Hash Collision Birthday Attempts Estimate
Birthday-Poisson inverse estimate for independent uniform digests, not an exact integer collision probability.
Description
Estimate the ideal digest attempts giving a selected birthday-collision probability.
The birthday model estimates how many ideal digest attempts give a selected probability of any collision. This is different from finding a preimage for one chosen digest.
When to use this tool
Estimate the ideal digest attempts giving a selected birthday-collision probability. Use it when the input measurements and conventions below match the operation you need.
- Prepare digestBits, targetProbability, respecting the measurement basis and boundaries below.
- Compare the worked example with your intended operation before reusing its result.
How to use the tool and how it works
- Enter every field in the input table using the stated units and exact supported selector spelling where applicable.
- Run the tool. Correct input errors before interpreting an output.
- Read the result fields below; use accompanying flags and the stated sign, boundary or model convention when interpreting a number.
For an integer digest width from 1 to 1,024 bits and probability p strictly between zero and one, the tool returns sqrt(2 times -ln(1 minus p)) times 2^(bits/2). It uses log1p internally for the logarithm.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| digestBits | Digest bits. | Integer; from 1 to 1024 inclusive |
| targetProbability | Target probability. | Finite number |
| Output field | Interpretation |
|---|---|
| result | Object containing the following named result fields. |
| result.approximateAttempts | Approximate attempts; use the stated units and sign convention. |
{
"input": {
"digestBits": 16,
"targetProbability": 0.3934693402873666
},
"output": {
"result": {
"approximateAttempts": 256
}
}
}Limitations and assumptions
- This is a birthday approximation for independent uniform outputs, especially limited for very small spaces. It is not a password-cracking estimate, an exact discrete trial count or evidence of a real hash weakness.
- Every declared field is required and unexpected fields are rejected. Numeric inputs must be finite; input errors are distinct from a valid false result or an explicitly qualified output.
- Extremely large inputs and nonfinite or excessively large outputs are rejected. List positions reported by the tool use zero-based indices unless stated otherwise.
Alternative or Complementary methods
Use the applicable protocol specification and a reviewed implementation for real verification, hashing or key management. A format label, probability model or tentative text mapping does not replace that operation. Compare the scope of the nearby tools below before substituting one.
References
Similar or alternative tools
- birthday bound collision probability
Independent uniform samples can collide even when the outcome space is much larger than the sample count.
- brute force time estimate at hashes per second
An exhaustive search model visits a finite set of candidates at a constant rate.