Hash

A hash is the output of a hash function: an algorithm that takes input of any size and produces a fixed-length, pseudorandom-looking output. Bitcoin uses SHA-256, which always produces 256 bits (64 hex characters), regardless of whether you fed it one byte or one terabyte.

Three properties make hashes useful for Bitcoin:

• Deterministic. The same input always produces the same hash.
• One-way. Given the output, there is no efficient way to find an input that produces it - except by guessing inputs until one happens to work. The expected number of guesses is ~2^256, which is unfathomable.
• Avalanche. Change one bit of input and roughly half the output bits change, unpredictably. Similar inputs produce wildly different hashes.

Bitcoin uses hashes everywhere:

• Block headers are hashed (twice, via double-SHA-256) and the result must be below the difficulty target to be valid. This is the search miners are racing to win.
• Each block references the previous block's hash, creating the tamper-evident blockchain.
• Transactions are organized into a Merkle tree whose root commits to every transaction in the block with a single hash.
• Addresses are hashes of public keys, which keeps the underlying public key private until you spend.
• TXIDs are hashes of serialized transactions.

The bet Bitcoin makes is that SHA-256 stays one-way for the foreseeable future. If that ever breaks, Bitcoin breaks. So far, after 16 years of being one of the most attacked cryptographic systems on Earth, SHA-256 has held.

The most plausible weakening, not break, is Grover's algorithm running on a quantum computer: it halves SHA-256's effective security from 256 bits to 128 bits via quadratic speedup on unstructured search. 128-bit symmetric security is still the standard floor for cryptography elsewhere - annoying for Bitcoin, not catastrophic. See Post-Quantum Bitcoin for the broader picture.

See the Mining rabbit hole §2 for how the one-way property turns into security, and Key Space rabbit hole for why 2^256 is bigger than your intuition wants it to be.