In probability theory , the birthday problem or birthday paradox concerns the probability that, in a set of n randomly chosen people, some pair of them will have the same birthday. These conclusions are based on the assumption that each day of the year excluding February 29 is equally probable for a birthday. Real-world applications for the birthday paradox 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. The history of the problem is obscure.
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