A mathematical function that takes a variable-size input (called a message) and produces a fixed-size output (called hash, hashing, digest, or fingerprint). Hash functions are widely used primitives in cryptography. They exhibit specific properties that make them suitable for use in secure contexts: Preimage resistance: it must be very difficult to find a message that produces a specific hash, i.e., to find a preimage for a hash such that , where is the hash function; Second preimage resistance: given a message , it must be very difficult to find another message (different from ) such that ; Collision resistance: it must be very difficult to find two distinct messages and such that ; Tamper resistance: small changes in the input must cause significant and unpredictable changes in the output.

In the context of Bitcoin, hash functions are used for several purposes, including the proof-of-work mechanism (Proof-of-Work), transaction identifiers, address generation, checksum calculations, and the creation of data structures such as Merkle trees. On the protocol side, Bitcoin exclusively uses the SHA256d function, also named HASH256, which consists of a double SHA256 hash. HASH256 is also used in the calculation of certain checksums, notably for extended keys (xpub, xprv...). On the wallet side, the following are also used: