What Is the Birthday Paradox and How Does It Relate to the Probability of Finding a Hash Collision?

The Birthday Paradox states that in a random set of people, the probability of two sharing a birthday is surprisingly high, needing only 23 people for a 50 percent chance. In cryptography, this translates to the fact that a collision can be found much faster than expected, in about 2 to the power of 128 attempts for a 256-bit hash.

This phenomenon dictates the effective security level of a hash function.