 The birthday problem is a paradox in the sense of something that seems contradictory at first, but which can be logically explained in a self-consistent manner..Real-world applications for the birthday problem include a cryptographic attack called the birthday attack, which uses this probabilistic model to reduce the complexity of finding a collision for a hash function, as well as calculating the approximate risk of a hash collision existing within the hashes of a given size of population.The history of the problem is obscure.