A/B Testing Encryption Strength Formula
Learn how projected annual attack capacity, key length, and average brute-force effort are calculated for two encryption variants.
This calculator estimates the relative brute-force key-search effort for two effective encryption key lengths. It projects an attacker’s annual guessing capacity, then compares the average time needed to search half of each theoretical keyspace.
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Variant B Relative Brute-Force Effort
Where:
Every additional effective key bit doubles the number of possible keys. The difference between Variant B and Variant A therefore determines how many times more brute-force work Variant B requires.
Variables Explained
| Variable | What It Means | Unit |
|---|---|---|
| keyBitsA - Variant A key length | The effective key length of encryption Variant A. | bits |
| keyBitsB - Variant B key length | The effective key length of encryption Variant B. | bits |
| guessesPerSecond - Current attack guesses per second | The assumed number of valid key guesses an attacker can test each second. | guesses per second |
| annualCapacityGrowth - Annual attack-capacity growth | The assumed compounded yearly growth rate in attacker guessing capacity. | percent |
| projectionYears - Projection period | The number of years over which attack capacity is projected. | years |
| projectedAnnualGuesses - Projected annual guesses | The assumed attacker capacity in guesses per year after the selected projection period. | guesses per year |
Step-by-Step Calculation
Set seconds per year
The calculation uses 365.25 days, or 31,557,600 seconds, per year.
secondsPerYear = 31557600
Convert the current rate to annual capacity
The attacker’s per-second guessing rate is converted into a yearly number of possible key guesses.
currentAnnualGuesses = guessesPerSecond * secondsPerYear
Project future annual capacity
The annual capacity is increased using the selected compounded annual growth assumption.
projectedAnnualGuesses = currentAnnualGuesses * pow(1 + annualCapacityGrowth / 100, projectionYears)
Calculate each theoretical keyspace
A key length of n bits represents a theoretical keyspace of 2 raised to n possible keys.
keyspaceA = pow(2, keyBitsA); keyspaceB = pow(2, keyBitsB)
Estimate average guesses to find a key
For a randomly located key searched without prior knowledge, the expected search position is halfway through the keyspace.
averageAttemptsA = keyspaceA / 2; averageAttemptsB = keyspaceB / 2
Estimate brute-force time
Average required guesses are divided by projected annual guesses to estimate time in years.
estimatedYearsA = averageAttemptsA / projectedAnnualGuesses; estimatedYearsB = averageAttemptsB / projectedAnnualGuesses
Compare relative effort
The key-length difference alone determines the relative brute-force work multiplier under the same assumptions.
strengthMultiplier = pow(2, keyBitsB - keyBitsA)
Comparing 128-bit Variant A with 256-bit Variant B
Current annual guesses
1,000,000,000,000 * 31,557,600
3.15576 × 10^19 guesses/year
Growth factor over 10 years
pow(1 + 20 / 100, 10)
6.1917
Projected annual guesses
3.15576 × 10^19 * 6.1917
1.953 × 10^20 guesses/year
Variant A average attempts
pow(2, 128) / 2
1.7014 × 10^38 guesses
Variant A estimated time
1.7014 × 10^38 / 1.953 × 10^20
about 8.71 × 10^17 years
Variant B relative effort
pow(2, 256 - 128)
about 3.40 × 10^38×
Variant B estimated time
8.71 × 10^17 * 3.40 × 10^38
about 2.96 × 10^56 years
Final Result
At the projected attack capacity, the 256-bit variant requires about 3.40 × 10^38 times the brute-force key-search effort of the 128-bit variant.
Assumptions
- ✓Each selected value represents an effective key length with a theoretical keyspace of 2 raised to that number of bits.
- ✓A direct conventional brute-force search is assumed.
- ✓A successful search requires half of the keyspace on average.
- ✓Attacker capacity grows at a constant compounded annual rate over the projection period.
- ✓Both variants are evaluated against the same projected annual guessing capacity.
Limitations
- !The estimate does not assess encryption algorithms, modes, protocols, authentication, or implementation quality.
- !Weak key generation, exposed keys, side-channel attacks, bugs, and operational failures can matter more than theoretical keyspace size.
- !The guesses-per-second input may not reflect practical restrictions such as rate limits, hardware cost, or offline versus online attack conditions.
- !The model does not account for quantum computing or other non-classical attack methods.
- !Very large duration outputs are theoretical comparisons, not practical security guarantees.
Common Mistakes to Avoid
Entering a nominal key size when the effective security strength is lower for the specific design.
Treating guesses per second as universally applicable without considering the target algorithm and attack setting.
Using a growth percentage as a decimal, such as entering 0.20 when the input expects 20%.
Reading the projected capacity as cumulative guesses across all future years rather than capacity in the selected future year.
Assuming a larger key length fixes poor key management or implementation vulnerabilities.
Related Formulas
Frequently Asked Questions
How is the encryption strength multiplier calculated?
It is calculated as 2 raised to the difference in effective key bits: 2^(B minus A). A 10-bit difference means a 1,024× difference in theoretical brute-force work.
Why does the calculation use half of the keyspace?
If the secret key is random and its position is unknown, a sequential brute-force search finds it halfway through the possible keys on average.
Does doubling the key length double encryption strength?
No. Adding one bit doubles the keyspace. Increasing a key length from 128 to 256 bits increases theoretical brute-force work by 2^128, not merely two times.
What does projected annual guesses mean?
It is the assumed number of key guesses an attacker could test in one year after applying the selected annual capacity-growth rate for the chosen number of years.
Can I compare two variants with the same key length?
Yes. The relative effort multiplier will be 1× under this model, although real security can still differ because of algorithm, implementation, and operational factors.
Does this formula measure complete encryption security?
No. It measures theoretical brute-force key-search effort only and should be treated as an educational estimate rather than a complete security assessment.
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