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.

This site’s browser forge uses ECDSA P-256 (Web Crypto), which is not Bitcoin’s secp256k1. Same family of ideas; different curve — do not mix keys across ecosystems.