curve.c File Reference

#include "curve.h"
#include <assert.h>
#include <string.h>

Go to the source code of this file.

Functions
static void	purify_curve_copy_u256 (uint64_t out[4], const uint64_t value[4])
static void	purify_curve_u256_narrow_u512_unchecked (uint64_t out[4], const uint64_t value[8])
static void	purify_curve_u256_add_one_unchecked (uint64_t value[4])
static void	purify_curve_u64_to_be (unsigned char out[8], uint64_t value)
static void	purify_curve_tag_hash (unsigned char out[32])
static int	purify_curve_hash_to_int_tagged_u320 (uint64_t out[5], const unsigned char *data, size_t data_len, const uint64_t range[5], unsigned char info_byte)
static purify_complete_projective_point	purify_curve_complete_identity (void)
static purify_complete_projective_point	purify_curve_secret_input_point (const purify_curve *curve, const purify_jacobian_point *point)
static void	purify_curve_complete_assign (purify_complete_projective_point *dst, const purify_complete_projective_point *src, int flag)
static void	purify_curve_complete_swap (purify_complete_projective_point *lhs, purify_complete_projective_point *rhs, int flag)
static purify_complete_projective_point	purify_curve_complete_add (const purify_curve *curve, const purify_complete_projective_point *lhs, const purify_complete_projective_point *rhs)
static purify_complete_projective_point	purify_curve_complete_double (const purify_curve *curve, const purify_complete_projective_point *point)
void	purify_curve_prime_p (uint64_t out[4])
void	purify_curve_order_n1 (uint64_t out[4])
void	purify_curve_order_n2 (uint64_t out[4])
void	purify_curve_half_n1 (uint64_t out[4])
void	purify_curve_half_n2 (uint64_t out[4])
void	purify_curve_packed_secret_key_space_size (uint64_t out[8])
void	purify_curve_packed_public_key_space_size (uint64_t out[8])
void	purify_curve_two_p (uint64_t out[5])
void	purify_curve_field_a (purify_fe *out)
void	purify_curve_field_b (purify_fe *out)
void	purify_curve_field_d (purify_fe *out)
void	purify_curve_field_di (purify_fe *out)
void	purify_curve_jacobian_infinity (purify_jacobian_point *out)
void	purify_curve_affine (purify_affine_point *out, const purify_curve *curve, const purify_jacobian_point *point)
void	purify_curve_negate (purify_jacobian_point *out, const purify_jacobian_point *point)
int	purify_curve_is_x_coord (const purify_curve *curve, const purify_fe *x)
int	purify_curve_lift_x (purify_jacobian_point *out, const purify_curve *curve, const purify_fe *x)
void	purify_curve_double (purify_jacobian_point *out, const purify_curve *curve, const purify_jacobian_point *point)
void	purify_curve_add_mixed (purify_jacobian_point *out, const purify_curve *curve, const purify_jacobian_point *lhs, const purify_affine_point *rhs)
void	purify_curve_add (purify_jacobian_point *out, const purify_curve *curve, const purify_jacobian_point *lhs, const purify_jacobian_point *rhs)
void	purify_curve_mul (purify_jacobian_point *out, const purify_curve *curve, const purify_jacobian_point *point, const uint64_t scalar[4])
static void	purify_curve_mul_secret_ladder_core (purify_complete_projective_point *out, const purify_curve *curve, const purify_jacobian_point *point, const uint64_t scalar[4])
int	purify_curve_mul_secret_affine (purify_affine_point *out, const purify_curve *curve, const purify_jacobian_point *point, const uint64_t scalar[4])
int	purify_curve_hash_to_curve (purify_jacobian_point *out, const purify_curve *curve, const unsigned char *data, size_t data_len)
int	purify_curve_is_valid_secret_key (const uint64_t value[8])
int	purify_curve_is_valid_public_key (const uint64_t value[8])
static void	purify_curve_unpack_secret_from_valid (uint64_t first[4], uint64_t second[4], const uint64_t value[8])
int	purify_curve_unpack_secret (uint64_t first[4], uint64_t second[4], const uint64_t value[8])
int	purify_curve_unpack_public (uint64_t first[4], uint64_t second[4], const uint64_t value[8])
void	purify_curve_pack_public (uint64_t out[8], const uint64_t x1[4], const uint64_t x2[4])
void	purify_curve_combine (purify_fe *out, const purify_fe *x1, const purify_fe *x2)
int	purify_curve_key_to_bits (int *out_bits, size_t out_len, const uint64_t value[4], const uint64_t max_value[4])

