How deeply does Real-World Cryptography cover P-256?

Defines the curve equation, parameters, point order, and base point without detailing implementation procedures.

P-256

P-256, also called secp256r1, is a standardized elliptic curve providing approximately 128 bits of security for elliptic-curve cryptography.

P-256, also called secp256r1, is a standardized elliptic curve widely used for internet cryptography. It commonly supports ECDH key exchange with approximately 128-bit security. section 5.3.3 section 5.5

Key points:

NIST FIPS 186-4 specifies P-256, while SEC 2 v2 specifies the same curve under the name secp256r1. section 5.3.3
Its short Weierstrass equation is y² = x³ + ax + b mod p, with a = −3 and standardized constants. section 5.3.3
ECDH implementations must verify received public keys; invalid keys are a recurring source of bugs. section 5.5

Choosing a curve for ECDH

For 128-bit security, ECDH commonly uses 256-bit parameters such as P-256 or Curve25519. Applications targeting 256-bit security can instead use P-521 or Curve448. section 5.5

How Real-World Cryptography covers it

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Also explained in

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Hacking CryptographyP-256 is a standardized elliptic curve over a 256-bit prime finite field used for public-key cryptography.
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Related concepts

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.
elliptic-curve diffie-hellmanconfigures · Elliptic-curve Diffie-Hellman is a public-key key-agreement method in which parties derive a shared secret through elliptic-curve point operations.
JSON Web Keyused by · A JSON Web Key is a JSON-based representation of a cryptographic key and its associated parameters and metadata.
secp256k1alternative to · secp256k1 is a standardized 256-bit Koblitz elliptic curve used in public-key cryptography and digital signatures.

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.