Module p256

NIST P-256 Elliptic Curve Primitives

This module implements the NIST P-256 elliptic curve operations in constant time. The curve equation is y² = x³ - 3x + b over the prime field F_p where:

• p = 2^256 - 2^224 + 2^192 + 2^96 - 1 (NIST P-256 prime)
• The curve order n = 0xFFFFFFFF00000000FFFFFFFFFFFFFFFFBCE6FAADA7179E84F3B9CAC2FC632551

All operations are implemented to be constant-time to prevent timing attacks. The implementation uses:

• Montgomery reduction for field arithmetic
• Jacobian projective coordinates for efficient point operations
• Binary scalar multiplication with constant-time point selection

Structs

FieldElement

P-256 field element representing values in F_p

Point

P-256 elliptic curve point in affine coordinates (x, y)

Scalar

P-256 scalar value for use in elliptic curve operations

Enums

PointFormat

Format of a serialized elliptic curve point

Constants

P256_FIELD_ELEMENT_SIZE

Size of a P-256 field element in bytes (32 bytes = 256 bits)

P256_KEM_SHARED_SECRET_KDF_OUTPUT_SIZE

Size of the KDF output for P-256 ECDH-KEM shared secret derivation

P256_POINT_COMPRESSED_SIZE

Size of a compressed P-256 point in bytes: format byte (0x02/0x03) + x-coordinate

P256_POINT_UNCOMPRESSED_SIZE

Size of an uncompressed P-256 point in bytes: format byte (0x04) + x-coordinate + y-coordinate

P256_SCALAR_SIZE

Size of a P-256 scalar in bytes (32 bytes = 256 bits)

Functions

base_point_g

Get the standard base point G of the P-256 curve

generate_keypair

Generate a cryptographically secure ECDH keypair

kdf_hkdf_sha256_for_ecdh_kem

Key derivation function for ECDH shared secret using HKDF-SHA256

scalar_mult

General scalar multiplication: compute scalar * point

scalar_mult_base_g

Scalar multiplication with the base point: scalar * G