Variables
static const uint64_t	kPurifyPrimeP [4]
static const uint64_t	kPurifyOrderN1 [4]
static const uint64_t	kPurifyOrderN2 [4]
static const uint64_t	kPurifyHalfN1 [4]
static const uint64_t	kPurifyHalfN2 [4]
static const uint64_t	kPurifyFieldDi [4]
static const char	kPurifyHashToCurveTag [] = "Purify/HashToCurve"

Function Documentation

purify_curve_add()

void purify_curve_add	(	purify_jacobian_point *	out,
		const purify_curve *	curve,
		const purify_jacobian_point *	lhs,
		const purify_jacobian_point *	rhs
	)

Definition at line 619 of file curve.c.

References purify_jacobian_point::infinity, purify_affine_point::infinity, purify_curve_add_mixed(), purify_curve_double(), purify_curve_jacobian_infinity(), purify_fe_eq(), purify_fe_is_one(), purify_fe_is_zero(), purify_fe_mul(), purify_fe_set_u64(), purify_fe_sub(), purify_jacobian_point::x, purify_affine_point::x, purify_jacobian_point::y, purify_affine_point::y, and purify_jacobian_point::z.

Referenced by purify::EllipticCurve::add(), and purify_curve_mul().

purify_curve_add_mixed()

void purify_curve_add_mixed	(	purify_jacobian_point *	out,
		const purify_curve *	curve,
		const purify_jacobian_point *	lhs,
		const purify_affine_point *	rhs
	)

Definition at line 566 of file curve.c.

References purify_jacobian_point::infinity, purify_affine_point::infinity, purify_curve_double(), purify_curve_jacobian_infinity(), purify_fe_eq(), purify_fe_is_zero(), purify_fe_mul(), purify_fe_set_u64(), purify_fe_sub(), purify_jacobian_point::x, purify_affine_point::x, purify_jacobian_point::y, purify_affine_point::y, and purify_jacobian_point::z.

Referenced by purify::EllipticCurve::add_mixed(), and purify_curve_add().

purify_curve_affine()

void purify_curve_affine	(	purify_affine_point *	out,
		const purify_curve *	curve,
		const purify_jacobian_point *	point
	)

Definition at line 450 of file curve.c.

References purify_jacobian_point::infinity, purify_affine_point::infinity, purify_fe_inverse_var(), purify_fe_is_zero(), purify_fe_mul(), purify_fe_set_zero(), purify_jacobian_point::x, purify_affine_point::x, purify_jacobian_point::y, purify_affine_point::y, and purify_jacobian_point::z.

Referenced by purify::EllipticCurve::affine(), and purify_curve_secret_input_point().

purify_curve_combine()

void purify_curve_combine	(	purify_fe *	out,
		const purify_fe *	x1,
		const purify_fe *	x2
	)

Definition at line 904 of file curve.c.

References purify_curve_field_a(), purify_curve_field_b(), purify_curve_field_di(), purify_fe_add(), purify_fe_inverse(), purify_fe_mul(), purify_fe_set_u64(), and purify_fe_sub().

Referenced by purify::combine().

purify_curve_complete_add()

static purify_complete_projective_point purify_curve_complete_add ( const purify_curve *  curve, const purify_complete_projective_point *  lhs, const purify_complete_projective_point *  rhs  )

static

Definition at line 275 of file curve.c.

References purify_curve::a, purify_curve::b, purify_fe_add(), purify_fe_mul(), purify_fe_sub(), purify_complete_projective_point::x, purify_complete_projective_point::y, and purify_complete_projective_point::z.

Referenced by purify_curve_mul_secret_ladder_core().

purify_curve_complete_assign()

static void purify_curve_complete_assign ( purify_complete_projective_point *  dst, const purify_complete_projective_point *  src, int  flag  )

static

Definition at line 258 of file curve.c.

References purify_fe_cmov(), purify_complete_projective_point::x, purify_complete_projective_point::y, and purify_complete_projective_point::z.

Referenced by purify_curve_complete_swap().

purify_curve_complete_double()

static purify_complete_projective_point purify_curve_complete_double ( const purify_curve *  curve, const purify_complete_projective_point *  point  )

static

Definition at line 340 of file curve.c.

