Bitcoin's ECDSA cryptography secures transactions with compact, efficient keys.

The Elliptic Curve Digital Signature Algorithm (ECDSA) is a cryptographic system used by Bitcoin for transaction authentication. It generates small, secure public and private keys by leveraging the mathematics of elliptic curves over a finite field. In the Bitcoin network, ECDSA verifies that only the holder of a private key can authorize spending from the associated public address. The algorithm creates a unique signature for each transaction, ensuring integrity while optimizing computational and storage efficiency.