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Please give help! how can I calculate the probability of collision? I need a mathematical equation for my studying.

Assume, I am using SHA256 to hash 100-bits. Thus:

SHA256 {100} = 256-bits (hash values) I would like to know the probability of collision.

This website: https://preshing.com/20110504/hash-collision-probabilities/

Gave an equation: $K^2 / 2N$

But I could not know what is $K$ and $N$? Is K is the output which is (256-bits) and $N$ is the input which is (100-bits)

Please Help and Thanks in advance...

kelalaka
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Al-Ani
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1 Answers1

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$n$ is the output size of the given hash function. To find a collision you try randomly generated $k$ different inputs. When we say the output size is $n$, it means that the output space has $2^n$ elements.

What you see on that website is the general case of collision probability. We normally talk about the 50% probability (birthday attack) on the hash collisions as

$$ k = \sqrt{2^n}$$ You can also see the general result from the birthday paradox.

To have a birthday attack with a 50% percentage you will need $k = 2^{128} \approx 4.0 × 10^{38}$ randomly generated differently input for a hash function with output size $n= 256$

Dear readers, I've only answered the question, however, it seems that it gets so much attention. We have a 101 for hash collisions answer, please refer to that for more detail about probability calculations;

kelalaka
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