Cryptography is the bedrock of all cryptocurrency security. Bitcoin relies on two core primitives: cryptographic hashing (used to link blocks and secure proof-of-work) and public-key cryptography (used to sign and verify transactions). A digital signature proves that the holder of a private key authorised a transaction, without ever exposing that key. These mathematical guarantees are what allow strangers across the world to transact securely without trusting one another or any central authority.