Module p384

NIST P-384 Elliptic Curve Primitives

This module implements the NIST P-384 elliptic curve operations in constant time. The curve equation is y² = x³ - 3x + b over the prime field F_p where:

• p = 2^384 - 2^128 - 2^96 + 2^32 - 1 (NIST P-384 prime)
• The curve order n = 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFC7634D81F4372DDF581A0DB248B0A77AECEC196ACCC52973

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

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

Structs

FieldElement

P-384 field element representing values in F_p

Point

P-384 elliptic curve point in affine coordinates (x, y)

Scalar

P-384 scalar value for use in elliptic curve operations

Enums

PointFormat

Format of a serialized elliptic curve point

Constants

P384_FIELD_ELEMENT_SIZE

Size of a P-384 field element in bytes (48 bytes = 384 bits)

P384_KEM_SHARED_SECRET_KDF_OUTPUT_SIZE

Size of the KDF output for P-384 ECDH-KEM shared secret derivation

P384_POINT_COMPRESSED_SIZE

Size of a compressed P-384 point in bytes: format byte (0x02/0x03) + x-coordinate

P384_POINT_UNCOMPRESSED_SIZE

Size of an uncompressed P-384 point in bytes: format byte (0x04) + x-coordinate + y-coordinate

P384_SCALAR_SIZE

Size of a P-384 scalar in bytes (48 bytes = 384 bits)

Functions

base_point_g

Get the standard base point G of the P-384 curve

generate_keypair

Generate a cryptographically secure ECDH keypair

kdf_hkdf_sha384_for_ecdh_kem

Key derivation function for ECDH shared secret using HKDF-SHA384

scalar_mult

General scalar multiplication: compute scalar * point

scalar_mult_base_g

Scalar multiplication with the base point: scalar * G