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

#include <pcurves_impl.h>

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

Public Member Functions
constexpr void	_const_time_poison () const
constexpr void	_const_time_unpoison () const
constexpr void	conditional_assign (CT::Choice cond, const Self &pt)
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 const FieldElement &	x () const
constexpr const FieldElement &	y () const
constexpr const FieldElement &	z () const
	~ProjectiveCurvePoint ()=default

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	add_or_sub (const Self &a, const AffinePoint &b, CT::Choice sub)
static constexpr Self	from_affine (const AffinePoint &pt)
static constexpr Self	identity ()

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 >

Projective curve point

This uses Jacobian coordinates

Definition at line 1000 of file pcurves_impl.h.

Member Typedef Documentation

AffinePoint

template<typename FieldElement, typename Params>

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

Definition at line 1011 of file pcurves_impl.h.

Self

template<typename FieldElement, typename Params>

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

Definition at line 1010 of file pcurves_impl.h.

Constructor & Destructor Documentation

ProjectiveCurvePoint() [1/5]

template<typename FieldElement, typename Params>

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

inlineconstexpr

Default constructor: the identity element

Definition at line 1043 of file pcurves_impl.h.

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

Referenced by from_affine(), operator=(), and operator=().

ProjectiveCurvePoint() [2/5]

template<typename FieldElement, typename Params>

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

inlineconstexpr

Affine constructor: take x/y coordinates

Definition at line 1049 of file pcurves_impl.h.

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

References x(), and y().

ProjectiveCurvePoint() [3/5]

template<typename FieldElement, typename Params>

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

inlineconstexpr

Projective constructor: take x/y/z coordinates

Definition at line 1055 of file pcurves_impl.h.

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

References x(), y(), and 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

~ProjectiveCurvePoint()

template<typename FieldElement, typename Params>

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

default

Member Function Documentation

_const_time_poison()

template<typename FieldElement, typename Params>

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

inlineconstexpr

Definition at line 1174 of file pcurves_impl.h.

{ CT::poison_all(m_x, m_y, m_z); }

References Botan::CT::poison_all().

_const_time_unpoison()

template<typename FieldElement, typename Params>

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

inlineconstexpr

Definition at line 1176 of file pcurves_impl.h.

{ CT::unpoison_all(m_x, m_y, m_z); }

References Botan::CT::unpoison_all().

add()

template<typename FieldElement, typename Params>

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

inlinestaticconstexpr

Projective point addition

Definition at line 1103 of file pcurves_impl.h.

{ return point_add<Self, FieldElement>(a, b); }

References Botan::point_add().

Referenced by operator+.

add_mixed()

template<typename FieldElement, typename Params>

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

inlinestaticconstexpr

Mixed (projective + affine) point addition

Definition at line 1091 of file pcurves_impl.h.

                                                                           {
         return point_add_mixed<Self, AffinePoint, FieldElement>(a, b, FieldElement::one());
      }

References Botan::point_add_mixed().

Referenced by operator+, and operator+.

add_or_sub()

template<typename FieldElement, typename Params>

constexpr Self Botan::ProjectiveCurvePoint< FieldElement, Params >::add_or_sub ( const Self & a, const AffinePoint & b, CT::Choice sub )

inlinestaticconstexpr

Definition at line 1096 of file pcurves_impl.h.

                                                                                          {
         return point_add_or_sub_mixed<Self, AffinePoint, FieldElement>(a, b, sub, FieldElement::one());
      }

References Botan::point_add_or_sub_mixed().

conditional_assign()

template<typename FieldElement, typename Params>

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

inlineconstexpr

Definition at line 1084 of file pcurves_impl.h.

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

References x(), y(), and z().

dbl()

template<typename FieldElement, typename Params>

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

inlineconstexpr

Point doubling

Definition at line 1121 of file pcurves_impl.h.

                                 {
         if constexpr(Self::A_is_minus_3) {
            return dbl_a_minus_3(*this);
         } else if constexpr(Self::A_is_zero) {
            return dbl_a_zero(*this);
         } else {
            return dbl_generic(*this, A);
         }
      }

References A, A_is_minus_3, A_is_zero, Botan::dbl_a_minus_3(), Botan::dbl_a_zero(), and Botan::dbl_generic().

dbl_n()

template<typename FieldElement, typename Params>

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

inlineconstexpr

Iterated point doubling

Definition at line 1108 of file pcurves_impl.h.

