prime256v1

prime256v1 is an elliptic curve used in public-key cryptography. It is the OpenSSL name for the NIST/SECG standardized curve known as P-256 or secp256r1. The curve is defined over a 256-bit prime field and provides about 128-bit security for ECDSA and ECDH, making it a common choice for digital signatures and key exchange in TLS and X.509 certificates.

The curve is a short Weierstrass form over the prime field F_p with the following domain parameters: p = FFFFFFFF00000001000000000000000000000000FFFFFFFFFFFFFFFFFFFFFFFF, a = FFFFFFFF00000001000000000000000000000000FFFFFFFFFFFFFFFFFFFFFFFC, b = 5AC635D8AA3A93E7B3EBBD55769886BC651D06B0CC53B0F63BCE3C3E27D2604B, Gx = 6B17D1F2E12C4247F8BCE6E563A440F277037D812DEB33A0F4A13945D898C296, Gy = 4FE342E2FE1A7F9B8EE7EB4A7C0F9E162BCE33576B315ECECBB6406837BF51F5, n = FFFFFFFF00000000FFFFFFFFFFFFFFFFBCE6FAADA7179E84F3B9CAC2FC632551, h = 1.

Naming and standardization: prime256v1 is widely recognized as P-256 by NIST and secp256r1 by SECG. It is standardized in FIPS 186-4 and is widely implemented in cryptographic libraries and protocols, including TLS, SSH, and various certificate infrastructures. The curve is selected for a balance of security and performance and remains a foundational choice for 256-bit elliptic-curve cryptography.