element class. Implements ecc group arithmetic using Jacobian coordinates See https://hyperelliptic.org/EFD/g1p/auto-shortw-jacobian-0.html#doubling-dbl-2009-l More...

#include <element.hpp>

Public Member Functions
	element () noexcept=default

constexpr	element (const Fq &a, const Fq &b, const Fq &c) noexcept

constexpr	element (const element &other) noexcept

constexpr	element (element &&other) noexcept

constexpr	element (const affine_element< Fq, Fr, Params > &other) noexcept

	~element () noexcept=default

constexpr element &	operator= (const element &other) noexcept

constexpr element &	operator= (element &&other) noexcept

constexpr	operator affine_element< Fq, Fr, Params > () const noexcept

constexpr element	dbl () const noexcept

constexpr void	self_dbl () noexcept

constexpr void	self_mixed_add_or_sub (const affine_element< Fq, Fr, Params > &other, uint64_t predicate) noexcept

constexpr element	operator+ (const element &other) const noexcept

constexpr element	operator+ (const affine_element< Fq, Fr, Params > &other) const noexcept

constexpr element	operator+= (const element &other) noexcept

constexpr element	operator+= (const affine_element< Fq, Fr, Params > &other) noexcept

constexpr element	operator- (const element &other) const noexcept

constexpr element	operator- (const affine_element< Fq, Fr, Params > &other) const noexcept

constexpr element	operator- () const noexcept

constexpr element	operator-= (const element &other) noexcept

constexpr element	operator-= (const affine_element< Fq, Fr, Params > &other) noexcept

element	operator* (const Fr &exponent) const noexcept

element	operator*= (const Fr &exponent) noexcept

constexpr element	normalize () const noexcept

BB_INLINE constexpr element	set_infinity () const noexcept

BB_INLINE constexpr void	self_set_infinity () noexcept

BB_INLINE constexpr bool	is_point_at_infinity () const noexcept

BB_INLINE constexpr bool	on_curve () const noexcept

BB_INLINE constexpr bool	operator== (const element &other) const noexcept

template<typename >
element< Fq, Fr, T >	random_coordinates_on_curve (numeric::RNG *engine) noexcept

Static Public Member Functions
static constexpr element	one () noexcept

static constexpr element	zero () noexcept

static element	random_element (numeric::RNG *engine=nullptr) noexcept

static element	infinity ()

static void	batch_normalize (element *elements, size_t num_elements) noexcept

static void	batch_affine_add (const std::span< affine_element< Fq, Fr, Params > > &first_group, const std::span< affine_element< Fq, Fr, Params > > &second_group, const std::span< affine_element< Fq, Fr, Params > > &results) noexcept
	Pairwise affine add points in first and second group.

static std::vector< affine_element< Fq, Fr, Params > >	batch_mul_with_endomorphism (const std::span< const affine_element< Fq, Fr, Params > > &points, const Fr &scalar) noexcept
	Multiply each point by the same scalar.

Public Attributes
Fq	x

Fq	y

Fq	z

Static Public Attributes
static constexpr Fq	curve_b = Params::b

Private Member Functions
element	mul_without_endomorphism (const Fr &scalar) const noexcept

element	mul_with_endomorphism (const Fr &scalar) const noexcept

Static Private Member Functions
template<typename = typename std::enable_if<Params::can_hash_to_curve>>
static element	random_coordinates_on_curve (numeric::RNG *engine=nullptr) noexcept

static void	conditional_negate_affine (const affine_element< Fq, Fr, Params > &in, affine_element< Fq, Fr, Params > &out, uint64_t predicate) noexcept

Friends
class	TestElementPrivate

constexpr element	operator+ (const affine_element< Fq, Fr, Params > &left, const element &right) noexcept

constexpr element	operator- (const affine_element< Fq, Fr, Params > &left, const element &right) noexcept

std::ostream &	operator<< (std::ostream &os, const element &a)

Detailed Description

template<class Fq, class Fr, class Params>
class bb::group_elements::element< Fq, Fr, Params >

element class. Implements ecc group arithmetic using Jacobian coordinates See https://hyperelliptic.org/EFD/g1p/auto-shortw-jacobian-0.html#doubling-dbl-2009-l

Note: Currently subgroup checks are NOT IMPLEMENTED Our current implementation uses G1 points that have a cofactor of 1. All G2 points are precomputed (generator [1]_2 and trusted setup point [x]_2). Explicitly assume precomputed points are valid members of the prime-order subgroup for G2.