                                           {
         if constexpr(Self::A_is_minus_3) {
            return dbl_n_a_minus_3(*this, n);
         } else if constexpr(Self::A_is_zero) {
            return dbl_n_a_zero(*this, n);
         } else {
            return dbl_n_generic(*this, A, n);
         }
      }

References A, A_is_minus_3, A_is_zero, Botan::dbl_n_a_minus_3(), Botan::dbl_n_a_zero(), and Botan::dbl_n_generic().

from_affine()

template<typename FieldElement, typename Params>

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

inlinestaticconstexpr

Convert a point from affine to projective form

Definition at line 1016 of file pcurves_impl.h.

                                                               {
         /*
         * If the point is the identity element (x=0, y=0) then instead of
         * creating (x, y, 1) = (0, 0, 1) we want our projective identity
         * encoding of (0, 1, 0)
         *
         * Which we can achieve by a conditional swap of y and z if the
         * affine point is the identity.
         */
 
         auto x = pt.x();
         auto y = pt.y();
         auto z = FieldElement::one();
 
         FieldElement::conditional_swap(pt.is_identity(), y, z);
 
         return ProjectiveCurvePoint(x, y, z);
      }

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

identity()

template<typename FieldElement, typename Params>

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

inlinestaticconstexpr

Return the identity element

Definition at line 1038 of file pcurves_impl.h.

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

is_identity()

template<typename FieldElement, typename Params>

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

inlineconstexpr

Definition at line 1082 of file pcurves_impl.h.

{ return z().is_zero(); }

References z().

negate()

template<typename FieldElement, typename Params>

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

inlineconstexpr

Point negation

Definition at line 1134 of file pcurves_impl.h.

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

References negate(), x(), y(), and z().

Referenced by negate(), and operator-.

operator+=() [1/2]

template<typename FieldElement, typename Params>

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

inlineconstexpr

Definition at line 1075 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 1070 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

References ProjectiveCurvePoint().

operator=() [2/2]

template<typename FieldElement, typename Params>

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

default

References ProjectiveCurvePoint().

randomize_rep()

template<typename FieldElement, typename Params>

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

inline

Randomize the point representation

Projective coordinates are redundant; if (x,y,z) is a projective point then so is (x*r^2,y*r^3,z*r) for any non-zero r.

Definition at line 1142 of file pcurves_impl.h.

                                                     {
         // In certain contexts we may be called with a Null_RNG; in that case the
         // caller is accepting that randomization will not occur
 
         // Conditional ok: caller's RNG state (seeded vs not) is presumed public
         if(rng.is_seeded()) {
            auto r = FieldElement::random(rng);
 
            auto r2 = r.square();
            auto r3 = r2 * r;
 
            m_x *= r2;
            m_y *= r3;
            m_z *= r;
         }
      }

References Botan::RandomNumberGenerator::is_seeded().

x()

template<typename FieldElement, typename Params>

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

inlineconstexpr

Return the projective x coordinate

Definition at line 1162 of file pcurves_impl.h.

{ return m_x; }

Referenced by conditional_assign(), from_affine(), negate(), ProjectiveCurvePoint(), and ProjectiveCurvePoint().

y()

template<typename FieldElement, typename Params>

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

inlineconstexpr

Return the projective y coordinate

Definition at line 1167 of file pcurves_impl.h.

{ return m_y; }

Referenced by conditional_assign(), from_affine(), negate(), ProjectiveCurvePoint(), and ProjectiveCurvePoint().

z()

template<typename FieldElement, typename Params>

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

inlineconstexpr

Return the projective z coordinate

Definition at line 1172 of file pcurves_impl.h.

{ return m_z; }

Referenced by conditional_assign(), from_affine(), is_identity(), negate(), and ProjectiveCurvePoint().

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 1068 of file pcurves_impl.h.

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

References add_mixed().

operator+ [2/3]

template<typename FieldElement, typename Params>

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

friend

Definition at line 1066 of file pcurves_impl.h.

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

References add_mixed().

operator+ [3/3]

template<typename FieldElement, typename Params>

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

friend

Definition at line 1064 of file pcurves_impl.h.

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

References add().

operator-

template<typename FieldElement, typename Params>

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

friend

Definition at line 1080 of file pcurves_impl.h.

{ return a + b.negate(); }

References 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 1005 of file pcurves_impl.h.

Referenced by dbl(), and dbl_n().

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 1008 of file pcurves_impl.h.

Referenced by dbl(), and dbl_n().

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 1007 of file pcurves_impl.h.

Referenced by dbl(), and dbl_n().

---

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

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