Botan::ProjectiveCurvePoint< FieldElement, Params > Class Template Reference

#include <pcurves_impl.h>

Public Types
using	AffinePoint = AffineCurvePoint<FieldElement, Params>
using	Self = ProjectiveCurvePoint<FieldElement, Params>

Public Member Functions
constexpr void	conditional_assign (CT::Choice cond, const Self &pt)
constexpr void	ct_poison () const
constexpr void	ct_unpoison () const
constexpr Self	dbl () const
constexpr Self	dbl_n (size_t n) const
constexpr CT::Choice	is_identity () const
constexpr Self	negate () const
constexpr Self &	operator+= (const AffinePoint &other)
constexpr Self &	operator+= (const Self &other)
ProjectiveCurvePoint &	operator= (const Self &other)=default
ProjectiveCurvePoint &	operator= (Self &&other)=default
constexpr	ProjectiveCurvePoint ()
constexpr	ProjectiveCurvePoint (const FieldElement &x, const FieldElement &y)
constexpr	ProjectiveCurvePoint (const FieldElement &x, const FieldElement &y, const FieldElement &z)
	ProjectiveCurvePoint (const Self &other)=default
	ProjectiveCurvePoint (Self &&other)=default
void	randomize_rep (RandomNumberGenerator &rng)
constexpr AffinePoint	to_affine () const
constexpr const FieldElement &	x () const
constexpr const FieldElement &	y () const
constexpr const FieldElement &	z () const

Static Public Member Functions
static constexpr Self	add (const Self &a, const Self &b)
static constexpr Self	add_mixed (const Self &a, const AffinePoint &b)
static constexpr Self	from_affine (const AffinePoint &pt)
static constexpr Self	identity ()
static std::vector< AffinePoint >	to_affine_batch (std::span< const Self > projective)

Static Public Attributes
static constexpr FieldElement	A = FieldElement::from_words(Params::AW)
static constexpr bool	A_is_minus_3 = (A == FieldElement::constant(-3)).as_bool()
static constexpr bool	A_is_zero = A.is_zero().as_bool()

Friends
constexpr Self	operator+ (const AffinePoint &a, const Self &b)
constexpr Self	operator+ (const Self &a, const AffinePoint &b)
constexpr Self	operator+ (const Self &a, const Self &b)
constexpr Self	operator- (const Self &a, const Self &b)

Detailed Description

template<typename FieldElement, typename Params>
class Botan::ProjectiveCurvePoint< FieldElement, Params >

Definition at line 541 of file pcurves_impl.h.

Member Typedef Documentation

AffinePoint

template<typename FieldElement , typename Params >

using Botan::ProjectiveCurvePoint< FieldElement, Params >::AffinePoint = AffineCurvePoint<FieldElement, Params>

Definition at line 552 of file pcurves_impl.h.

Self

template<typename FieldElement , typename Params >

using Botan::ProjectiveCurvePoint< FieldElement, Params >::Self = ProjectiveCurvePoint<FieldElement, Params>

Definition at line 551 of file pcurves_impl.h.

Constructor & Destructor Documentation

ProjectiveCurvePoint() [1/5]

template<typename FieldElement , typename Params >

Botan::ProjectiveCurvePoint< FieldElement, Params >::ProjectiveCurvePoint ( )

inlineconstexpr

Definition at line 564 of file pcurves_impl.h.

                                       :
            m_x(FieldElement::zero()), m_y(FieldElement::one()), m_z(FieldElement::zero()) {}

Referenced by Botan::ProjectiveCurvePoint< FieldElement, Params >::from_affine().

ProjectiveCurvePoint() [2/5]

template<typename FieldElement , typename Params >

Botan::ProjectiveCurvePoint< FieldElement, Params >::ProjectiveCurvePoint ( const FieldElement & x, const FieldElement & y )

inlineconstexpr

Definition at line 567 of file pcurves_impl.h.

