Module p192 

NIST P-192 Elliptic Curve Primitives

This module implements NIST P-192 elliptic curve operations in constant time. Curve equation: y² = x³ - 3x + b over 𝔽ₚ, where

• p = 2¹⁹² − 2⁶⁴ − 1,
• Curve order n = 0xFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFFFFFFFFFF. (NIST P-192 order).

Implements:

• Mersenne reduction for 𝔽ₚ (2¹⁹² ≡ 2⁶⁴ + 1),
• Jacobian projective coordinates for point operations,
• Constant‐time scalar multiplication, addition, etc.

Structs

FieldElement

P-192 field element representing values in 𝔽ₚ, where p = 2¹⁹² − 2⁶⁴ − 1. Internally stored as 6 little‐endian 32‐bit limbs.

Point

Affine coordinates (x, y) or identity; 𝔽ₚ is built from FieldElement

Scalar

P-192 scalar: integers mod n, where n = 0xFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFFFFFFFFFF (curve order).

Enums

PointFormat

Format of a serialized elliptic‐curve point

Constants

P192_FIELD_ELEMENT_SIZE

Size of a P-192 field element in bytes (24 bytes = 192 bits)

P192_KEM_SHARED_SECRET_KDF_OUTPUT_SIZE

Size of the KDF output for P-192 ECDH‐KEM shared secret derivation

P192_POINT_COMPRESSED_SIZE

Size of a compressed P-192 point in bytes: format byte (0x02/0x03) + x-coordinate

P192_POINT_UNCOMPRESSED_SIZE

Size of an uncompressed P-192 point in bytes: format byte (0x04) + x-coordinate + y-coordinate

P192_SCALAR_SIZE

Size of a P-192 scalar in bytes (24 bytes = 192 bits)

Functions

base_point_g

Get the standard base point G of the P-192 curve

generate_keypair

Generate a cryptographically secure ECDH keypair

kdf_hkdf_sha256_for_ecdh_kem

Key derivation for ECDH shared secret using HKDF-SHA256

scalar_mult

General scalar multiplication: compute scalar * arbitrary point

scalar_mult_base_g

Scalar multiplication with the base point: scalar * G