An effective attack on a hash function
Take a function f() that seems to map an input to a random output of some fixed size (a pseudo-random function or PRF). A birthday attack is simply selecting random inputs for f() and checking to see if any previous values gave the same output. Statistically, if the output size is S bits, then one can find a collision in 2^(S/2) operations, on average.
A brute force attach method, used to narrow the number of alternatives required to be tried. It gets its name from the curious fact that in a room of 23 people it is more than 50% likely that two of them will have the same birthday.
A brute-force attack used to find collisions. It gets its name from the surprising result that the probability of two or more people in a group of 23 sharing the same birthday is greater than 1/2.
A birthday attack is a type of cryptographic attack which exploits the mathematics behind the birthday paradox, making use of a space-time tradeoff. Specifically, if a function yields any of H different outputs with equal probability and H is sufficiently large, then after evaluating the function for about 1.2 \cdot \sqrt H different arguments we expect to obtain a pair of different arguments x_1 and x_2 with f(x_1) = f(x_2), known as a collision.
