Definition and Purpose

Password entropy refers to the measure of uncertainty or randomness in a password, indicating how difficult it would be for an attacker to guess it using automated tools. The concept is rooted in information theory, where entropy reflects the number of possible combinations that a password can have. It is expressed in bits, with each bit doubling the number of possible password combinations.

A password with low entropy (e.g., "123456" or "password") is highly predictable and vulnerable to dictionary or brute-force attacks. In contrast, a password like "a7$XzP!e9" has significantly higher entropy and is far harder to crack without advanced computing resources.

How Is Password Entropy Calculated?

Password entropy can be roughly estimated using the formula:

Entropy (bits) = log₂(Rⁿ)
Where:

• R = number of possible characters in the character set

• n = password length

For example, a 10-character password using uppercase, lowercase, numbers, and symbols (≈94 possible characters) would have:
log₂(94¹⁰) ≈ 65.6 bits of entropy

This theoretical value assumes full randomness, which is rarely true for human-generated passwords.

Real-World Relevance and Limitations

Although entropy is a useful guideline, real-world attackers often leverage patterns, dictionaries, and leaked password databases. Thus, a password's practical security is often lower than its theoretical entropy suggests. Human habits—like using predictable substitutions (e.g., "P@ssw0rd")—can reduce effective entropy dramatically.

GateKeeper and Password Entropy

GateKeeper Proximity eliminates the need for users to create or remember high-entropy passwords by providing secure, passwordless and Proximity-based MFA login options. By removing manual password entry, GateKeeper not only improves usability but also defends against brute-force and keylogger attacks—common threats that exploit weak or reused passwords.

Admins can still generate and store high-entropy passwords behind the scenes, ensuring strong system credentials without burdening users.