Security Model & Mathematics
How PassCheck models password search spaces, Shannon entropy, crack resistances, and brute-force complexity.
Information-Theoretic Entropy Model
Shannon entropy in passwords estimates the number of bits of randomness. The formula is based on the size of the character pool N and length L:
Character Pool Sizes (N):
- Lowercase alphabet (
a-z): 26 characters - Uppercase alphabet (
A-Z): 26 characters - Numeric digits (
0-9): 10 characters - ASCII Special Symbols: 33 characters
- Extended Unicode / Emojis: 128+ characters
Pattern Deductions: If a password contains predictable structures such as keyboard walks (qwerty), simple runs (12345), or dictionary roots (password), the effective search space drops precipitously. The effective entropy subtracts penalty bits derived from structural pattern detections.
Simulated Hardware Attack Scenarios in PassCheck
Average number of guesses required to find a password is 2^(E - 1) (assuming an exhaustive search of 50% of the key space).
Represents distributed cracking rigs targeting unsalted or fast hashes.
Standard single modern GPU (RTX 4090 class) benchmark.
Industry standard memory-hard key derivation functions.
Simulates web authentication forms with CAPTCHA and IP throttling.