Calculating Cryptographic String Entropy & Password Brute-Force Resilience
NIST Special Publication 800-63B (Digital Identity Guidelines)
How Mathematical Entropy (Bits) is Evaluated
The security strength of a generated string or password is not measured merely by length, but by its total information entropy in bits ($E$). Entropy quantifies how many binary guesses an attacker would have to make to brute-force the value:
| Character Pool Configuration | Pool Size (R) | Length (L = 32) Entropy | Brute-Force Resistance |
|---|---|---|---|
| Numeric Only (0-9) | 10 | ≈ 106.3 bits | Suitable for short PINs / OTPs. |
| Alphanumeric (A-Z, a-z, 0-9) | 62 | ≈ 190.5 bits | Exceeds enterprise password standards. |
| Full ASCII Symbols & Glyphs | 94 | ≈ 209.7 bits | Immune to supercomputer brute-force attacks. |
Eliminating Visually Confusing Characters
When passwords or verification keys must be manually typed or read across phone calls, human errors arise from glyph ambiguity. Our Unambiguous Preset automatically removes confusing lookalikes:
1, l, I, | (ones, ells, eyes, pipes) and 0, O, o (zeros and ohs).