                                                                                   :
            m_x(x), m_y(y), m_z(FieldElement::one()) {}

ProjectiveCurvePoint() [3/5]

template<typename FieldElement , typename Params >

Botan::ProjectiveCurvePoint< FieldElement, Params >::ProjectiveCurvePoint ( const FieldElement & x, const FieldElement & y, const FieldElement & z )

inlineconstexpr

Definition at line 570 of file pcurves_impl.h.

                                                                                                          :
            m_x(x), m_y(y), m_z(z) {}

ProjectiveCurvePoint() [4/5]

template<typename FieldElement , typename Params >

Botan::ProjectiveCurvePoint< FieldElement, Params >::ProjectiveCurvePoint ( const Self & other )

default

ProjectiveCurvePoint() [5/5]

template<typename FieldElement , typename Params >

Botan::ProjectiveCurvePoint< FieldElement, Params >::ProjectiveCurvePoint ( Self && other )

default

Member Function Documentation

add()

template<typename FieldElement , typename Params >

static constexpr Self Botan::ProjectiveCurvePoint< FieldElement, Params >::add ( const Self & a, const Self & b )

inlinestaticconstexpr

Definition at line 655 of file pcurves_impl.h.

                                                              {
         const auto a_is_identity = a.is_identity();
         const auto b_is_identity = b.is_identity();
         if((a_is_identity && b_is_identity).as_bool()) {
            return Self::identity();
         }
 
         /*
         https://hyperelliptic.org/EFD/g1p/auto-shortw-jacobian-3.html#addition-add-1998-cmo-2
         */
 
         const auto Z1Z1 = a.z().square();
         const auto Z2Z2 = b.z().square();
         const auto U1 = a.x() * Z2Z2;
         const auto U2 = b.x() * Z1Z1;
         const auto S1 = a.y() * b.z() * Z2Z2;
         const auto S2 = b.y() * a.z() * Z1Z1;
         const auto H = U2 - U1;
         const auto r = S2 - S1;
 
         if(r.is_zero().as_bool()) {
            return a.dbl();
         }
 
         const auto HH = H.square();
         const auto HHH = H * HH;
         const auto V = U1 * HH;
         const auto t2 = r.square();
         const auto t3 = V + V;
         const auto t4 = t2 - HHH;
         auto X3 = t4 - t3;
         const auto t5 = V - X3;
         const auto t6 = S1 * HHH;
         const auto t7 = r * t5;
         auto Y3 = t7 - t6;
         const auto t8 = b.z() * H;
         auto Z3 = a.z() * t8;
 
         // TODO these could be combined
         // if a is identity then return b
         X3.conditional_assign(a_is_identity, b.x());
         Y3.conditional_assign(a_is_identity, b.y());
         Z3.conditional_assign(a_is_identity, b.z());
 
         // if b is identity then return a
         X3.conditional_assign(b_is_identity, a.x());
         Y3.conditional_assign(b_is_identity, a.y());
         Z3.conditional_assign(b_is_identity, a.z());
 
         return Self(X3, Y3, Z3);
      }

References Botan::ProjectiveCurvePoint< FieldElement, Params >::dbl(), Botan::ProjectiveCurvePoint< FieldElement, Params >::identity(), Botan::ProjectiveCurvePoint< FieldElement, Params >::is_identity(), Botan::ProjectiveCurvePoint< FieldElement, Params >::x(), Botan::ProjectiveCurvePoint< FieldElement, Params >::y(), and Botan::ProjectiveCurvePoint< FieldElement, Params >::z().

add_mixed()

template<typename FieldElement , typename Params >

static constexpr Self Botan::ProjectiveCurvePoint< FieldElement, Params >::add_mixed ( const Self & a, const AffinePoint & b )

inlinestaticconstexpr

Definition at line 604 of file pcurves_impl.h.

