How many people do you need in a room before there is a 50% chance that least two of them share the same birthday? It’s only 23, though unless you have heard about this paradox before, you might expect it to be much larger. This is the well-known birthday paradox: it’s called a paradox only because collisions happen much faster than one naively expects. Collisions here means an event where two or more observed values are equal. This paradox is important in cryptography as it’s relevant for many topics like cryptographic hash functions, which are designed to be collision-resistant one-way functions.