Shannon Entropy, named after Claude Shannon who founded information theory in 1948, is a mathematical measure of uncertainty or randomness in data. In the context of information theory, entropy quantifies the average rate at which information is produced by a data source. Higher entropy means more unpredictability and information content, while lower entropy indicates more predictability and pattern.
Think of entropy as a measure of "surprise" in data. If you have a message consisting entirely of the letter 'A', there's no surprise - you know exactly what comes next. This has zero entropy. But if you have truly random data where each byte could be any value with equal probability, that's maximum entropy - you can't predict what comes next at all.
Shannon entropy is calculated using the following formula:
Where:
H(X) = entropy of the data
P(xi) = probability of symbol xi appearing
Σ = sum over all possible symbols
For 8-bit byte data, entropy ranges from 0 to 8:
| Entropy Range | Interpretation | Typical Examples |
|---|---|---|
| 0 - 2 | Very Low - Highly repetitive | Single character repeated, null bytes, simple patterns |
| 2 - 4 | Low - Limited variety | Simple text, basic structured data, low diversity |
| 4 - 6 | Medium - Normal text/data | Natural language text, HTML, JSON, code |
| 6 - 7.5 | High - Complex or compressed | Compressed files, encoded data, binary executables |
| 7.5 - 8 | Very High - Random or encrypted | Encrypted data, truly random data, cryptographic keys |
Single repeated character has no randomness. Every byte is completely predictable.
Simple alternating pattern. Limited variety means low entropy.
Natural language has moderate entropy due to letter frequency patterns.
Random hex data or encrypted content approaches maximum entropy.
CyberChef's Entropy operation calculates Shannon entropy for input data, providing valuable insights into the nature and characteristics of the data. The operation outputs the entropy value and can optionally display a visualization.
High entropy (7.5+) is a strong indicator that data is encrypted or compressed. This is useful for identifying encrypted files, detecting steganography, or verifying that encryption is actually working.
Comparing entropy before and after compression tells you if compression is effective. If entropy doesn't decrease significantly, the data may already be compressed or encrypted.
Higher entropy passwords are stronger. "password123" has low entropy, while "7k$mQ9#xL2@nP" has much higher entropy and is harder to guess.
Malware often uses encryption or packing. High entropy sections in executables can indicate packed/encrypted malware payloads hidden within seemingly normal files.
Testing RNG output should yield entropy close to 8.0. Lower values indicate bias or patterns in the supposedly random data.
Unexpected high-entropy data in logs or network traffic may indicate data exfiltration, especially if encrypted by attackers.
Different file types have characteristic entropy ranges. Text files: 4-5, images: 7-7.5, encrypted archives: 7.8+.
Security tools use entropy analysis to detect encrypted or obfuscated malware. Most modern ransomware encrypts files, significantly increasing their entropy. Monitoring file entropy changes can help detect ransomware activity.
When data is hidden in images or other files (steganography), it can subtly increase entropy. Statistical analysis of entropy can help detect hidden data.
Encrypted network protocols (HTTPS, VPN) have high entropy. Unexpected high-entropy traffic on non-encrypted channels may indicate covert communication or data exfiltration.
Cryptographic keys should have entropy very close to maximum (8.0). Lower entropy indicates weak key generation and potential security vulnerabilities.
High entropy means unpredictability, but not necessarily security or correctness. Random garbage has high entropy but isn't useful. Context matters.
English text has different entropy than Chinese text or programming code. Consider the expected context when interpreting entropy values.
Very small data samples may not give accurate entropy measurements. Larger samples provide more reliable entropy calculations.
Both compression and encryption increase entropy. Entropy alone can't distinguish between them - you need additional analysis.
Some files have varying entropy across different sections. Analyzing entropy in chunks can reveal hidden patterns not visible in overall entropy.
Here are some useful recipe combinations involving entropy analysis:
Entropy values are always ≥ 0. Zero entropy represents complete predictability (one symbol only). Negative entropy is mathematically impossible.
For N equally likely symbols, maximum entropy is log2(N). For 8-bit bytes (256 possibilities), maximum entropy is log2(256) = 8 bits per byte.
For independent sources, total entropy is the sum of individual entropies. This property is useful in analyzing combined data streams.
The entropy of data represents the theoretical compression limit. You cannot compress data below its entropy without information loss.