Template Parameters

Fq	prime field the curve is defined over
Fr	prime field whose characteristic equals the size of the prime-order elliptic curve subgroup
Params	curve parameters

Definition at line 33 of file element.hpp.

Constructor & Destructor Documentation

◆ element() [1/5]

template<class Fq , class Fr , class Params >

bb::group_elements::element< Fq, Fr, Params >::element ( )

defaultnoexcept

◆ element() [2/5]

template<class Fq , class Fr , class T >

constexpr bb::group_elements::element< Fq, Fr, T >::element	(	const Fq &	a,
		const Fq &	b,
		const Fq &	c
	)

constexprnoexcept

Definition at line 18 of file element_impl.hpp.

◆ element() [3/5]

template<class Fq , class Fr , class T >

constexpr bb::group_elements::element< Fq, Fr, T >::element ( const element< Fq, Fr, Params > & other )

constexprnoexcept

Definition at line 25 of file element_impl.hpp.

◆ element() [4/5]

template<class Fq , class Fr , class T >

constexpr bb::group_elements::element< Fq, Fr, T >::element ( element< Fq, Fr, Params > && other )

constexprnoexcept

Definition at line 32 of file element_impl.hpp.

◆ element() [5/5]

template<class Fq , class Fr , class Params >

constexpr bb::group_elements::element< Fq, Fr, Params >::element ( const affine_element< Fq, Fr, Params > & other )

constexprnoexcept

◆ ~element()

template<class Fq , class Fr , class Params >

bb::group_elements::element< Fq, Fr, Params >::~element ( )

defaultnoexcept

Member Function Documentation

◆ batch_affine_add()

template<class Fq , class Fr , class Params >

void bb::group_elements::element< Fq, Fr, T >::batch_affine_add	(	const std::span< affine_element< Fq, Fr, Params > > &	first_group,
		const std::span< affine_element< Fq, Fr, Params > > &	second_group,
		const std::span< affine_element< Fq, Fr, Params > > &	results
	)

staticnoexcept

Pairwise affine add points in first and second group.

Parameters

first_group
second_group
results

Perform point addition rhs[i]=rhs[i]+lhs[i] with batch inversion

Perform batch affine addition in parallel

Definition at line 722 of file element_impl.hpp.

◆ batch_mul_with_endomorphism()

template<class Fq , class Fr , class Params >

std::vector< affine_element< Fq, Fr, T > > bb::group_elements::element< Fq, Fr, T >::batch_mul_with_endomorphism	(	const std::span< const affine_element< Fq, Fr, Params > > &	points,
		const Fr &	scalar
	)

staticnoexcept

Multiply each point by the same scalar.

We use the fact that all points are being multiplied by the same scalar to batch the operations (perform batch affine additions and doublings with batch inversion trick)

Parameters

points	The span of individual points that need to be scaled
scalar	The scalar we multiply all the points by

Returns: std::vector<affine_element<Fq, Fr, T>> Vector of new points where each point is exponent⋅points[i]

Perform point addition rhs[i]=rhs[i]+lhs[i] with batch inversion

Perform point doubling lhs[i]=lhs[i]+lhs[i] with batch inversion

Definition at line 794 of file element_impl.hpp.

◆ batch_normalize()

template<typename Fq , typename Fr , typename T >

void bb::group_elements::element< Fq, Fr, T >::batch_normalize	(	element< Fq, Fr, Params > *	elements,
		size_t	num_elements
	)

staticnoexcept

We now proceed to iterate back down the array of points. At each iteration we update the accumulator to contain the z-coordinate of the currently worked-upon z-coordinate. We can then multiply this accumulator with temporaries, to get a scalar that is equal to the inverse of the z-coordinate of the point at the next iteration cycle e.g. Imagine we have 4 points, such that:

accumulator = 1 / z.data[0]*z.data[1]*z.data[2]*z.data[3] temporaries[3] = z.data[0]*z.data[1]*z.data[2] temporaries[2] = z.data[0]*z.data[1] temporaries[1] = z.data[0] temporaries[0] = 1

At the first iteration, accumulator * temporaries[3] = z.data[0]*z.data[1]*z.data[2] / z.data[0]*z.data[1]*z.data[2]*z.data[3] = (1 / z.data[3]) We then update accumulator, such that:

accumulator = accumulator * z.data[3] = 1 / z.data[0]*z.data[1]*z.data[2]

At the second iteration, accumulator * temporaries[2] = z.data[0]*z.data[1] / z.data[0]*z.data[1]*z.data[2] = (1 z.data[2]) And so on, until we have computed every z-inverse!