References purify_curve::a, purify_curve::b, purify_fe_add(), purify_fe_mul(), purify_fe_sub(), purify_complete_projective_point::x, purify_complete_projective_point::y, and purify_complete_projective_point::z.

Referenced by purify_curve_mul_secret_ladder_core().

purify_curve_complete_identity()

static purify_complete_projective_point purify_curve_complete_identity ( void  )

static

Definition at line 228 of file curve.c.

References purify_fe_set_u64(), purify_fe_set_zero(), purify_complete_projective_point::x, purify_complete_projective_point::y, and purify_complete_projective_point::z.

Referenced by purify_curve_mul_secret_ladder_core(), and purify_curve_secret_input_point().

purify_curve_complete_swap()

static void purify_curve_complete_swap ( purify_complete_projective_point *  lhs, purify_complete_projective_point *  rhs, int  flag  )

static

Definition at line 266 of file curve.c.

References purify_curve_complete_assign().

Referenced by purify_curve_mul_secret_ladder_core().

purify_curve_copy_u256()

static void purify_curve_copy_u256 ( uint64_t  out[4], const uint64_t  value[4]  )

static

Definition at line 79 of file curve.c.

Referenced by purify_curve_half_n1(), purify_curve_half_n2(), purify_curve_key_to_bits(), purify_curve_order_n1(), purify_curve_order_n2(), and purify_curve_prime_p().

purify_curve_double()

void purify_curve_double	(	purify_jacobian_point *	out,
		const purify_curve *	curve,
		const purify_jacobian_point *	point
	)

Definition at line 517 of file curve.c.

References purify_curve::a, purify_jacobian_point::infinity, purify_curve_jacobian_infinity(), purify_fe_add(), purify_fe_is_zero(), purify_fe_mul(), purify_fe_set_u64(), purify_fe_sub(), purify_jacobian_point::x, purify_jacobian_point::y, and purify_jacobian_point::z.

Referenced by purify::EllipticCurve::double_point(), purify_curve_add(), purify_curve_add_mixed(), and purify_curve_mul().

purify_curve_field_a()

void purify_curve_field_a

(

purify_fe *

out

)

Definition at line 425 of file curve.c.

References purify_fe_set_u64().

Referenced by purify::field_a(), and purify_curve_combine().

purify_curve_field_b()

void purify_curve_field_b

(

purify_fe *

out

)

Definition at line 429 of file curve.c.

References purify_fe_set_u64().

Referenced by purify::field_b(), and purify_curve_combine().

purify_curve_field_d()

void purify_curve_field_d

(

purify_fe *

out

)

Definition at line 433 of file curve.c.

References purify_fe_set_u64().

Referenced by purify::field_d().

purify_curve_field_di()

void purify_curve_field_di

(

purify_fe *

out

)

Definition at line 437 of file curve.c.

References kPurifyFieldDi, and purify_fe_set_u256().

Referenced by purify::field_di(), and purify_curve_combine().

purify_curve_half_n1()

void purify_curve_half_n1

(

uint64_t

out[4]

)

Definition at line 404 of file curve.c.

References kPurifyHalfN1, and purify_curve_copy_u256().

Referenced by purify::half_n1().

purify_curve_half_n2()

void purify_curve_half_n2

(

uint64_t

out[4]

)

Definition at line 408 of file curve.c.

References kPurifyHalfN2, and purify_curve_copy_u256().

Referenced by purify::half_n2().

purify_curve_hash_to_curve()

int purify_curve_hash_to_curve	(	purify_jacobian_point *	out,
		const purify_curve *	curve,
		const unsigned char *	data,
		size_t	data_len
	)

Definition at line 778 of file curve.c.

References purify_curve_hash_to_int_tagged_u320(), purify_curve_is_x_coord(), purify_curve_jacobian_infinity(), purify_curve_lift_x(), purify_curve_negate(), purify_curve_two_p(), purify_fe_set_u256(), and purify_u256_try_narrow_u320().

Referenced by purify::hash_to_curve().

purify_curve_hash_to_int_tagged_u320()

static int purify_curve_hash_to_int_tagged_u320 ( uint64_t  out[5], const unsigned char *  data, size_t  data_len, const uint64_t  range[5], unsigned char  info_byte  )

static

Definition at line 111 of file curve.c.

