secp256k1

secp256k1 is the elliptic curve Bitcoin uses for its public-key cryptography. Every standard Bitcoin private key maps to a public key on this curve, and both legacy ECDSA signatures and the Schnorr signatures introduced by Taproot use that same key space.

The curve was defined in the SEC 2 standards as a Koblitz curve over a 256-bit prime field. In practice, Bitcoin developers care less about the label and more about the tradeoffs: secp256k1 supports fast, specialized arithmetic, and its parameters were chosen in a transparent way instead of from an opaque seed. That made it a good fit for a system that needs signatures verified everywhere, from full nodes to hardware wallets.

Most Bitcoin software relies on libsecp256k1, the optimized C library maintained under the Bitcoin Core organization. It provides high-assurance implementations of core operations such as key generation, ECDSA signing and verification, and optional modules for Schnorr signatures, BIP 324, and MuSig2.

References

• SEC 2 v2: Recommended Elliptic Curve Domain Parameters
• Bitcoin Wiki: secp256k1
• bitcoin-core/secp256k1
• BIP 340: Schnorr Signatures for secp256k1