How deeply does Real-World Cryptography cover secp256k1?

Defines the curve type, equation, modulus, group order, and generator coordinates without developing implementation formulas.

Secp256k1

As explained in Real-World Cryptography

secp256k1 is a standardized Koblitz elliptic curve used for public-key cryptography and digital signatures.

secp256k1 is a Koblitz elliptic curve used with ECDSA for digital signatures. It gained major traction after Bitcoin selected it instead of NIST curves. section 7.3.3

Its curve equation is y² = x³ + ax + b, with a = 0 and b = 7. Coordinates use arithmetic modulo the prime p = 2²⁵⁶ − 2³² − 2⁹ − 2⁸ − 2⁷ − 2⁶ − 2⁴ − 1, forming a group of prime order. section 7.3.3

Key parameters include:

The generator G has fixed coordinates x = 55066263022277343669578718895168534326250603453777594175500187360389116729240 and y = 32670510020758816978083085130507043184471273380659243275938904335757337482424. section 7.3.3
Koblitz constraints allow implementations to optimize some curve operations. section 7.3.3

How Real-World Cryptography covers it

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Related concepts

Bitcoinused by · Bitcoin is a decentralized digital currency and cryptocurrency system that records and verifies transactions on a peer-to-peer network using a distributed ledger.
elliptic curvekind of · An elliptic curve is a nonsingular algebraic curve defined by a cubic equation whose points, including a point at infinity, support a group operation.
ECDSAuses · ECDSA is a public-key digital signature algorithm that uses elliptic-curve arithmetic to generate and verify signatures.
P-256alternative to · P-256, also called secp256r1, is a standardized elliptic curve over a 256-bit prime finite field used in public-key cryptography.

This explainer was generated by Manning's knowledge graph from the text of Real-World Cryptography. The section links point to the parts of the book it draws on.