                                                                           {
         const auto a_is_identity = a.is_identity();
         const auto b_is_identity = b.is_identity();
         if((a_is_identity && b_is_identity).as_bool()) {
            return Self::identity();
         }
 
         /*
         https://hyperelliptic.org/EFD/g1p/auto-shortw-jacobian-3.html#addition-add-1998-cmo-2
 
         12M + 4S + 6add + 1*2
         */
 
         const auto Z1Z1 = a.z().square();
         const auto U2 = b.x() * Z1Z1;
         const auto S2 = b.y() * a.z() * Z1Z1;
         const auto H = U2 - a.x();
         const auto r = S2 - a.y();
 
         // If r is zero then we are in the doubling case
         if(r.is_zero().as_bool()) {
            return a.dbl();
         }
 
         const auto HH = H.square();
         const auto HHH = H * HH;
         const auto V = a.x() * HH;
         const auto t2 = r.square();
         const auto t3 = V + V;
         const auto t4 = t2 - HHH;
         auto X3 = t4 - t3;
         const auto t5 = V - X3;
         const auto t6 = a.y() * HHH;
         const auto t7 = r * t5;
         auto Y3 = t7 - t6;
         auto Z3 = a.z() * H;
 
         // TODO these could be combined
         // if a is identity then return b
         X3.conditional_assign(a_is_identity, b.x());
         Y3.conditional_assign(a_is_identity, b.y());
         Z3.conditional_assign(a_is_identity, FieldElement::one());
 
         // if b is identity then return a
         X3.conditional_assign(b_is_identity, a.x());
         Y3.conditional_assign(b_is_identity, a.y());
         Z3.conditional_assign(b_is_identity, a.z());
 
         return Self(X3, Y3, Z3);
      }

References Botan::ProjectiveCurvePoint< FieldElement, Params >::dbl(), Botan::ProjectiveCurvePoint< FieldElement, Params >::identity(), Botan::AffineCurvePoint< FieldElement, Params >::is_identity(), Botan::ProjectiveCurvePoint< FieldElement, Params >::is_identity(), Botan::AffineCurvePoint< FieldElement, Params >::x(), Botan::ProjectiveCurvePoint< FieldElement, Params >::x(), Botan::AffineCurvePoint< FieldElement, Params >::y(), Botan::ProjectiveCurvePoint< FieldElement, Params >::y(), and Botan::ProjectiveCurvePoint< FieldElement, Params >::z().

conditional_assign()

template<typename FieldElement , typename Params >

void Botan::ProjectiveCurvePoint< FieldElement, Params >::conditional_assign ( CT::Choice cond, const Self & pt )

inlineconstexpr

Definition at line 598 of file pcurves_impl.h.

                                                                       {
         m_x.conditional_assign(cond, pt.x());
         m_y.conditional_assign(cond, pt.y());
         m_z.conditional_assign(cond, pt.z());
      }

References Botan::ProjectiveCurvePoint< FieldElement, Params >::x(), Botan::ProjectiveCurvePoint< FieldElement, Params >::y(), and Botan::ProjectiveCurvePoint< FieldElement, Params >::z().

ct_poison()

template<typename FieldElement , typename Params >

void Botan::ProjectiveCurvePoint< FieldElement, Params >::ct_poison ( ) const

inlineconstexpr

Definition at line 841 of file pcurves_impl.h.

                                       {
         x().ct_poison();
         y().ct_poison();
         z().ct_poison();
      }

References Botan::ProjectiveCurvePoint< FieldElement, Params >::x(), Botan::ProjectiveCurvePoint< FieldElement, Params >::y(), and Botan::ProjectiveCurvePoint< FieldElement, Params >::z().

ct_unpoison()

template<typename FieldElement , typename Params >

void Botan::ProjectiveCurvePoint< FieldElement, Params >::ct_unpoison ( ) const

inlineconstexpr

Definition at line 847 of file pcurves_impl.h.

