#include <pcurves_impl.h>

Classes
class	FieldParams
class	ScalarParams

Public Types
using	AffinePoint = AffineCurvePoint<FieldElement, Params>
using	FieldElement = IntMod<FieldRep<FieldParams>>
using	ProjectivePoint = ProjectiveCurvePoint<FieldElement, Params>
using	Scalar = IntMod<MontgomeryRep<ScalarParams>>
typedef Params::W	W
typedef W	WordType

Static Public Member Functions
static constexpr FieldElement	x3_ax_b (const FieldElement &x)

Static Public Attributes
static constexpr FieldElement	A = FieldElement::from_words(Params::AW)
static constexpr auto	AW = Params::AW
static constexpr FieldElement	B = FieldElement::from_words(Params::BW)
static constexpr AffinePoint	G
static constexpr auto	NW = Params::NW
static constexpr size_t	OrderBits = Scalar::BITS
static constexpr bool	OrderIsLessThanField = bigint_cmp(NW.data(), Words, PW.data(), Words) == -1
static constexpr size_t	PrimeFieldBits = FieldElement::BITS
static constexpr auto	PW = Params::PW
static constexpr FieldElement	SSWU_Z = FieldElement::constant(Params::Z)
static constexpr bool	ValidForSswuHash
static constexpr size_t	Words = PW.size()

Detailed Description

template<typename Params, template< typename FieldParamsT > typename FieldRep = MontgomeryRep>
class Botan::EllipticCurve< Params, FieldRep >

Elliptic Curve

Takes as input a set of parameters, and instantiates the elliptic curve

Definition at line 1194 of file pcurves_impl.h.

Member Typedef Documentation

◆ AffinePoint

template<typename Params, template< typename FieldParamsT > typename FieldRep = MontgomeryRep>

using Botan::EllipticCurve< Params, FieldRep >::AffinePoint = AffineCurvePoint<FieldElement, Params>

Definition at line 1217 of file pcurves_impl.h.

◆ FieldElement

template<typename Params, template< typename FieldParamsT > typename FieldRep = MontgomeryRep>

using Botan::EllipticCurve< Params, FieldRep >::FieldElement = IntMod<FieldRep<FieldParams>>

Definition at line 1215 of file pcurves_impl.h.

◆ ProjectivePoint

template<typename Params, template< typename FieldParamsT > typename FieldRep = MontgomeryRep>

using Botan::EllipticCurve< Params, FieldRep >::ProjectivePoint = ProjectiveCurvePoint<FieldElement, Params>

Definition at line 1218 of file pcurves_impl.h.

◆ Scalar

template<typename Params, template< typename FieldParamsT > typename FieldRep = MontgomeryRep>

using Botan::EllipticCurve< Params, FieldRep >::Scalar = IntMod<MontgomeryRep<ScalarParams>>

Definition at line 1211 of file pcurves_impl.h.

◆ W

template<typename Params, template< typename FieldParamsT > typename FieldRep = MontgomeryRep>

typedef Params::W Botan::EllipticCurve< Params, FieldRep >::W

Definition at line 1196 of file pcurves_impl.h.

◆ WordType

template<typename Params, template< typename FieldParamsT > typename FieldRep = MontgomeryRep>

typedef W Botan::EllipticCurve< Params, FieldRep >::WordType

Definition at line 1198 of file pcurves_impl.h.

Member Function Documentation

◆ x3_ax_b()

template<typename Params, template< typename FieldParamsT > typename FieldRep = MontgomeryRep>

constexpr FieldElement Botan::EllipticCurve< Params, FieldRep >::x3_ax_b ( const FieldElement & x )

inlinestaticconstexpr

Return (x^3 + A*x + B) mod p

Definition at line 1241 of file pcurves_impl.h.

1241{ return (x.square() + A) * x + B; }

Botan::EllipticCurve

Definition pcurves_impl.h:1194

Botan::EllipticCurve::A

static constexpr FieldElement A

Definition pcurves_impl.h:1223

Botan::EllipticCurve::B

static constexpr FieldElement B

Definition pcurves_impl.h:1224

References A, B, and Botan::IntMod< Rep >::square().

Member Data Documentation

◆ A

template<typename Params, template< typename FieldParamsT > typename FieldRep = MontgomeryRep>

FieldElement Botan::EllipticCurve< Params, FieldRep >::A = FieldElement::from_words(Params::AW)

staticconstexpr

Definition at line 1223 of file pcurves_impl.h.

Referenced by x3_ax_b().

