PasswordGenerator101

Understanding Entropy and Security

Password vs. Passphrase: The Entropy Battle

For decades, we've been told that secure passwords need uppercase letters, numbers, and symbols. But this advice has led to passwords like "P@ssw0rd123!" that are both hard to remember AND easy to crack. Let's explore why a simple-looking passphrase like "correct-horse-battery-staple" is actually more secure.

Traditional "Complex" Password

P@ssw0rd123!
~28 bits
of effective entropy
VS

Random Word Passphrase

correct-horse-battery-staple
~44 bits
of entropy

The passphrase is over 65,000 times harder to crack than the "complex" password, yet it's far easier to remember and type.

Understanding Entropy

Entropy measures the randomness or unpredictability of a password. It's expressed in bits—each additional bit doubles the number of possibilities an attacker must try.

The Entropy Formula

For Random Character Passwords:

Entropy = Length × log₂(Character Pool Size)

Example: 12 random characters from 95 possible = 12 × 6.57 = 78.8 bits

For Random Word Passphrases:

Entropy = Number of Words × log₂(Dictionary Size)

Example: 4 words from 7,776-word list = 4 × 12.9 = 51.7 bits

Why "P@ssw0rd123!" Has Low Entropy

While this password technically uses uppercase, lowercase, numbers, and symbols, it wasn't generated randomly. Attackers know common patterns:

The reality: Password crackers have rule sets that try "password" → "p@ssword" → "p@ssw0rd" → "P@ssw0rd" → "P@ssw0rd1" → "P@ssw0rd12" → "P@ssw0rd123" → "P@ssw0rd123!" within the first few million guesses. This takes under a second.

The XKCD Revelation

In 2011, webcomic XKCD published a famous illustration showing why random word passphrases beat traditional complex passwords. The core insight: length and true randomness matter more than character complexity.

How Attackers Actually Crack Passwords

  1. Dictionary attacks: Try common passwords and words
  2. Rule-based attacks: Apply transformations (capitalize first letter, add numbers, substitute letters with symbols)
  3. Hybrid attacks: Combine dictionary words with rules
  4. Brute force: Try every possible combination (last resort)

Human-created "complex" passwords follow predictable patterns that rules can exploit. Truly random passphrases force attackers into slower dictionary combination attacks.

Entropy Comparison Table

Password Type Example Theoretical Entropy Effective Entropy
Common password password123 72 bits ~0 bits (in dictionaries)
Predictable substitution P@ssw0rd123! 79 bits ~28 bits (rule-based)
Random 8-char password Kx9#mP2$ 52 bits 52 bits
Random 12-char password vL4@nQ8&jR2! 79 bits 79 bits
4-word passphrase (Diceware) correct-horse-battery-staple 51 bits 51 bits
5-word passphrase piano-zebra-mountain-clock-river 64 bits 64 bits
6-word passphrase ocean-laptop-forest-puzzle-train-maple 77 bits 77 bits
Random 16-char password Kx9#mP2$vL4@nQ8& 105 bits 105 bits

Key insight: "Theoretical entropy" assumes random generation. "Effective entropy" accounts for how attackers actually crack passwords. Human-created passwords almost always have lower effective entropy than theoretical.

When to Use Each Approach

Use Random Character Passwords When:

Use Passphrases When:

Best practice for 2026: Use a password manager with a 6+ word passphrase as your master password. Let the manager generate random 16-20 character passwords for individual sites.

How to Generate Strong Passphrases

The Diceware Method

Diceware is a proven method for generating truly random passphrases:

  1. Roll five dice (or use a secure random generator)
  2. Look up the resulting number in the Diceware word list
  3. Repeat for each word you need (minimum 5 words for modern security)
  4. Optionally add separators (hyphens, spaces, or numbers)

Critical Rules for Secure Passphrases

Passphrase Strength by Word Count

Words Entropy (7,776-word list) Crack Time (10B guesses/sec) Recommendation
3 words ~39 bits ~1 minute Not recommended
4 words ~52 bits ~52 days Minimum acceptable
5 words ~65 bits ~1,100 years Good for most uses
6 words ~78 bits ~9 million years Strong
7 words ~90 bits ~70 billion years Very strong

The Bottom Line

Both strong random passwords and properly generated passphrases can be highly secure. The key differences are:

What matters most is that your credentials are truly random—whether that's random characters or random words. Human-chosen "complex" passwords remain the weakest option regardless of how many symbols they contain.

Action item: Generate a secure password now using our password generator, or create a 6-word Diceware passphrase for credentials you need to memorize.