                                         {
         x().ct_unpoison();
         y().ct_unpoison();
         z().ct_unpoison();
      }

References Botan::ProjectiveCurvePoint< FieldElement, Params >::x(), Botan::ProjectiveCurvePoint< FieldElement, Params >::y(), and Botan::ProjectiveCurvePoint< FieldElement, Params >::z().

dbl()

template<typename FieldElement , typename Params >

Self Botan::ProjectiveCurvePoint< FieldElement, Params >::dbl ( ) const

inlineconstexpr

Definition at line 718 of file pcurves_impl.h.

                                 {
         //https://hyperelliptic.org/EFD/g1p/auto-shortw-jacobian.html#doubling-dbl-1998-cmo-2
 
         FieldElement m = FieldElement::zero();
 
         if constexpr(Self::A_is_minus_3) {
            /*
            if a == -3 then
            3*x^2 + a*z^4 == 3*x^2 - 3*z^4 == 3*(x^2-z^4) == 3*(x-z^2)*(x+z^2)
 
            Cost: 2M + 2A + 1*3
            */
            const auto z2 = z().square();
            m = (x() - z2).mul3() * (x() + z2);
         } else if constexpr(Self::A_is_zero) {
            // If a == 0 then 3*x^2 + a*z^4 == 3*x^2
            // Cost: 1S + 1*3
            m = x().square().mul3();
         } else {
            // Cost: 1M + 3S + 1A + 1*3
            const auto z2 = z().square();
            m = x().square().mul3() + A * z2.square();
         }
 
         const auto y2 = y().square();
         const auto s = x().mul4() * y2;
         const auto nx = m.square() - s.mul2();
         const auto ny = m * (s - nx) - y2.square().mul8();
         const auto nz = y().mul2() * z();
 
         return Self(nx, ny, nz);
      }

References Botan::ProjectiveCurvePoint< FieldElement, Params >::A, Botan::ProjectiveCurvePoint< FieldElement, Params >::A_is_minus_3, Botan::ProjectiveCurvePoint< FieldElement, Params >::A_is_zero, Botan::ProjectiveCurvePoint< FieldElement, Params >::x(), Botan::ProjectiveCurvePoint< FieldElement, Params >::y(), and Botan::ProjectiveCurvePoint< FieldElement, Params >::z().

Referenced by Botan::ProjectiveCurvePoint< FieldElement, Params >::add(), Botan::ProjectiveCurvePoint< FieldElement, Params >::add_mixed(), and Botan::ProjectiveCurvePoint< FieldElement, Params >::dbl_n().

dbl_n()

template<typename FieldElement , typename Params >

Self Botan::ProjectiveCurvePoint< FieldElement, Params >::dbl_n ( size_t n ) const

inlineconstexpr

Definition at line 707 of file pcurves_impl.h.

                                           {
         // TODO it is possible to optimize this by carrying over values from
         // the previous iteration into the next
 
         Self pt = (*this);
         for(size_t i = 0; i != n; ++i) {
            pt = pt.dbl();
         }
         return pt;
      }

References Botan::ProjectiveCurvePoint< FieldElement, Params >::dbl().

from_affine()

template<typename FieldElement , typename Params >

static constexpr Self Botan::ProjectiveCurvePoint< FieldElement, Params >::from_affine ( const AffinePoint & pt )

inlinestaticconstexpr

Definition at line 554 of file pcurves_impl.h.

                                                               {
         if(pt.is_identity().as_bool()) {
            return Self::identity();
         } else {
            return ProjectiveCurvePoint(pt.x(), pt.y());
         }
      }

References Botan::CT::Choice::as_bool(), Botan::ProjectiveCurvePoint< FieldElement, Params >::identity(), Botan::AffineCurvePoint< FieldElement, Params >::is_identity(), Botan::ProjectiveCurvePoint< FieldElement, Params >::ProjectiveCurvePoint(), Botan::AffineCurvePoint< FieldElement, Params >::x(), and Botan::AffineCurvePoint< FieldElement, Params >::y().

identity()

template<typename FieldElement , typename Params >

static constexpr Self Botan::ProjectiveCurvePoint< FieldElement, Params >::identity ( )

inlinestaticconstexpr

Definition at line 562 of file pcurves_impl.h.

