curve.hpp File Reference

Elliptic-curve helpers, fixed parameters, and hash-to-curve utilities for Purify. More...

#include "purify/numeric.hpp"

Go to the source code of this file.

Data Structures
struct	purify::JacobianPoint
	Jacobian point representation used for curve arithmetic. More...
struct	purify::AffinePoint
	Affine point representation used for serialization and lookup tables. More...
struct	purify::CompleteProjectivePoint
	Projective point used by the hardened secret-scalar multiplication path. More...
class	purify::EllipticCurve
	Minimal elliptic-curve arithmetic over the Purify base field. More...
class	purify::TaggedHash
	Reusable BIP340-style tagged SHA-256 helper. More...

Namespaces
namespace	purify

Functions
Bytes	purify::bytes_from_ascii (std::string_view input)
	Encodes an ASCII string as a byte vector.
Bytes	purify::operator+ (Bytes lhs, const Bytes &rhs)
	Concatenates two byte vectors.
std::uint64_t	purify::ceil_div (std::uint64_t lhs, std::uint64_t rhs)
	Computes ceiling division for unsigned 64-bit values.
Bytes	purify::hmac_sha256 (const Bytes &key, const Bytes &data)
	Computes an HMAC-SHA256 digest using the secp bridge implementation.
Bytes	purify::hkdf (std::size_t length, const Bytes &ikm, const Bytes &salt={}, const Bytes &info={})
	Expands input key material using HKDF-SHA256.
template<std::size_t Words>
std::optional< BigUInt< Words > >	purify::hash_to_int (const Bytes &data, const BigUInt< Words > &range, const Bytes &info={})
	Rejection-samples a uniformly distributed integer below range.
template<std::size_t Words>
std::optional< BigUInt< Words > >	purify::tagged_hash_to_int (std::span< const unsigned char > data, const BigUInt< Words > &range, const TaggedHash &tag, std::span< const unsigned char > info={})
	Rejection-samples a uniformly distributed integer below range using repeated tagged hashes.
const UInt256 &	purify::order_n1 ()
	Returns the subgroup order for the first curve.
const UInt256 &	purify::order_n2 ()
	Returns the subgroup order for the second curve.
const UInt256 &	purify::half_n1 ()
	Returns floor(order_n1 / 2).
const UInt256 &	purify::half_n2 ()
	Returns floor(order_n2 / 2).
const UInt512 &	purify::packed_secret_key_space_size ()
	Returns the size of the packed secret-key encoding space.
const UInt512 &	purify::packed_public_key_space_size ()
	Returns the size of the packed public-key encoding space.
const UInt320 &	purify::two_p ()
	Returns 2 * prime_p() as a widened integer for hash-to-curve sampling.
FieldElement	purify::field_a ()
	Returns the shared Weierstrass a coefficient used by Purify.
FieldElement	purify::field_b ()
	Returns the shared Weierstrass b coefficient used by Purify.
FieldElement	purify::field_d ()
	Returns the twist factor used to derive the second curve.
FieldElement	purify::field_di ()
	Returns the inverse of the twist factor in the field.
const EllipticCurve &	purify::curve1 ()
	Returns the first Purify curve instance.
const EllipticCurve &	purify::curve2 ()
	Returns the second Purify curve instance.
Result< JacobianPoint >	purify::hash_to_curve (const Bytes &data, const EllipticCurve &curve)
	Hashes arbitrary data onto the supplied curve by rejection sampling x-coordinates.
const JacobianPoint &	purify::generator1 ()
	Returns the fixed generator for the first curve.
const JacobianPoint &	purify::generator2 ()
	Returns the fixed generator for the second curve.
bool	purify::is_valid_secret_key (const UInt512 &z)
	Returns true when a packed secret is encoded canonically.
bool	purify::is_valid_public_key (const UInt512 &packed)
	Returns true when a packed public key is encoded canonically.
Status	purify::validate_secret_key (const UInt512 &z)
	Validates the packed secret-key encoding range.
Status	purify::validate_public_key (const UInt512 &packed)
	Validates the packed public-key encoding range.
Result< std::pair< UInt256, UInt256 > >	purify::unpack_secret (const UInt512 &z)
	Splits a packed private key into its two per-curve secret scalars.
Result< std::pair< UInt256, UInt256 > >	purify::unpack_public (const UInt512 &packed)
	Splits a packed public key into its two x-coordinates.
UInt512	purify::pack_public (const UInt256 &x1, const UInt256 &x2)
	Packs two x-coordinates into the reference 512-bit public-key encoding.
FieldElement	purify::combine (const FieldElement &x1, const FieldElement &x2)
	Applies the Purify curve-combination map to two x-coordinates.
Result< std::vector< int > >	purify::key_to_bits (UInt256 n, const UInt256 &max_value)
	Encodes a scalar into the signed 3-bit window bit schedule used by the circuit.