nil::crypto3::algebra::curves::detail::element_edwards_g2< 183 > Struct Reference

A struct representing an elememnt from the group G2 of Edwards curve. More...

#include <element_g2.hpp>

Collaboration diagram for nil::crypto3::algebra::curves::detail::element_edwards_g2< 183 >:

Public Types
typedef policy_type::g1_field_type::value_type	g1_field_type_value
typedef policy_type::g2_field_type::value_type	g2_field_type_value
using	group_type = edwards_g2< 183, forms::twisted_edwards, coordinates::inverted >
using	policy_type = edwards_basic_policy< 183 >
using	underlying_field_value_type = g2_field_type_value

Public Member Functions
constexpr element_edwards_g2	doubled () const
constexpr	element_edwards_g2 ()
constexpr	element_edwards_g2 (underlying_field_value_type in_X, underlying_field_value_type in_Y, underlying_field_value_type in_Z)
constexpr	element_edwards_g2 (underlying_field_value_type X, underlying_field_value_type Y)
constexpr bool	is_special () const
constexpr bool	is_zero () const
constexpr element_edwards_g2	mixed_add (const element_edwards_g2 &other) const
	“Mixed addition” refers to the case Z2 known to be 1. More...
constexpr bool	operator!= (const element_edwards_g2 &other) const
constexpr element_edwards_g2	operator+ (const element_edwards_g2 &other) const
constexpr element_edwards_g2	operator- () const
constexpr element_edwards_g2	operator- (const element_edwards_g2 &other) const
constexpr element_edwards_g2	operator= (const element_edwards_g2 &other)
constexpr bool	operator== (const element_edwards_g2 &other) const
constexpr element_edwards_g2	to_affine () const
constexpr element_edwards_g2	to_projective () const

Static Public Member Functions
constexpr static underlying_field_value_type	mul_by_a (const underlying_field_value_type &elt)
constexpr static underlying_field_value_type	mul_by_d (const underlying_field_value_type &elt)
constexpr static element_edwards_g2	one ()
	Get the generator of group G2. More...
constexpr static element_edwards_g2	zero ()
	Get the point at infinity. More...

Public Attributes
underlying_field_value_type	X
underlying_field_value_type	Y
underlying_field_value_type	Z

Static Public Attributes
constexpr static const g2_field_type_value	twist

Detailed Description

A struct representing an elememnt from the group G2 of Edwards curve.

Member Typedef Documentation

g1_field_type_value

typedef policy_type::g1_field_type::value_type nil::crypto3::algebra::curves::detail::element_edwards_g2< 183 >::g1_field_type_value

g2_field_type_value

typedef policy_type::g2_field_type::value_type nil::crypto3::algebra::curves::detail::element_edwards_g2< 183 >::g2_field_type_value

group_type

using nil::crypto3::algebra::curves::detail::element_edwards_g2< 183 >::group_type = edwards_g2<183, forms::twisted_edwards, coordinates::inverted>

policy_type

using nil::crypto3::algebra::curves::detail::element_edwards_g2< 183 >::policy_type = edwards_basic_policy<183>

underlying_field_value_type

using nil::crypto3::algebra::curves::detail::element_edwards_g2< 183 >::underlying_field_value_type = g2_field_type_value

Constructor & Destructor Documentation

element_edwards_g2() [1/3]

constexpr nil::crypto3::algebra::curves::detail::element_edwards_g2< 183 >::element_edwards_g2 ( )

inlineconstexpr

Returns

the point at infinity by default

element_edwards_g2() [2/3]

constexpr nil::crypto3::algebra::curves::detail::element_edwards_g2< 183 >::element_edwards_g2 ( underlying_field_value_type  in_X, underlying_field_value_type  in_Y, underlying_field_value_type  in_Z  )

inlineconstexpr

Returns

the selected point $(X:Y:Z)$ in the projective coordinates

element_edwards_g2() [3/3]

constexpr nil::crypto3::algebra::curves::detail::element_edwards_g2< 183 >::element_edwards_g2 ( underlying_field_value_type  X, underlying_field_value_type  Y  )

inlineconstexpr

Returns

the selected point $(X:Y:X*Y)$ in the inverted coordinates

Member Function Documentation

doubled()