References purify_curve_tag_hash(), purify_curve_u64_to_be(), and purify_sha256_many().

Referenced by purify_curve_hash_to_curve().

purify_curve_is_valid_public_key()

int purify_curve_is_valid_public_key

(

const uint64_t

value[8]

)

Definition at line 837 of file curve.c.

References purify_curve_packed_public_key_space_size().

Referenced by purify::is_valid_public_key(), and purify_curve_unpack_public().

purify_curve_is_valid_secret_key()

int purify_curve_is_valid_secret_key

(

const uint64_t

value[8]

)

Definition at line 831 of file curve.c.

References purify_curve_packed_secret_key_space_size().

Referenced by purify::is_valid_secret_key(), and purify_curve_unpack_secret().

purify_curve_is_x_coord()

int purify_curve_is_x_coord	(	const purify_curve *	curve,
		const purify_fe *	x
	)

Definition at line 482 of file curve.c.

References purify_curve::a, purify_curve::b, purify_fe_add(), purify_fe_legendre_symbol(), and purify_fe_mul().

Referenced by purify::EllipticCurve::is_x_coord(), and purify_curve_hash_to_curve().

purify_curve_jacobian_infinity()

void purify_curve_jacobian_infinity

(

purify_jacobian_point *

out

)

Definition at line 443 of file curve.c.

References purify_jacobian_point::infinity, purify_fe_set_u64(), purify_fe_set_zero(), purify_jacobian_point::x, purify_jacobian_point::y, and purify_jacobian_point::z.

Referenced by purify::JacobianPoint::infinity_point(), purify_curve_add(), purify_curve_add_mixed(), purify_curve_double(), purify_curve_hash_to_curve(), and purify_curve_mul().

purify_curve_key_to_bits()

int purify_curve_key_to_bits	(	int *	out_bits,
		size_t	out_len,
		const uint64_t	value[4],
		const uint64_t	max_value[4]
	)

Definition at line 937 of file curve.c.

References purify_curve_copy_u256().

Referenced by purify::key_to_bits().

purify_curve_lift_x()

int purify_curve_lift_x	(	purify_jacobian_point *	out,
		const purify_curve *	curve,
		const purify_fe *	x
	)

Definition at line 496 of file curve.c.

References purify_curve::a, purify_curve::b, purify_jacobian_point::infinity, purify_fe_add(), purify_fe_mul(), purify_fe_set_u64(), purify_fe_sqrt(), purify_jacobian_point::x, purify_jacobian_point::y, and purify_jacobian_point::z.

Referenced by purify::EllipticCurve::lift_x(), and purify_curve_hash_to_curve().

purify_curve_mul()

void purify_curve_mul	(	purify_jacobian_point *	out,
		const purify_curve *	curve,
		const purify_jacobian_point *	point,
		const uint64_t	scalar[4]
	)

Definition at line 697 of file curve.c.

References purify_curve_add(), purify_curve_double(), purify_curve_jacobian_infinity(), and scalar.

Referenced by purify::EllipticCurve::mul().

purify_curve_mul_secret_affine()

int purify_curve_mul_secret_affine	(	purify_affine_point *	out,
		const purify_curve *	curve,
		const purify_jacobian_point *	point,
		const uint64_t	scalar[4]
	)

Definition at line 759 of file curve.c.

References purify_affine_point::infinity, purify_curve_mul_secret_ladder_core(), purify_fe_inverse(), purify_fe_is_zero(), purify_fe_mul(), scalar, purify_affine_point::x, purify_complete_projective_point::x, purify_affine_point::y, purify_complete_projective_point::y, and purify_complete_projective_point::z.

Referenced by purify::EllipticCurve::mul_secret_affine().

purify_curve_mul_secret_ladder_core()

static void purify_curve_mul_secret_ladder_core ( purify_complete_projective_point *  out, const purify_curve *  curve, const purify_jacobian_point *  point, const uint64_t  scalar[4]  )

static

Definition at line 716 of file curve.c.

References bit(), purify_curve::n, purify_curve_complete_add(), purify_curve_complete_double(), purify_curve_complete_identity(), purify_curve_complete_swap(), purify_curve_secret_input_point(), and scalar.

Referenced by purify_curve_mul_secret_affine().

purify_curve_negate()

void purify_curve_negate	(	purify_jacobian_point *	out,
		const purify_jacobian_point *	point
	)

Definition at line 471 of file curve.c.

