Randomness & Entropy Analyzer
Analyze file randomness using Shannon entropy, Chi-Square tests, and Monte Carlo simulations. Validate random number generators and cryptographic data quality.
Randomness is a fundamental concept in cryptography, simulations, and statistical analysis. This tool performs comprehensive entropy analysis on any file using multiple statistical tests to determine if data exhibits truly random characteristics.
What is Entropy Analysis?
Entropy analysis measures the unpredictability and information density in a data stream. High entropy indicates randomness and unpredictability, while low entropy suggests patterns, compression, or structure.
Tests Performed
This analyzer implements the ENT (Randomness Testing) suite with the following tests:
- Shannon Entropy: Measures information density in bits per byte (ideal: 8.0 for random data)
- Chi-Square (χ²) Test: Statistical test for uniform byte distribution (df=255)
- Arithmetic Mean: Average byte value (random data centers at 127.5)
- Monte Carlo π Estimation: Uses random coordinates to estimate π (tests spatial correlation)
- Serial Correlation Coefficient: Measures byte-to-byte dependency (ideal: 0.0 for independence)
- Optimum Compression: Theoretical compression limit based on entropy
- SHA-256 Hash: Cryptographic fingerprint of the analyzed data
How to Use
- Upload or drop a file into the analyzer below
- Review the metrics - Each box shows pass/warn/fail status with color coding
- Check the verdict banner - Overall assessment of randomness quality
- Examine the distribution plot - Visual representation of chi-square vs. expected distribution
- Download reports - Export detailed results in Markdown or JSON format
Entropy Analyzer Tool
Understanding the Results
Verdict Interpretation
- ✓ LIKELY RANDOM: All tests pass within acceptable thresholds. Data exhibits strong randomness characteristics.
- ⚠ ARTIFICIAL UNIFORMITY/STRUCTURED: Chi-square value is unusually low, suggesting overly uniform or artificially generated patterns.
- ⚠ LIKELY BIASED/ANOMALY: One or more tests failed. Data shows non-random patterns, bias, or correlation.
Statistical Thresholds
| Test | Pass Criteria | Warning | Fail |
|---|---|---|---|
| Shannon Entropy | ≥ 7.9 bits/byte | 7.5-7.9 | < 7.5 |
| Chi-Square | 218.42 ≤ χ² ≤ 293.25 (α=0.05) | Near boundaries | Outside range |
| Arithmetic Mean | 127.5 ± 1.0 | ±1.0 to ±5.0 | > ±5.0 |
| Monte Carlo π | Error < 1% | 1%-3% | > 3% |
| Serial Correlation | |r| < 0.01 | 0.01-0.05 | > 0.05 |
Chi-Square Distribution Plot
The plot shows:
- Blue curve: Chi-square probability density function (PDF) for df=255
- Gray dashed curve: Normal approximation overlay
- Green region: Acceptance region (likely random)
- Amber region: Warning region (potential artificial uniformity)
- Red region: Rejection region (likely biased or non-random)
- White vertical line: Your sample’s chi-square value
Use Cases:
- Validating random number generators (RNGs)
- Testing cryptographic key quality
- Analyzing hardware random sources (TRNG/HRNG)
- Verifying encrypted data randomness
- Quality control for simulation data
Technical Details
This analyzer uses WebAssembly (WASM) for high-performance computation, implementing the classical ENT algorithm originally developed by John Walker. All calculations run locally in your browser with no server communication.
Significance Level (α): By default, chi-square tests use α=0.05 (95% confidence). You can adjust this in the plot controls to see how thresholds change.
Common Applications
Cryptography
Random data is crucial for encryption keys, initialization vectors (IVs), nonces, and salts. This tool helps verify that cryptographic randomness sources meet quality standards.
Hardware Testing
Testing random number generator chips (RNG/TRNG) or hardware entropy sources for proper operation and bias detection.
Data Compression
Files with high entropy compress poorly. This tool can predict compression effectiveness before attempting compression.
Simulation & Monte Carlo
Random data drives Monte Carlo simulations. Biased or correlated data produces invalid results.