Blockchain & Bitcoin cryptography
SHA-256
A cryptographic hash: fixed-size fingerprint, one-way, collision-resistant in practice. Bitcoin proof-of-work and many address pipelines lean on SHA-256 (often double-SHA-256).
ECDSA on secp256k1
Bitcoin signatures use the elliptic curve secp256k1. A private key is a large integer; the public key is priv · G on the curve. Signing proves knowledge of the private key without revealing it.
Merkle trees
Transactions in a block are hashed into a binary tree; the Merkle root commits to the whole set. Light clients can verify inclusion with a short proof — like checking one leaf without carrying Fangorn forest.
Addresses
Addresses are encodings (Base58Check, Bech32, …) of hashed public-key material plus version/checksum. Losing the private key loses the coins; publishing only the address does not reveal the private key.