References purify_jacobian_point::infinity, purify_fe_negate(), purify_jacobian_point::x, purify_jacobian_point::y, and purify_jacobian_point::z.

Referenced by purify::EllipticCurve::negate(), and purify_curve_hash_to_curve().

purify_curve_order_n1()

void purify_curve_order_n1

(

uint64_t

out[4]

)

Definition at line 396 of file curve.c.

References kPurifyOrderN1, and purify_curve_copy_u256().

Referenced by purify::order_n1().

purify_curve_order_n2()

void purify_curve_order_n2

(

uint64_t

out[4]

)

Definition at line 400 of file curve.c.

References kPurifyOrderN2, and purify_curve_copy_u256().

Referenced by purify::order_n2().

purify_curve_pack_public()

void purify_curve_pack_public	(	uint64_t	out[8],
		const uint64_t	x1[4],
		const uint64_t	x2[4]
	)

Definition at line 897 of file curve.c.

References kPurifyPrimeP, purify_u512_multiply_u256(), and purify_u512_widen_u256().

Referenced by purify::pack_public().

purify_curve_packed_public_key_space_size()

void purify_curve_packed_public_key_space_size

(

uint64_t

out[8]

)

Definition at line 416 of file curve.c.

References kPurifyPrimeP, and purify_u512_multiply_u256().

Referenced by purify::packed_public_key_space_size(), and purify_curve_is_valid_public_key().

purify_curve_packed_secret_key_space_size()

void purify_curve_packed_secret_key_space_size

(

uint64_t

out[8]

)

Definition at line 412 of file curve.c.

References kPurifyHalfN1, kPurifyHalfN2, and purify_u512_multiply_u256().

Referenced by purify::packed_secret_key_space_size(), and purify_curve_is_valid_secret_key().

purify_curve_prime_p()

void purify_curve_prime_p

(

uint64_t

out[4]

)

Definition at line 392 of file curve.c.

References kPurifyPrimeP, and purify_curve_copy_u256().

Referenced by purify::prime_p().

purify_curve_secret_input_point()

static purify_complete_projective_point purify_curve_secret_input_point ( const purify_curve *  curve, const purify_jacobian_point *  point  )

static

Definition at line 237 of file curve.c.

References purify_jacobian_point::infinity, purify_curve_affine(), purify_curve_complete_identity(), purify_fe_is_one(), purify_fe_is_zero(), purify_fe_set_u64(), purify_jacobian_point::x, purify_affine_point::x, purify_complete_projective_point::x, purify_jacobian_point::y, purify_affine_point::y, purify_complete_projective_point::y, purify_jacobian_point::z, and purify_complete_projective_point::z.

Referenced by purify_curve_mul_secret_ladder_core().

purify_curve_tag_hash()

static void purify_curve_tag_hash ( unsigned char  out[32] )

static

Definition at line 107 of file curve.c.

References kPurifyHashToCurveTag, and purify_sha256().

Referenced by purify_curve_hash_to_int_tagged_u320().

purify_curve_two_p()

void purify_curve_two_p

(

uint64_t

out[5]

)

Definition at line 420 of file curve.c.

References kPurifyPrimeP, and purify_u320_widen_u256().

Referenced by purify_curve_hash_to_curve(), and purify::two_p().

purify_curve_u256_add_one_unchecked()

static void purify_curve_u256_add_one_unchecked ( uint64_t  value[4] )

static

Definition at line 87 of file curve.c.

Referenced by purify_curve_unpack_secret_from_valid().

purify_curve_u256_narrow_u512_unchecked()

static void purify_curve_u256_narrow_u512_unchecked ( uint64_t  out[4], const uint64_t  value[8]  )

static

Definition at line 83 of file curve.c.

Referenced by purify_curve_unpack_secret_from_valid().

purify_curve_u64_to_be()

static void purify_curve_u64_to_be ( unsigned char  out[8], uint64_t  value  )

static

Definition at line 99 of file curve.c.

Referenced by purify_curve_hash_to_int_tagged_u320().

purify_curve_unpack_public()

int purify_curve_unpack_public	(	uint64_t	first[4],
		uint64_t	second[4],
		const uint64_t	value[8]
	)

Definition at line 878 of file curve.c.