{ return Self(FieldElement::zero(), FieldElement::one(), FieldElement::zero()); }

Referenced by Botan::ProjectiveCurvePoint< FieldElement, Params >::add(), Botan::ProjectiveCurvePoint< FieldElement, Params >::add_mixed(), and Botan::ProjectiveCurvePoint< FieldElement, Params >::from_affine().

is_identity()

template<typename FieldElement , typename Params >

CT::Choice Botan::ProjectiveCurvePoint< FieldElement, Params >::is_identity ( ) const

inlineconstexpr

Definition at line 596 of file pcurves_impl.h.

{ return z().is_zero(); }

References Botan::ProjectiveCurvePoint< FieldElement, Params >::z().

Referenced by Botan::ProjectiveCurvePoint< FieldElement, Params >::add(), Botan::ProjectiveCurvePoint< FieldElement, Params >::add_mixed(), Botan::ProjectiveCurvePoint< FieldElement, Params >::to_affine(), and Botan::ProjectiveCurvePoint< FieldElement, Params >::to_affine_batch().

negate()

template<typename FieldElement , typename Params >

Self Botan::ProjectiveCurvePoint< FieldElement, Params >::negate ( ) const

inlineconstexpr

Definition at line 751 of file pcurves_impl.h.

{ return Self(x(), y().negate(), z()); }

References Botan::ProjectiveCurvePoint< FieldElement, Params >::negate(), Botan::ProjectiveCurvePoint< FieldElement, Params >::x(), Botan::ProjectiveCurvePoint< FieldElement, Params >::y(), and Botan::ProjectiveCurvePoint< FieldElement, Params >::z().

Referenced by Botan::ProjectiveCurvePoint< FieldElement, Params >::negate().

operator+=() [1/2]

template<typename FieldElement , typename Params >

Self & Botan::ProjectiveCurvePoint< FieldElement, Params >::operator+= ( const AffinePoint & other )

inlineconstexpr

Definition at line 589 of file pcurves_impl.h.

                                                           {
         (*this) = (*this) + other;
         return (*this);
      }

operator+=() [2/2]

template<typename FieldElement , typename Params >

Self & Botan::ProjectiveCurvePoint< FieldElement, Params >::operator+= ( const Self & other )

inlineconstexpr

Definition at line 584 of file pcurves_impl.h.

                                                    {
         (*this) = (*this) + other;
         return (*this);
      }

operator=() [1/2]

template<typename FieldElement , typename Params >

ProjectiveCurvePoint & Botan::ProjectiveCurvePoint< FieldElement, Params >::operator= ( const Self & other )

default

operator=() [2/2]

template<typename FieldElement , typename Params >

ProjectiveCurvePoint & Botan::ProjectiveCurvePoint< FieldElement, Params >::operator= ( Self && other )

default

randomize_rep()

template<typename FieldElement , typename Params >

void Botan::ProjectiveCurvePoint< FieldElement, Params >::randomize_rep ( RandomNumberGenerator & rng )

inline

Definition at line 824 of file pcurves_impl.h.

                                                     {
         auto r = FieldElement::random(rng);
 
         auto r2 = r.square();
         auto r3 = r2 * r;
 
         m_x *= r2;
         m_y *= r3;
         m_z *= r;
      }

to_affine()

template<typename FieldElement , typename Params >

AffinePoint Botan::ProjectiveCurvePoint< FieldElement, Params >::to_affine ( ) const

inlineconstexpr

Definition at line 753 of file pcurves_impl.h.

