A/B Testing Encryption Strength Per-User Formula
Learn how the calculator estimates brute-force keyspace, per-user compromise likelihood, expected crack time, and population-level exposure.
This calculator compares two stated encryption strengths under a simplified brute-force model. It estimates how much of each keyspace an attacker could search during a chosen period, then applies that per-user probability across independently protected users.
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Per-User Compromise Likelihood
Where:
Multiply the attacker's guesses per second by the attack duration in seconds, divide by the number of possible keys, and convert the result to a percentage. The result is capped at 100%.
Variables Explained
| Variable | What It Means | Unit |
|---|---|---|
| p - Per-user compromise likelihood | Approximate probability that one independently generated key is found during the selected attack period. | percent |
| R - Attack rate | Hypothetical sustained number of valid brute-force guesses per second against one user's key. | guesses per second |
| Y - Attack duration | Time available to attack each user's encryption key. | years |
| b - Security strength | Effective symmetric brute-force security strength of the encryption setting. | bits |
| N - User count | Number of users protected by separate, independently generated keys. | number |
Step-by-Step Calculation
Calculate the keyspace
A stated strength of b bits represents approximately 2 raised to the power of b possible keys.
keyspace = pow(2, securityBits)
Convert years to seconds
The calculation uses 365.25 days, or 31,557,600 seconds, per year.
attackSeconds = attackDurationYears * 31557600
Calculate total guesses
This estimates the number of valid key guesses available against one user's key during the selected period.
attackGuesses = attackRate * attackSeconds
Estimate per-user likelihood
The likelihood is approximated by the fraction of the keyspace searched.
perUserCompromisePercent = min(100, 100 * attackGuesses / keyspace)
Estimate average crack time
A uniformly random key is expected to be found halfway through a systematic exhaustive search.
expectedCrackYears = keyspace / 2 / attackRate / 31557600
Estimate compromised users
This applies the per-user estimate to a population where every user has a separate key.
expectedCompromisedUsers = userCount * perUserCompromisePercent / 100
Estimate any-compromise likelihood
This estimates the chance that at least one independent user key is compromised.
atLeastOneCompromisePercent = 100 * (1 - pow(1 - perUserCompromisePercent / 100, userCount))
Comparing 64-bit and 80-bit effective strength
Attack guesses in one year
1,000,000,000 × 31,557,600
31,557,600,000,000,000 guesses
Version A keyspace
2^64
18,446,744,073,709,551,616 keys
Version A per-user likelihood
100 × 31,557,600,000,000,000 ÷ 2^64
About 0.1711%
Version B keyspace
2^80
1,208,925,819,614,629,174,706,176 keys
Version B per-user likelihood
100 × 31,557,600,000,000,000 ÷ 2^80
About 0.00000261%
Expected compromised users
1,000,000 × per-user likelihood
About 1,711 users for A; about 0.026 users for B
Final Result
Version B has 16 additional bits of stated brute-force strength and an estimated per-user brute-force likelihood about 65,536 times lower than Version A under the same inputs.
Assumptions
- ✓Each user has a separate, uniformly random key with the stated effective security strength.
- ✓The attacker makes valid brute-force guesses at a constant rate throughout the full period.
- ✓The stated attack effort is evaluated separately for each user rather than divided across a shared attack budget.
- ✓The chance of success is approximated by the proportion of the keyspace searched.
- ✓Expected crack time assumes exhaustive search and an average successful search position halfway through the keyspace.
Limitations
- !The model covers brute-force guessing only and does not measure overall real-world security.
- !Weak passwords, low-entropy key material, implementation defects, exposed keys, malware, and side channels can dominate the risk.
- !The attack rate is hypothetical and may not reflect a practical attack against a particular implementation.
- !Independent-user results do not apply when users share a key, credential, secret, or encryption failure.
- !Very small percentages may be rounded by a display even though they are not mathematically zero.
Common Mistakes to Avoid
Entering an algorithm's nominal key size when the effective security strength is lower.
Treating the estimated brute-force likelihood as the total probability of a security incident.
Using one shared key while interpreting the result as an independent per-user-key model.
Assuming attack capacity grows linearly with added bits; every extra bit doubles the keyspace.
Interpreting expected compromised users as a guaranteed count rather than a statistical expectation.
Related Formulas
Frequently Asked Questions
How is encryption keyspace calculated from bits?
The simplified keyspace is 2^b, where b is the effective security strength in bits. Each additional bit doubles the number of possible keys.
Why does the formula use half of the keyspace for crack time?
In a systematic search of a uniformly random key, the correct key is found halfway through the keyspace on average.
How is the per-user compromise percentage calculated?
It is the number of assumed guesses during the period divided by the keyspace, expressed as a percentage and capped at 100%.
Does a 16-bit increase always make brute force 65,536 times harder?
Under this keyspace model, yes. A difference of 16 bits changes the search space by 2^16, or 65,536.
What does the chance of at least one compromise measure?
It combines the estimated per-user probability across the entered number of independent users to estimate whether any one user is compromised.
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