Password Strength by Time

The Brute-Force Model

A brute-force attack tries every possible combination until it finds the correct password. The total search space is:

$S = N^L$

Where:

• $S$ = total number of possible passwords
• $N$ = character set size (distinct characters the attacker considers)
• $L$ = password length

The average crack time assumes the attacker finds the password halfway through the search space:

$T = \frac{S \times p}{G}$

Where:

• $T$ = average crack time in seconds
• $p$ = fraction of search space checked (typically 50% for average)
• $G$ = attacker guesses per second

Attack Speed by Scenario

The most important variable is $G$ — which depends entirely on the attack scenario:

bcrypt (and Argon2, scrypt) are designed to be slow. A 1-second bcrypt verification with 1 GPU allows only ~1,000 guesses per second. The same password behind MD5 takes microseconds per guess — making bcrypt cost 12 vs MD5 a 6-order-of-magnitude difference in real attack resistance.

Worked Example

Password: 10 characters, letters + numbers + symbols ($N = 94$) Attack speed: $10^{10}$ guesses/sec (offline MD5)

$S = 94^{10} \approx 5.39 \times 10^{19}$

$T = \frac{5.39 \times 10^{19} \times 0.5}{10^{10}} \approx 2.7 \times 10^9 \text{ seconds} \approx 85 \text{ years}$

Same password against online rate-limited login ($G = 10$/sec):

$T \approx \frac{5.39 \times 10^{19} \times 0.5}{10} \approx 2.7 \times 10^{18} \text{ seconds}$

The same 10-character password becomes uncrackable in practice against a rate-limited form — not because the password is stronger, but because the attack speed dropped by 9 orders of magnitude.

Length vs Complexity: The Real Impact

Same character set ($N = 94$), different lengths, MD5 offline:

Each additional character multiplies the search space by $N = 94$. Adding 2 characters changes crack time from days to centuries.

What This Calculator Does Not Capture

Dictionary attacks — real attacks start with wordlists and rule sets before brute-forcing. Password1! has theoretical crack time of centuries but falls in seconds to a dictionary attack.

Credential stuffing — if the password appeared in a breach, it is instantly cracked regardless of entropy.

Salt — proper salting prevents precomputed rainbow table attacks. Unsalted MD5 hashes can be cracked using lookup tables with near-zero computation.