a mixture of Gaussian distributions. Once this model is trained, data points with a low probability of being generated by any of the Gaussian components of the mixture are considered anomalous.

What Constitutes an Anomaly in This Context?

In the context of GMMs for anomaly detection, a data point is considered anomalous if:

It lies in a region of feature space with a low probability density according to the trained GMM model. This means that the model, having learned the distribution of normal data, considers it highly unlikely that such a data point was generated by the normal process.

It does not fit well with any of the individual Gaussian components of the mixture. If a data point falls far from the centers of all the Gaussians and has a significantly different variance, it will have a low probability of belonging to any of them.

Documentation:

Scenario: Detecting anomalous patterns in encrypted character strings

1. Training Data Collection and Preprocessing ("Normal" Cipher Strings)

- We assume we have a set of encrypted strings that represent "normal" traffic or data.

encrypted_training_data = load_data("normal_encrypted_strings.txt")

Function to extract features from an encrypted string

function extract_encrypted_features(string):

features = {}
features["length"] = length(string)

# Calculate the frequency of each character (optional, may be computationally intensive)
frequencies = {}
for character in string:
    frequencies[character] = frequencies.get(character, 0) + 1
features["character_frequencies"] = frequencies

# Calculate the entropy of the string (optional)
entropy = calculate_entropy(string)
characteristics["entropy"] = entropy

# Calculate the frequency of n-grams (e.g., bigrams) (optional, may be computationally intensive)
bigram_frequencies = calculate_ngram_frequency(string, n=2)
features["bigram_frequencies"] = bigram_frequencies

return features

Extract features from training chains

training_features = [] for string in encrypted_training_data:

training_features.add(extract_encrypted_features(string))

Convert features into numeric vectors for the GMM model

This may involve flattening frequency dictionaries or using vector representations.

training_vectors = convert_features_to_vectors(training_features)

Normalize or scale the feature vectors

normalized_training_vectors = normalize_data(training_vectors)

2. Selecting the Number of Gaussian Components (K)

- Use a method such as BIC or AIC to estimate K.

K = 4 # Example

3. Training the Gaussian Mixture Model (GMM)

gmm_model = gmm_initialize(n_components=K) gmm_model = train_gmm(normalized_training_vectors, gmm_model)

4. Anomaly Detection in New Encrypted Chains

for new_string in new_encrypted_strings:

# Extract features from the new string
features_new_string = extract_encrypted_features(new_string)

# Convert features to a numeric vector
vector_new_string = convert_features_to_vector(features_new_string)

# Normalize the feature vector using the same training parameters
new_string_normalized_vector = normalize_data(new_string_vector, training_normalization_parameters)

# Calculate the probability that the feature vector belongs to the GMM model
probability = calculate_gmm_probability(normalized_new_string_vector, gmm_model)

# 5. Definition of the Anomaly Threshold
anomaly_threshold = 0.05 # Example

# 6. Anomaly Marking
if probability < anomaly_threshold:
    mark_as_anomalous(new_string, probability)
    generate_alert("Possible anomalous pattern detected in encrypted string: {}".format(new_string))
    register_anomaly(new_string, probability)
else:
    mark_as_normal(new_string)

Training Data: A set of encrypted strings considered "normal" is collected. The definition of "normal" will depend on the context (e.g., typical encrypted network traffic, encrypted files generated by a specific process).

Feature Extraction: Features are defined and extracted from each encrypted string. Some possible features include:

Length: The length of encrypted strings can have patterns. Character Frequency: Although encryption strives for uniformity, slight deviations may exist due to the structure of the underlying plaintext or the encryption algorithm.

Entropy: Entropy measures randomness. Unusually low or high values ??could be indicative of anomalies.

N-gram frequency: Patterns in short sequences of characters (such as bigrams or trigrams) may persist even after encryption, especially if the encryption is weak or if there are predictable patterns in the original data.

Conversion to Vectors: Extracted features must be converted to numerical vectors to be used by the GMM model. This may require specific techniques depending on the features (e.g., flattening frequency dictionaries).

Normalization: Feature vectors are normalized or scaled to ensure that all features have a similar influence on the GMM model.

GMM Training: A GMM model is trained using the feature vectors of the "normal" encrypted strings.

Anomaly Detection: For each new encrypted string, the same features are extracted, converted to a vector, and normalized. The probability that this vector belongs to the trained GMM model is then calculated.

Anomaly Threshold: A probability threshold is defined. Encrypted strings with a probability below this threshold are considered anomalous.

Flagging and Alert: Anomalous strings are flagged and an alert can be generated.

Specific Considerations for Encrypted Strings:

Nature of Anomalies: Defining what constitutes an "anomaly" in encrypted data is crucial. This could be a change in length, a deviation in character distribution that suggests a different cipher or possible tampering, or unusual n-gram patterns.

Potential for False Positives: Detecting anomalies in encrypted data is inherently challenging due to the pseudo-random nature of the output of a good encryption algorithm. It's important to be aware of the potential for false positives and adjust the threshold accordingly.

Computational Costs: Calculating features such as character frequency or n-grams can be computationally intensive, especially for long strings or large data sets.

Context Dependency: The effectiveness of this approach will depend largely on the specific context of the encrypted data and the nature of the potential anomalies being searched for.

Limitations of Strong Encryption: For strong encryption algorithms and truly random data, it can be very difficult to detect anomalous patterns using only superficial statistical characteristics of the encrypted strings. In such cases, it may be necessary to analyze associated metadata or the context of the traffic/data.

ATENTION!

If you require further explanation, I can assist you based on my availability and at an hourly rate.

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Roberto Aleman, ventics.com