◆ AW

template<typename Params, template< typename FieldParamsT > typename FieldRep = MontgomeryRep>

auto Botan::EllipticCurve< Params, FieldRep >::AW = Params::AW

staticconstexpr

Definition at line 1202 of file pcurves_impl.h.

◆ B

template<typename Params, template< typename FieldParamsT > typename FieldRep = MontgomeryRep>

FieldElement Botan::EllipticCurve< Params, FieldRep >::B = FieldElement::from_words(Params::BW)

staticconstexpr

Definition at line 1224 of file pcurves_impl.h.

Referenced by x3_ax_b().

◆ G

template<typename Params, template< typename FieldParamsT > typename FieldRep = MontgomeryRep>

AffinePoint Botan::EllipticCurve< Params, FieldRep >::G

staticconstexpr

Initial value:

=

AffinePoint(FieldElement::from_words(Params::GXW), FieldElement::from_words(Params::GYW))

Botan::EllipticCurve::AffinePoint

AffineCurvePoint< FieldElement, Params > AffinePoint

Definition pcurves_impl.h:1217

Botan::IntMod< FieldRep< FieldParams > >::from_words

static constexpr Self from_words(std::array< W, L > w)

Definition pcurves_impl.h:190

Definition at line 1228 of file pcurves_impl.h.

◆ NW

template<typename Params, template< typename FieldParamsT > typename FieldRep = MontgomeryRep>

auto Botan::EllipticCurve< Params, FieldRep >::NW = Params::NW

staticconstexpr

Definition at line 1201 of file pcurves_impl.h.

◆ OrderBits

template<typename Params, template< typename FieldParamsT > typename FieldRep = MontgomeryRep>

size_t Botan::EllipticCurve< Params, FieldRep >::OrderBits = Scalar::BITS

staticconstexpr

Definition at line 1220 of file pcurves_impl.h.

◆ OrderIsLessThanField

template<typename Params, template< typename FieldParamsT > typename FieldRep = MontgomeryRep>

bool Botan::EllipticCurve< Params, FieldRep >::OrderIsLessThanField = bigint_cmp(NW.data(), Words, PW.data(), Words) == -1

staticconstexpr

Definition at line 1236 of file pcurves_impl.h.

◆ PrimeFieldBits

template<typename Params, template< typename FieldParamsT > typename FieldRep = MontgomeryRep>

size_t Botan::EllipticCurve< Params, FieldRep >::PrimeFieldBits = FieldElement::BITS

staticconstexpr

Definition at line 1221 of file pcurves_impl.h.

◆ PW

template<typename Params, template< typename FieldParamsT > typename FieldRep = MontgomeryRep>

auto Botan::EllipticCurve< Params, FieldRep >::PW = Params::PW

staticconstexpr

Definition at line 1200 of file pcurves_impl.h.

◆ SSWU_Z

template<typename Params, template< typename FieldParamsT > typename FieldRep = MontgomeryRep>

FieldElement Botan::EllipticCurve< Params, FieldRep >::SSWU_Z = FieldElement::constant(Params::Z)

staticconstexpr

Definition at line 1231 of file pcurves_impl.h.

◆ ValidForSswuHash

template<typename Params, template< typename FieldParamsT > typename FieldRep = MontgomeryRep>

bool Botan::EllipticCurve< Params, FieldRep >::ValidForSswuHash

staticconstexpr

Initial value:

=

(Params::Z != 0 && A.is_nonzero().as_bool() && B.is_nonzero().as_bool() && FieldElement::P_MOD_4 == 3)

Botan::IntMod< FieldRep< FieldParams > >::P_MOD_4

static constexpr auto P_MOD_4

Definition pcurves_impl.h:154

Definition at line 1233 of file pcurves_impl.h.

◆ Words

template<typename Params, template< typename FieldParamsT > typename FieldRep = MontgomeryRep>

size_t Botan::EllipticCurve< Params, FieldRep >::Words = PW.size()

staticconstexpr

Definition at line 1207 of file pcurves_impl.h.

The documentation for this class was generated from the following file:

src/lib/math/pcurves/pcurves_impl/pcurves_impl.h

Classes

Public Types

Static Public Member Functions

Static Public Attributes

Detailed Description

Member Typedef Documentation

◆ AffinePoint

◆ FieldElement

◆ ProjectivePoint

◆ Scalar

◆ W

◆ WordType

Member Function Documentation

◆ x3_ax_b()

Member Data Documentation

◆ A

◆ AW

◆ B

◆ G

◆ NW

◆ OrderBits

◆ OrderIsLessThanField

◆ PrimeFieldBits

◆ PW

◆ SSWU_Z

◆ ValidForSswuHash

◆ Words