A/B Testing Encryption Strength Formula
Learn how effective security bits, attack rate, and a security target are used to compare two encryption configurations.
This calculator estimates relative resistance to exhaustive key-search attacks. It shows why a difference of only a few effective security bits can translate into a much larger difference in possible keys and estimated search time.
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Configuration B Strength Relative to A
Where:
Subtract Configuration A's effective bits from Configuration B's. Every additional bit doubles the estimated key-search space, so the result grows exponentially.
Variables Explained
| Variable | What It Means | Unit |
|---|---|---|
| encryptionBitsA - Configuration A effective security bits | Estimated effective key-search strength of Configuration A. | bits |
| encryptionBitsB - Configuration B effective security bits | Estimated effective key-search strength of Configuration B. | bits |
| attackRate - Assumed attack rate | Number of candidate keys an attacker is assumed able to test each second. | keys per second |
| securityTargetBits - Security target | Minimum effective security level used for the target comparison. | bits |
Step-by-Step Calculation
Find the bit difference
A positive result means B has more estimated key-search strength than A.
strengthDifferenceBits = encryptionBitsB - encryptionBitsA
Calculate the relative key-search multiplier
Each extra effective bit doubles the number of keys that may need to be searched.
strengthMultiplierBvsA = pow(2, strengthDifferenceBits)
Estimate average keys to try for A
An exhaustive search is assumed to find the correct key halfway through the key space on average.
averageKeysToTryA = pow(2, encryptionBitsA - 1)
Estimate average keys to try for B
The same halfway-through-the-key-space assumption is applied to Configuration B.
averageKeysToTryB = pow(2, encryptionBitsB - 1)
Convert key-search effort into years
The average number of keys is divided by the assumed rate and by seconds in a 365.25-day year. The same formula is used for B.
bruteForceYearsA = averageKeysToTryA / attackRate / 31557600
Check each configuration against the target
Zero means the configuration equals the target, while a negative value means it is below the target in this model.
targetGapA = encryptionBitsA - securityTargetBits; targetGapB = encryptionBitsB - securityTargetBits
Comparing 128-bit and 256-bit effective security
Find the bit difference
256 - 128
128 bits
Calculate B's relative strength
2^128
approximately 3.40 × 10^38×
Estimate average keys for A
2^(128 - 1)
approximately 1.70 × 10^38 keys
Estimate A search time
2^127 / 1,000,000,000,000 / 31,557,600
approximately 5.39 × 10^18 years
Estimate B search time
2^255 / 1,000,000,000,000 / 31,557,600
approximately 1.83 × 10^57 years
Check the target
128 - 128; 256 - 128
A: 0 bits; B: +128 bits
Final Result
Configuration B has 128 additional effective bits and an estimated brute-force key-search space approximately 3.40 × 10^38 times larger than Configuration A.
Assumptions
- ✓The entered effective security bits accurately represent practical resistance to the relevant key-search attack.
- ✓An attacker uses exhaustive key search and, on average, tests half of the possible keys before success.
- ✓The assumed attack rate stays constant for the full modeled period.
- ✓The model uses 31,557,600 seconds per year.
- ✓The comparison concerns key-search resistance only.
Limitations
- !The estimate does not assess implementation defects, side channels, protocol weaknesses, poor randomness, or key-management failures.
- !A stated key length and effective security bits are not always equivalent; use an effective-strength estimate where possible.
- !Real attack rates depend on the algorithm, hardware, parallelism, cost, and whether offline testing is possible.
- !The calculation does not model quantum-computing effects or future cryptanalytic developments.
- !Very large time values are mathematical estimates, not predictions of real-world security outcomes.
Common Mistakes to Avoid
Entering nominal key length when the effective security strength is lower for the configuration being compared.
Treating a high brute-force estimate as proof that the entire system is secure.
Using an attack rate for one algorithm or environment to compare a materially different algorithm or environment.
Reading a negative target gap as a number of years rather than a number of effective bits below target.
Assuming that a 10-bit increase is a 10% increase; it represents a 1,024-fold key-search-space multiplier.
Related Formulas
Frequently Asked Questions
How is encryption strength calculated from effective bits?
The model treats effective bits as a base-2 measure of key-search work. A configuration with b effective bits has an estimated key space of 2^b possibilities.
Why does one additional effective bit matter?
One extra bit doubles the estimated number of candidate keys. For example, 20 extra bits represent a multiplier of 2^20, or 1,048,576.
Why does the calculator use half the key space for brute-force time?
If the correct key is equally likely to appear anywhere in the space, an exhaustive search finds it halfway through on average.
What does a target gap of zero mean?
It means the entered effective security bits equal the selected target. A positive gap is above target and a negative gap is below it.
Can I use this formula to assess overall encryption security?
No. It is an educational estimate of exhaustive key-search resistance, not a complete security assessment.
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