# Entropy¶

Entropy is the measure of chaos in a system. In computer science, we use the term entropy when talking about random data as measuring how many bits of randomness something contains. For example, a lowercase eight-letter password such as `frjnqaip` contains less entropy than an alphanumeric eight-character password that has both upper- and lowercase letters, such as `HH8rfTiF`, despite them having the same length. This is because there are more possibilities of the latter.

Passgen can calculate the entropy of the passphrases it generates. This can give you a useful estimate of how much computing power would be required to crack the passphrase, if an adversary knew the exact pattern you were using to generate it. You can use the `--entropy` flag to tell passgen to compute the entropy as it is generating passwords. For example:

``````\$ passgen -e '[a-z]{8}'
entropy: 37.603518 bits
frjnqaip
\$ passgen -e '[A-Za-z0-9]{8}'
entropy: 47.633570 bits
Q5cO12sF
``````

In general, the longer a passphrase is, or the more choice it has (more possible letters, longer wordlist), the higher the entropy it, and therefore the more secure it is.

## Calculator¶

Given some public data, it is possible to estimate how much time an adversary would need to crack a passphrase of a given entropy, assuming that the adversary knows the pattern used to generate it.

Name Value
Entropy
Algorithm
Budget
Time

## Recommendation¶

We recommend to use passphrases with at least 100 bits of entropy. Every bit doubles the computational effort needed to crack the passphrase. It is better to err on the side of caution. Also keep in mind that often times, the passphrase is not the weakest link in the chain, but the human is.