A birthday attack targets hash functions by exploiting the birthday paradox: collisions (two different inputs producing the same hash output) can be found much faster than brute-forcing a specific preimage. For an n-bit hash, the expected work t o find any collision is on the order of 2^(n/2), not 2^n. The attack is relevant because many security constructions rely on collision resistance—digital signatures, certificate fingerprints, integrity checks, and some commitment schemes. If an attacker ca n generate two different documents with the same hash, they may trick a signer into signing one version while later presenting the other as “signed,” depending on the protocol. Linear cryptanalysis and differential cryptanalysis are primarily techniques ag ainst block ciphers, analyzing relationships between plaintext/ciphertext differences or linear approximations across rounds. Algebraic attacks treat the cipher as a system of equations. The description “looking for different inputs that generate the same hash” is the hallmark of collision-finding, and the classic framing for that is the birthday attack.