constexpr element_edwards_g2 nil::crypto3::algebra::curves::detail::element_edwards_g2< 183 >::doubled ( ) const

inlineconstexpr

Returns

doubled element from group G2

is_special()

constexpr bool nil::crypto3::algebra::curves::detail::element_edwards_g2< 183 >::is_special ( ) const

inlineconstexpr

Returns

true if element from group G2 in affine coordinates

is_zero()

constexpr bool nil::crypto3::algebra::curves::detail::element_edwards_g2< 183 >::is_zero ( ) const

inlineconstexpr

Returns

true if element from group G2 is the point at infinity

mixed_add()

constexpr element_edwards_g2 nil::crypto3::algebra::curves::detail::element_edwards_g2< 183 >::mixed_add ( const element_edwards_g2< 183 > &  other ) const

inlineconstexpr

“Mixed addition” refers to the case Z2 known to be 1.

Returns

addition of two elements from group G2

mul_by_a()

constexpr static underlying_field_value_type nil::crypto3::algebra::curves::detail::element_edwards_g2< 183 >::mul_by_a ( const underlying_field_value_type &  elt )

inlinestaticconstexpr

mul_by_d()

constexpr static underlying_field_value_type nil::crypto3::algebra::curves::detail::element_edwards_g2< 183 >::mul_by_d ( const underlying_field_value_type &  elt )

inlinestaticconstexpr

one()

constexpr static element_edwards_g2 nil::crypto3::algebra::curves::detail::element_edwards_g2< 183 >::one ( )

inlinestaticconstexpr

Get the generator of group G2.

operator!=()

constexpr bool nil::crypto3::algebra::curves::detail::element_edwards_g2< 183 >::operator!= ( const element_edwards_g2< 183 > &  other ) const

inlineconstexpr

operator+()

constexpr element_edwards_g2 nil::crypto3::algebra::curves::detail::element_edwards_g2< 183 >::operator+ ( const element_edwards_g2< 183 > &  other ) const

inlineconstexpr

operator-() [1/2]

constexpr element_edwards_g2 nil::crypto3::algebra::curves::detail::element_edwards_g2< 183 >::operator- ( ) const

inlineconstexpr

operator-() [2/2]

constexpr element_edwards_g2 nil::crypto3::algebra::curves::detail::element_edwards_g2< 183 >::operator- ( const element_edwards_g2< 183 > &  other ) const

inlineconstexpr

operator=()

constexpr element_edwards_g2 nil::crypto3::algebra::curves::detail::element_edwards_g2< 183 >::operator= ( const element_edwards_g2< 183 > &  other )

inlineconstexpr

operator==()

constexpr bool nil::crypto3::algebra::curves::detail::element_edwards_g2< 183 >::operator== ( const element_edwards_g2< 183 > &  other ) const

inlineconstexpr

to_affine()

constexpr element_edwards_g2 nil::crypto3::algebra::curves::detail::element_edwards_g2< 183 >::to_affine ( ) const

inlineconstexpr

Returns

return the corresponding element from inverted coordinates to affine coordinates

to_projective()

constexpr element_edwards_g2 nil::crypto3::algebra::curves::detail::element_edwards_g2< 183 >::to_projective ( ) const

inlineconstexpr

Returns

return the corresponding element from projective coordinates to affine coordinates

zero()

constexpr static element_edwards_g2 nil::crypto3::algebra::curves::detail::element_edwards_g2< 183 >::zero ( )

inlinestaticconstexpr

Get the point at infinity.

Member Data Documentation

twist

constexpr static const g2_field_type_value nil::crypto3::algebra::curves::detail::element_edwards_g2< 183 >::twist

staticconstexpr

Initial value:

= g2_field_type_value(
                            g2_field_type_value::underlying_type::zero(), g2_field_type_value::underlying_type::one(),
                            g2_field_type_value::underlying_type::zero())

X

underlying_field_value_type nil::crypto3::algebra::curves::detail::element_edwards_g2< 183 >::X

Y

underlying_field_value_type nil::crypto3::algebra::curves::detail::element_edwards_g2< 183 >::Y

Z

underlying_field_value_type nil::crypto3::algebra::curves::detail::element_edwards_g2< 183 >::Z

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

• algebra/include/nil/crypto3/algebra/curves/detail/edwards/element_g2.hpp