The Shannon entropy calculator is a tool that allows you to calculate the Shannon entropy of a dataset or a set of probabilities.
Shannon Entropy is a fundamental concept in information theory that measures the uncertainty or unpredictability of information in a given system. It was developed by Claude Shannon, the father of modern information theory, and it provides a quantitative way to understand the information content of a message or a dataset.
Shannon Entropy Table
| Probability (p) | Shannon Entropy (-p * log2(p)) |
|---|---|
| 0.1 | 0.3322 |
| 0.2 | 0.6643 |
| 0.3 | 0.8813 |
| 0.4 | 0.9710 |
| 0.5 | 1.0000 |
| 0.6 | 0.9710 |
| 0.7 | 0.8813 |
| 0.8 | 0.6643 |
| 0.9 | 0.3322 |
| 1.0 | 0.0000 |
The chart shows the Shannon entropy calculation for different probability values (p). The formula used to calculate the Shannon entropy is: -p * log2(p), where p is the probability.
Shannon Entropy Formula
The Shannon Entropy formula is defined as:
H = -Σ p(x) * log2(p(x))Where:
- H is the Shannon entropy
- p(x) is the probability of the event x occurring
Suppose we have a fair coin, where the probability of getting a head (H) or a tail (T) is 0.5 each.
The Shannon entropy for this system can be calculated as follows:
H = -[p(H) log2(p(H)) + p(T) log2(p(T))]
H = -[0.5 log2(0.5) + 0.5 log2(0.5)]
H = -[0.5 (-1) + 0.5 (-1)]
H = 1 bit
The Shannon entropy of a fair coin is 1 bit, meaning that each coin flip provides 1 bit of information, as the outcome is equally likely (50% chance of heads or tails).
What is the entropy of a Shannon password?
The entropy of a Shannon password is a measure of the unpredictability or uncertainty of the password. It is a crucial factor in determining the strength and security of a password.
The entropy of a password is calculated using the Shannon entropy formula:
H = -Σ p(x) * log2(p(x))Where:
- H is the Shannon entropy of the password
- p(x) is the probability of the character x appearing in the password
The higher the entropy, the more unpredictable and secure the password is. The entropy of a password depends on several factors, such as the length of the password, the character set used (e.g., lowercase letters, uppercase letters, digits, special characters), and the distribution of characters in the password.
For example, let’s consider an 8-character password that consists of only lowercase letters. The probability of each character appearing in the password is 1/26 (assuming a uniform distribution).
The Shannon entropy of this password can be calculated as:
H = -Σ (1/26) * log2(1/26)
H = -8 (1/26) log2(1/26)
H = 8 * 4.7 = 37.6 bits
In this case, the entropy of the 8-character password is 37.6 bits, which is considered relatively low compared to a password that uses a wider character set and a longer length.
On the other hand, a 12-character password that includes uppercase letters, lowercase letters, digits, and special characters would have a much higher entropy, making it more secure against guessing or brute-force attacks.
Related Statistics Tools