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Question 95. What is a birthday
attack?

A *birthday attack* is a name used to refer to a class of
brute-force attacks. It gets its name from the surprising result
that the probability that two or more people in a group of 23
share the same birthday is greater than 1/2; such a result is
called a *birthday paradox*.

If some function, when supplied with a random input, returns one
of *k* equally-likely values, then by repeatedly evaluating
the function for different inputs, we expect to obtain the same
output after about 1.2*k*^{1/2}. For the above birthday paradox,
replace *k* with 365.

Birthday attacks are often used to find collisions of hash functions
(see Question 96).