A birthday attack is a type of cryptographic attack that exploits the mathematics behind the birthday problem in probability theory. This attack can be used to abuse communication between two or more parties. The attack depends on the higher likelihood of collisions found between random attack attempts and a fixed degree of permutations (pigeonholes), as described in the birthday problem/paradox.
Read more about Birthday Attack: Understanding The Problem, Mathematics, Digital Signature Susceptibility
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—Oliver St. John Gogarty (1878–1957)