ECDSA

ECDSA, or Elliptic Curve Digital Signature Algorithm, is a cryptographic method used to create digital signatures based on elliptic curve mathematics. In the Bitcoin network, all keys and signatures rely on ECDSA for security.

With ECDSA, a user generates a private key—a very large random number—which is then used to compute a public key via a mathematical operation called point multiplication on an elliptic curve. The specific curve used in Bitcoin is known as secp256k1, defined by the equation y² = x³ + 7.

A private key allows the owner to sign data, and the resulting signature can be verified by anyone using the public key. This process ensures that only the holder of the private key could have produced the signature, while it remains computationally impossible to uncover the private key from either the public key or the signature. Furthermore, ECDSA signatures cannot be forged for other data.

These security benefits make ECDSA central to Bitcoin: every transaction is authorized with these digital signatures, ensuring asset security and authenticity across the network.