The password entropy analyzer evaluates theoretical cryptographic strength and brute-force cracking duration based on character length and alphabet pool selection. Designed for IT security auditors and developers establishing organizational password policies, it calculates exact permutations and benchmarks them against high-speed GPU cluster attack rates.

### Mathematical Formulation

Given password length $L$ and alphabet pool diversity $R$: - **Numbers Only:** $R = 10$ ($0-9$) - **Lowercase Letters:** $R = 26$ ($a-z$) - **Letters (Upper + Lower):** $R = 52$ ($A-Z, a-z$) - **Alphanumeric:** $R = 62$ ($A-Z, a-z, 0-9$) - **Alphanumeric + Special Symbols:** $R = 94$ (ASCII printable characters)

Key security equations: - **Shannon Entropy:** $E = L \times \log_2(R)$ - **Total Permutations:** $N = R^L$ - **Expected Brute-Force Time:** $T = \frac{N / 2}{\text{Guesses per Second}}$ (assuming average success at 50% search space).

### Worked Theoretical Example

Evaluating a mandatory 14-character alphanumeric plus symbol policy ($L=14, R=94$): 1. **Entropy Bits:** $14 \times \log_2(94) = 14 \times 6.554588 = \mathbf{91.8\text{ bits}}$. 2. **Total Combinations:** $94^{14} \approx 4.19 \times 10^{27}$ possibilities. 3. **Cracking Duration at 100 Billion H/s:** $\frac{4.19 \times 10^{27} / 2}{100 \times 10^9} \approx 2.095 \times 10^{16}\text{ seconds} \approx \mathbf{660\text{ Million Years}}.$ 4. **Compliance Status:** Fortress rating, comfortably passing the NIST SP 800-63B 64-bit minimum baseline.

### Local Client Execution

All mathematical operations execute synchronously in local browser memory. No user inputs, simulated parameters, or organizational policies are logged or transmitted across the internet.