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Hash functions are mathematical algorithms that transform data of arbitrary size into a fixed-size string of characters, typically a sequence of numbers and letters. The output, known as a hash or digest, is designed to be unique for different input values; even a tiny change in the input usually produces a dramatically different hash. Hash functions are fundamental in computer science for tasks such as data retrieval, cryptography, and data integrity verification.

The key properties of a good hash function include determinism, fast computation, uniform distribution of hash values, and resistance to collisions. A collision occurs when two distinct inputs produce the same hash output, and minimizing collisions is crucial for efficient hashing. For digital signatures and password storage, cryptographic hash functions add further security requirements: they should be one-way, meaning it is computationally infeasible to reconstruct the original input from its hash.

Common non-cryptographic hash functions used in data structures are MurmurHash, FNV-1a, and CityHash, which emphasize speed and low collision rates. Cryptographic hash functions such as SHA‑256, SHA‑3, and MD5 (though now considered insecure) are employed in security contexts. MD5 and SHA‑1 were once standard but have been largely replaced due to collision vulnerabilities.

Hash functions also underpin blockchain technology, where they provide data integrity, consensus mechanisms, and proof-of-work calculations. In networking, hashing can be used for load balancing and routing decisions. Despite their widespread use, careful selection of hash functions is essential: choosing the wrong type or insecure algorithm can lead to data breaches, performance degradation, or system vulnerabilities.