                                              {
         // Not strictly required right? - default should work as long
         // as (0,0) is identity and invert returns 0 on 0
         if(this->is_identity().as_bool()) {
            return AffinePoint::identity();
         }
 
         const auto z_inv = m_z.invert();
         const auto z2_inv = z_inv.square();
         const auto z3_inv = z_inv * z2_inv;
 
         const auto x = m_x * z2_inv;
         const auto y = m_y * z3_inv;
         return AffinePoint(x, y);
      }

References Botan::AffineCurvePoint< FieldElement, Params >::identity(), Botan::ProjectiveCurvePoint< FieldElement, Params >::is_identity(), Botan::ProjectiveCurvePoint< FieldElement, Params >::x(), and Botan::ProjectiveCurvePoint< FieldElement, Params >::y().

to_affine_batch()

template<typename FieldElement , typename Params >

static std::vector< AffinePoint > Botan::ProjectiveCurvePoint< FieldElement, Params >::to_affine_batch ( std::span< const Self > projective )

inlinestatic

Definition at line 769 of file pcurves_impl.h.

                                                                                    {
         const size_t N = projective.size();
         std::vector<AffinePoint> affine(N, AffinePoint::identity());
 
         bool any_identity = false;
         for(size_t i = 0; i != N; ++i) {
            if(projective[i].is_identity().as_bool()) {
               any_identity = true;
               // If any of the elements are the identity we fall back to
               // performing the conversion without a batch
               break;
            }
         }
 
         if(N <= 2 || any_identity) {
            for(size_t i = 0; i != N; ++i) {
               affine[i] = projective[i].to_affine();
            }
         } else {
            std::vector<FieldElement> c(N);
 
            /*
            Batch projective->affine using Montgomery's trick
 
            See Algorithm 2.26 in "Guide to Elliptic Curve Cryptography"
            (Hankerson, Menezes, Vanstone)
            */
 
            c[0] = projective[0].z();
            for(size_t i = 1; i != N; ++i) {
               c[i] = c[i - 1] * projective[i].z();
            }
 
            auto s_inv = c[N - 1].invert();
 
            for(size_t i = N - 1; i > 0; --i) {
               const auto& p = projective[i];
 
               const auto z_inv = s_inv * c[i - 1];
               const auto z2_inv = z_inv.square();
               const auto z3_inv = z_inv * z2_inv;
 
               s_inv = s_inv * p.z();
 
               affine[i] = AffinePoint(p.x() * z2_inv, p.y() * z3_inv);
            }
 
            const auto z2_inv = s_inv.square();
            const auto z3_inv = s_inv * z2_inv;
            affine[0] = AffinePoint(projective[0].x() * z2_inv, projective[0].y() * z3_inv);
         }
 
         return affine;
      }

References Botan::AffineCurvePoint< FieldElement, Params >::identity(), Botan::ProjectiveCurvePoint< FieldElement, Params >::is_identity(), Botan::ProjectiveCurvePoint< FieldElement, Params >::x(), and Botan::ProjectiveCurvePoint< FieldElement, Params >::y().

x()

template<typename FieldElement , typename Params >

const FieldElement & Botan::ProjectiveCurvePoint< FieldElement, Params >::x ( ) const

inlineconstexpr

Definition at line 835 of file pcurves_impl.h.

{ return m_x; }

Referenced by Botan::ProjectiveCurvePoint< FieldElement, Params >::add(), Botan::ProjectiveCurvePoint< FieldElement, Params >::add_mixed(), Botan::ProjectiveCurvePoint< FieldElement, Params >::conditional_assign(), Botan::ProjectiveCurvePoint< FieldElement, Params >::ct_poison(), Botan::ProjectiveCurvePoint< FieldElement, Params >::ct_unpoison(), Botan::ProjectiveCurvePoint< FieldElement, Params >::dbl(), Botan::ProjectiveCurvePoint< FieldElement, Params >::negate(), Botan::ProjectiveCurvePoint< FieldElement, Params >::to_affine(), and Botan::ProjectiveCurvePoint< FieldElement, Params >::to_affine_batch().

y()

template<typename FieldElement , typename Params >

const FieldElement & Botan::ProjectiveCurvePoint< FieldElement, Params >::y ( ) const

inlineconstexpr

Definition at line 837 of file pcurves_impl.h.

