Curve reference
secp256k1
secp256k1 is the 256-bit prime-field elliptic curve standardized by SECG in SEC 2 and used in Bitcoin's signature stack.
- Equation
y^2 = x^3 + 7 mod p- Field modulus
2^256 - 2^32 - 977- a, b, h
a = 0,b = 7,h = 1- Order
FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEBAAEDCE6AF48A03BBFD25E8CD0364141
Why it matters
- It is foundational to Bitcoin ECDSA and BIP 340 Schnorr signatures.
- Its compact equation still requires careful finite-field arithmetic, validation, cleanup, and side-channel discipline.
- Contest tracks make arithmetic and ECDLP research reproducible through versioned benchmarks.
Generator
G compressed: 0279BE667EF9DCBBAC55A06295CE870B07029BFCDB2DCE28D959F2815B16F81798 Gx: 79BE667EF9DCBBAC55A06295CE870B07029BFCDB2DCE28D959F2815B16F81798 Gy: 483ADA7726A3C4655DA4FBFC0E1108A8FD17B448A68554199C47D08FFB10D4B8
Safety notes
- Do not treat secp256k1 as quantum safe; Shor's algorithm would break ECDLP on a capable fault-tolerant quantum computer.
- Do not claim the curve was generated verifiably at random; SEC 2 classifies it as Koblitz-type.
- Implementation safety depends on nonce handling, public-key validation, constant-time code, and side-channel resistance.