What elliptic curve does Bitcoin use for key generation?

Bitcoin uses the secp256k1 elliptic curve for key generation.

A Bitcoin wallet begins with a private key: a secret 256-bit number selected from the curve’s valid range. The corresponding public key is produced through elliptic-curve point multiplication, a one-way operation that is easy to perform but infeasible to reverse with current computing methods.

Bitcoin traditionally uses secp256k1 with ECDSA to authenticate transactions. The curve’s name identifies its standardized parameters, including a 256-bit prime field and a particular generator point. Bitcoin later also adopted Schnorr signatures through Taproot, but those signatures still use secp256k1.

The other choices are real cryptographic curves, which makes them tempting distractors. Curve25519 is widely associated with modern key-exchange systems, while secp256r1 is a different NIST curve. Neither is Bitcoin’s standard curve for its native key system.