{ return m_y; }

Referenced by Botan::ProjectiveCurvePoint< FieldElement, Params >::add(), Botan::ProjectiveCurvePoint< FieldElement, Params >::add_mixed(), Botan::ProjectiveCurvePoint< FieldElement, Params >::conditional_assign(), Botan::ProjectiveCurvePoint< FieldElement, Params >::ct_poison(), Botan::ProjectiveCurvePoint< FieldElement, Params >::ct_unpoison(), Botan::ProjectiveCurvePoint< FieldElement, Params >::dbl(), Botan::ProjectiveCurvePoint< FieldElement, Params >::negate(), Botan::ProjectiveCurvePoint< FieldElement, Params >::to_affine(), and Botan::ProjectiveCurvePoint< FieldElement, Params >::to_affine_batch().

z()

template<typename FieldElement , typename Params >

const FieldElement & Botan::ProjectiveCurvePoint< FieldElement, Params >::z ( ) const

inlineconstexpr

Definition at line 839 of file pcurves_impl.h.

{ return m_z; }

Referenced by Botan::ProjectiveCurvePoint< FieldElement, Params >::add(), Botan::ProjectiveCurvePoint< FieldElement, Params >::add_mixed(), Botan::ProjectiveCurvePoint< FieldElement, Params >::conditional_assign(), Botan::ProjectiveCurvePoint< FieldElement, Params >::ct_poison(), Botan::ProjectiveCurvePoint< FieldElement, Params >::ct_unpoison(), Botan::ProjectiveCurvePoint< FieldElement, Params >::dbl(), Botan::ProjectiveCurvePoint< FieldElement, Params >::is_identity(), and Botan::ProjectiveCurvePoint< FieldElement, Params >::negate().

Friends And Related Symbol Documentation

operator+ [1/3]

template<typename FieldElement , typename Params >

Self operator+ ( const AffinePoint & a, const Self & b )

friend

Definition at line 582 of file pcurves_impl.h.

{ return Self::add_mixed(b, a); }

operator+ [2/3]

template<typename FieldElement , typename Params >

Self operator+ ( const Self & a, const AffinePoint & b )

friend

Definition at line 580 of file pcurves_impl.h.

{ return Self::add_mixed(a, b); }

operator+ [3/3]

template<typename FieldElement , typename Params >

Self operator+ ( const Self & a, const Self & b )

friend

Definition at line 578 of file pcurves_impl.h.

{ return Self::add(a, b); }

operator-

template<typename FieldElement , typename Params >

Self operator- ( const Self & a, const Self & b )

friend

Definition at line 594 of file pcurves_impl.h.

{ return a + b.negate(); }

Member Data Documentation

A

template<typename FieldElement , typename Params >

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

staticconstexpr

Definition at line 546 of file pcurves_impl.h.

Referenced by Botan::ProjectiveCurvePoint< FieldElement, Params >::dbl().

A_is_minus_3

template<typename FieldElement , typename Params >

bool Botan::ProjectiveCurvePoint< FieldElement, Params >::A_is_minus_3 = (A == FieldElement::constant(-3)).as_bool()

staticconstexpr

Definition at line 549 of file pcurves_impl.h.

Referenced by Botan::ProjectiveCurvePoint< FieldElement, Params >::dbl().

A_is_zero

template<typename FieldElement , typename Params >

bool Botan::ProjectiveCurvePoint< FieldElement, Params >::A_is_zero = A.is_zero().as_bool()

staticconstexpr

Definition at line 548 of file pcurves_impl.h.

Referenced by Botan::ProjectiveCurvePoint< FieldElement, Params >::dbl().

---

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

• src/lib/math/pcurves/pcurves_impl.h