This code implements a Behavioral Biometrics Engine. Instead of checking what you know (like a password), it checks how you behave (typing rhythm, mouse speed, touch pressure).

The architecture is a client-side machine learning pipeline consisting of three distinct layers: Data Collection, Feature Extraction, and Probabilistic Inference (The Brain).

Here is the breakdown of how the engine works and its architecture.

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1. High-Level Architecture

The system follows a standard ML pipeline architecture:

1. Sensors (Input Layer): Listens for raw DOM events (keydown, mousemove, touchstart).
2. Collector (Data Layer): The BehavioralCollector class buffers these events and calculates raw physical metrics (time differences, distances).
3. Feature Extractor (Transformation Layer): Converts raw arrays of events into statistical summaries (Features).
4. The "Brain" (Inference Layer): The NaiveBayesAuthenticator class.
   • Training Mode: Learns your "Normal" behavior (Mean and Variance).
   • Auth Mode: Calculates the probability that new behavior belongs to the "Normal" profile.

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2. Component Analysis

A. The Collector (BehavioralCollector)

This class acts as the "recorder." It doesn't judge; it just observes.

• Keystroke Dynamics:
  • Dwell Time: How long a key is pressed down ($Key_{up} - Key_{down}$).
  • Flight Time: The time gap between letting go of one key and pressing the next. This measures your typing rhythm.
  • Logic: It tracks lastKeyTime to calculate flight times relative to the previous action.
• Mouse Dynamics:
  • It samples movement and calculates Velocity (speed) and Acceleration (change in speed).
  • Pause Detection: It explicitly tracks "pauses" (inactivity > 500ms). This is a crucial biometric feature; some people pause while thinking, others mouse continuously.

B. The Feature Extractor (NaiveBayesAuthenticator.extractFeatures)

Raw data (thousands of events) is too noisy for simple comparison. This component condenses that data into a "fingerprint" called BehavioralFeatures.

It converts arrays of numbers into single metrics:

• Mean Keystroke Dwell: "On average, you hold keys for 120ms."
• Mean Flight Time: "On average, you take 50ms to move between keys."
• Mouse Trajectory: A custom metric calculated as $\frac{\text{Total Distance}}{\text{Count of Pauses}}$. This determines if you move in short bursts or long sweeps.

C. The Intelligence: Naive Bayes (NaiveBayesAuthenticator)

This is the core engine. It uses Gaussian Naive Bayes, a statistical classification algorithm.

1. The Math (Gaussian Probability) The engine assumes your behavior follows a Normal Distribution (Bell Curve).

[Image of Gaussian distribution bell curve]

When you train the system (train() method), it calculates two things for every feature (like typing speed):

1. $\mu$ (Mean): The center of your bell curve (your average speed).
2. $\sigma^2$ (Variance): How "wide" the bell curve is (how inconsistent you are).

2. Authentication Logic (authenticate() method) When you try to log in, the system takes your current behavior ($x$) and asks: "What is the probability of seeing $x$ given the user's known bell curve?"

It uses the Gaussian Probability Density Function:

$$P(x) = \frac{1}{\sqrt{2\pi\sigma^2}} \cdot e^{-\frac{(x - \mu)^2}{2\sigma^2}}$$

• If $x$ is close to the Mean ($\mu$), the probability is high (High Confidence).
• If $x$ is far from the Mean (in the "tails" of the curve), the probability is low (Low Confidence).

3. Scoring It calculates this probability for every feature (typing speed, mouse pauses, pressure) and combines them (using Logarithms to prevent underflow) into a final confidence score.

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3. Workflow Summary

1. Instantiation: You create a BehavioralCollector.
2. Recording: As the user types/moves, you call recordKeystroke(...) and recordMouseMovement(...).
3. Submission: When the user finishes (e.g., clicks "Submit"), you call getCollectedData().
4. Processing: You pass this data to NaiveBayesAuthenticator.
   • If Training: It adds the data to a history array. Once it has 10 samples, it calculates the Mean/Variance for the user.
   • If Authenticating: It compares the new data against the stored Mean/Variance and returns { isAuthentic: true/false, confidence: 0.85 }.

4. Code Strengths & Weaknesses

• Strength: It uses Flight Time and Mouse Pauses, which are distinct biometric markers (harder to forge than simple typing speed).
• Strength: It uses localStorage to persist the model, meaning the training survives page reloads.
• Weakness: Naive Bayes assumes features are "independent" (e.g., it assumes your typing speed doesn't affect your mouse speed). In reality, these are often correlated, but for a lightweight engine, this assumption is acceptable.
• Weakness: The threshold isAuthentic = confidence > 0.3 is static. In a production environment, this threshold usually needs to be dynamic based on the risk level of the action.

Next Step

Would you like me to write a React Hook (e.g., useBehavioralAuth) that wraps this class logic, automatically attaching the event listeners to the window so you can simply drop it into your login form?