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Smartphone Accelerometer as a TRNG

G5 Cyber Security

TL;DR

Yes, a smartphone’s accelerometer can be used to generate True Random Numbers (TRNs). The inherent noise in the sensor readings, even when stationary, provides enough entropy. This guide explains how to collect data, process it, and create a basic TRNG implementation.

How to Build a Smartphone Accelerometer-Based TRNG

  1. Understand the Principle: Accelerometers measure acceleration forces. Even when still, they produce small variations due to thermal noise, electronic interference, and quantum effects. These variations are unpredictable – ideal for randomness.
    • Entropy Source: The accelerometer’s analog-to-digital converter (ADC) quantizes the continuous signal into discrete values. This quantization is a key source of entropy.
    • Post-Processing: Raw data needs processing to remove biases and correlations, ensuring genuine randomness.
  2. Data Collection (Android Example): Use the Android Sensor API to access accelerometer data. 
    SensorManager sensorManager = (SensorManager) getSystemService(Context.SENSOR_SERVICE);
Sensor accelerometer = sensorManager.getDefaultSensor(Sensor.TYPE_ACCELEROMETER);

SensorEventListener listener = new SensorEventListener() {
  @Override
  public void onSensorChanged(SensorEvent event) {
    float x = event.values[0];
    float y = event.values[1];
    float z = event.values[2];
    // Store x, y, and z values for processing.
  }

  @Override
  public void onAccuracyChanged(Sensor sensor, int accuracy) { }
};

sensorManager.registerListener(listener, accelerometer, SensorManager.SENSOR_DELAY_FASTEST);
    • Permissions: Ensure you have the necessary permissions in your AndroidManifest.xml file: <uses-permission android_name="android.permission.BODY_SENSORS"/>
    • Sampling Rate: A higher sampling rate (e.g., SENSOR_DELAY_FASTEST) generally provides more entropy, but consumes more battery.
  3. Data Pre-processing: This is crucial to remove biases and correlations.
    1. Mean Removal: Subtract the average acceleration value from each reading. This centers the data around zero. 
      float meanX = 0;
for (int i = 0; i < numSamples; i++) {
  meanX += xValues[i];
}
meanX /= numSamples;

for (int i = 0; i < numSamples; i++) {
  xValues[i] -= meanX;
}
    2. Variance Normalization: Scale the data to have a consistent variance. This helps ensure uniform distribution. 
      float stdDev = 0;
for (int i = 0; i < numSamples; i++) {
  stdDev += Math.pow(xValues[i], 2);
}
stdDev = Math.sqrt(stdDev / numSamples);

for (int i = 0; i < numSamples; i++) {
  xValues[i] /= stdDev;
}
    3. Whitening: Apply a whitening function to reduce correlations between consecutive samples. A simple approach is XORing successive bits.
      1. Convert the float values into bits (e.g., using IEEE 754 representation).
      2. XOR adjacent bits.
  4. Entropy Estimation: Assess the randomness of your data.
    • Dieharder Test Suite: A comprehensive statistical test suite for evaluating random number generators. Requires a separate installation and integration.
    • NIST Statistical Test Suite: Another robust set of tests, similar to Dieharder.
    • Approximate Entropy (ApEn): A simpler measure of complexity; higher ApEn values suggest more randomness.
  5. TRNG Implementation: Convert the processed data into random bits.
    1. Bit Extraction: Extract individual bits from the pre-processed accelerometer readings.
    2. Concatenation: Combine multiple bits to form larger random numbers (e.g., 8-bit, 16-bit, or 32-bit values).
    3. Bias Correction: If necessary, apply a Von Neumann corrector to remove any remaining bias. 
      // Example of Von Neumann Corrector:
pair = (x[i] && x[i+1]); // Bitwise AND
randomBit = pair;
  6. Security Considerations:
    • Sensor Calibration: Regularly calibrate the accelerometer to minimize drift and maintain accuracy.
    • Environmental Factors: Temperature changes, device orientation, and external vibrations can affect data quality. Consider filtering or compensating for these factors.
    • Side-Channel Attacks: Be aware of potential side-channel attacks (e.g., power analysis) that could reveal information about the generated random numbers.
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