Secp256k1

Secp256k1 is an elliptic curve used in public key cryptography, selected for widespread use in digital signatures. Defined over a prime field, it is one of the curves standardized by the Standards for Efficient Cryptography Group (SECG) and described in SEC 2. The curve equation is y^2 = x^3 + 7 (mod p), where p = 2^256 − 2^32 − 977. The group generated by a chosen base point G provides the basis for deriving public keys by multiplying G by a private scalar.

Field, order, and generator: The finite field prime is p = 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFC2F. The base point G has coordinates Gx = 0x79BE667EF9DCBBAC55A06295CE870B07029BFCDB2DCE28D959F2815B16F81798 and Gy = 0x483ADA7726A3C4655DA4FBFC0E1108A8FD17B448A68554199C47D08FFB10D4B8. The order of the generated subgroup is n = 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEBAAEDCE6AF48A03BBFD25E8CD0364141, and the cofactor h = 1.

Usage: Secp256k1 is the elliptic curve used by Bitcoin for ECDSA signatures, enabling private keys to sign messages and produce verifiable public keys. It is also used in other blockchain platforms, including Ethereum, for account signing. Public keys derived from secp256k1 form the basis of addresses in those systems.

Security and characteristics: The curve provides roughly 128 bits of security, based on the difficulty of the elliptic curve discrete logarithm problem for 256-bit parameters. No practical flaws or widely accepted backdoors are known in the standard parameters, and the cofactor of 1 means the base point generates the large subgroup used for cryptographic operations. The parameters are defined by SECG and are widely implemented in cryptographic libraries and blockchain software.