Editing Birthday attack (section)

===Simple approximation===
A good [[rule of thumb]] which can be used for [[mental calculation]] is the relation

:<math>p(n) \approx {n^2 \over 2H}</math>

which can also be written as

:<math>H \approx {n^2 \over 2p(n)}</math>.

or

:<math>n \approx \sqrt { 2H \times p(n)}</math>.

This works well for probabilities less than or equal to 0.5.

This approximation scheme is especially easy to use when working with exponents. For instance, suppose you are building 32-bit hashes (<math>H = 2^{32}</math>) and want the chance of a collision to be at most one in a million (<math> p \approx 2^{-20} </math>), how many documents could we have at the most?

:<math>n \approx \sqrt { 2 \times 2^{32} \times 2^{-20}} = \sqrt { 2^{1+32-20} } = \sqrt { 2^{13} } = 2^{6.5} \approx 90.5 </math>

which is close to the correct answer of 93.