Password Strength Analyzer

Discrete Math · Axiom Academy

REAL WORLD Password Strength Analyzer Discover the mathematics behind password security and why character variety matters exponentially Every day, millions of passwords are tested by attackers using automated tools. But what makes a password truly secure? The answer lies in combinatorics —specifically, how many possible combinations exist. Real-World Context: In 2024, attackers can test billions of password combinations per second using modern GPUs. The only defense? Creating passwords with so many possible combinations that testing them all would take centuries. Character Sets: The Building Blocks Passwords are built from different character sets . Each set you include multiplies the number of possibilities. Let's see how: Think About It: If you use only lowercase letters (26 options per position), how many possible 8-character passwords exist? The total number of possible passwords follows a simple but powerful formula: C = Total number of characters available (character set size) Using lowercase + uppercase + digits (26 + 26 + 10 = 62 characters) with length 8: That's over 218 trillion possible passwords! Now it's your turn! Adjust the settings below to see how different choices affect password security in real-time. How long would it take an attacker to crack your password? The answer depends on their computing power and your password's complexity. Current Attack Speeds (2024 Technology)

This is the written version of the interactive lesson above. See the full Discrete Math course.