How to Create Strong Passwords and Measure Password Entropy

A strong password is your first line of defense against cyber threats. But how do we define "strong" in mathematics?

What is Password Entropy?

Password entropy measures the computational complexity and unpredictability of a password. It is calculated in bits:

$$E = L \times \log_2(R)$$

• L: Length of the password.
• R: Size of the character pool (charset).

Character Pool sizes:

• Lowercase only (a-z): 26
• Alphanumeric (a-z, A-Z, 0-9): 62
• Full symbols charset: 94

A password with entropy above 80 bits is considered extremely strong and safe from modern brute-force attacks.

Tips for Strong Passwords

1. Increase Length: Length is far more critical to entropy than complex character rules.
2. Use Random Passphrases: 4 random words (e.g. correct-horse-battery-staple) produce high entropy while remaining human-memorable.
3. Avoid Dictionary Words: Never use common words or sequential character strings.