References kPurifyPrimeP, purify_curve_is_valid_public_key(), purify_u256_try_narrow_u512(), purify_u512_try_divmod_same(), and purify_u512_widen_u256().

Referenced by purify::unpack_public().

purify_curve_unpack_secret()

int purify_curve_unpack_secret	(	uint64_t	first[4],
		uint64_t	second[4],
		const uint64_t	value[8]
	)

Definition at line 863 of file curve.c.

References purify_curve_is_valid_secret_key(), and purify_curve_unpack_secret_from_valid().

Referenced by purify::unpack_secret().

purify_curve_unpack_secret_from_valid()

static void purify_curve_unpack_secret_from_valid ( uint64_t  first[4], uint64_t  second[4], const uint64_t  value[8]  )

static

Definition at line 843 of file curve.c.

References kPurifyHalfN1, purify_curve_u256_add_one_unchecked(), purify_curve_u256_narrow_u512_unchecked(), purify_u512_try_divmod_same_consttime(), and purify_u512_widen_u256().

Referenced by purify_curve_unpack_secret().

Variable Documentation

kPurifyFieldDi

const uint64_t kPurifyFieldDi[4]

static

Initial value:

= {
 
 
 
    UINT64_C(0x4CBA8C385348E6E7),
    UINT64_C(0xE445F1F5DFB6A67E),
    UINT64_C(0x6666666666666665),
    UINT64_C(0x6666666666666666),
 
}

Definition at line 66 of file curve.c.

Referenced by purify_curve_field_di().

kPurifyHalfN1

const uint64_t kPurifyHalfN1[4]

static

Initial value:

= {
 
 
 
    UINT64_C(0x452D15162C72A3F4),
    UINT64_C(0xD1947922029A3909),
    UINT64_C(0xFFFFFFFFFFFFFFFF),
    UINT64_C(0x7FFFFFFFFFFFFFFF),
 
}

Definition at line 44 of file curve.c.

Referenced by purify_curve_half_n1(), purify_curve_packed_secret_key_space_size(), and purify_curve_unpack_secret_from_valid().

kPurifyHalfN2

const uint64_t kPurifyHalfN2[4]

static

Initial value:

= {
 
 
 
    UINT64_C(0x7AA54976A3C39D4D),
    UINT64_C(0xE91A63C4ACAE6732),
    UINT64_C(0xFFFFFFFFFFFFFFFE),
    UINT64_C(0x7FFFFFFFFFFFFFFF),
 
}

Definition at line 55 of file curve.c.

Referenced by purify_curve_half_n2(), and purify_curve_packed_secret_key_space_size().

kPurifyHashToCurveTag

const char kPurifyHashToCurveTag[] = "Purify/HashToCurve"

static

Definition at line 77 of file curve.c.

Referenced by purify_curve_tag_hash().

kPurifyOrderN1

const uint64_t kPurifyOrderN1[4]

static

Initial value:

= {
 
 
 
    UINT64_C(0x8A5A2A2C58E547E9),
    UINT64_C(0xA328F24405347212),
    UINT64_C(0xFFFFFFFFFFFFFFFF),
    UINT64_C(0xFFFFFFFFFFFFFFFF),
 
}

Definition at line 22 of file curve.c.

Referenced by purify_curve_order_n1().

kPurifyOrderN2

const uint64_t kPurifyOrderN2[4]

static

Initial value:

= {
 
 
 
    UINT64_C(0xF54A92ED47873A9B),
    UINT64_C(0xD234C789595CCE64),
    UINT64_C(0xFFFFFFFFFFFFFFFD),
    UINT64_C(0xFFFFFFFFFFFFFFFF),
 
}

Definition at line 33 of file curve.c.

Referenced by purify_curve_order_n2().

kPurifyPrimeP

const uint64_t kPurifyPrimeP[4]

static

Initial value:

= {
 
 
 
 
    UINT64_C(0xBFD25E8CD0364141),
    UINT64_C(0xBAAEDCE6AF48A03B),
    UINT64_C(0xFFFFFFFFFFFFFFFE),
    UINT64_C(0xFFFFFFFFFFFFFFFF),
 
}

Definition at line 10 of file curve.c.

Referenced by purify_curve_pack_public(), purify_curve_packed_public_key_space_size(), purify_curve_prime_p(), purify_curve_two_p(), and purify_curve_unpack_public().