We can then convert out of Jacobian form (x = X / Z^2, y = Y / Z^3) with 4 muls and 1 square.

Definition at line 1013 of file element_impl.hpp.

◆ conditional_negate_affine()

template<class Fq , class Fr , class Params >

void bb::group_elements::element< Fq, Fr, T >::conditional_negate_affine	(	const affine_element< Fq, Fr, Params > &	in,
		affine_element< Fq, Fr, Params > &	out,
		uint64_t	predicate
	)

staticprivatenoexcept

Definition at line 1005 of file element_impl.hpp.

◆ dbl()

template<class Fq , class Fr , class T >

constexpr element< Fq, Fr, T > bb::group_elements::element< Fq, Fr, T >::dbl ( ) const

constexprnoexcept

Definition at line 151 of file element_impl.hpp.

◆ infinity()

template<class Fq , class Fr , class T >

element< Fq, Fr, T > bb::group_elements::element< Fq, Fr, T >::infinity ( )

static

Definition at line 497 of file element_impl.hpp.

◆ is_point_at_infinity()

template<class Fq , class Fr , class T >

constexpr bool bb::group_elements::element< Fq, Fr, T >::is_point_at_infinity ( ) const

constexprnoexcept

Definition at line 527 of file element_impl.hpp.

◆ mul_with_endomorphism()

template<class Fq , class Fr , class T >

element< Fq, Fr, T > bb::group_elements::element< Fq, Fr, T >::mul_with_endomorphism ( const Fr & scalar ) const

privatenoexcept

Definition at line 658 of file element_impl.hpp.

◆ mul_without_endomorphism()

template<class Fq , class Fr , class T >

element< Fq, Fr, T > bb::group_elements::element< Fq, Fr, T >::mul_without_endomorphism ( const Fr & scalar ) const

privatenoexcept

Definition at line 603 of file element_impl.hpp.

◆ normalize()

template<class Fq , class Fr , class T >

constexpr element< Fq, Fr, T > bb::group_elements::element< Fq, Fr, T >::normalize ( ) const

constexprnoexcept

Definition at line 491 of file element_impl.hpp.

◆ on_curve()

template<class Fq , class Fr , class T >

constexpr bool bb::group_elements::element< Fq, Fr, T >::on_curve ( ) const

constexprnoexcept

Definition at line 538 of file element_impl.hpp.

◆ one()

template<class Fq , class Fr , class Params >

static constexpr element bb::group_elements::element< Fq, Fr, Params >::one ( )

inlinestaticconstexprnoexcept

Definition at line 45 of file element.hpp.

◆ operator affine_element< Fq, Fr, Params >()

template<class Fq , class Fr , class Params >

constexpr bb::group_elements::element< Fq, Fr, Params >::operator affine_element< Fq, Fr, Params > ( ) const

constexprnoexcept

◆ operator*()

template<class Fq , class Fr , class T >

element< Fq, Fr, T > bb::group_elements::element< Fq, Fr, T >::operator* ( const Fr & exponent ) const

noexcept

Definition at line 477 of file element_impl.hpp.

◆ operator*=()

template<class Fq , class Fr , class T >

element< Fq, Fr, T > bb::group_elements::element< Fq, Fr, T >::operator*= ( const Fr & exponent )

noexcept

Definition at line 485 of file element_impl.hpp.

◆ operator+() [1/2]

template<class Fq , class Fr , class Params >

constexpr element bb::group_elements::element< Fq, Fr, Params >::operator+ ( const affine_element< Fq, Fr, Params > & other ) const

constexprnoexcept

◆ operator+() [2/2]

template<class Fq , class Fr , class T >

constexpr element< Fq, Fr, T > bb::group_elements::element< Fq, Fr, T >::operator+ ( const element< Fq, Fr, Params > & other ) const

constexprnoexcept

Definition at line 451 of file element_impl.hpp.

◆ operator+=() [1/2]

template<class Fq , class Fr , class Params >

constexpr element bb::group_elements::element< Fq, Fr, Params >::operator+= ( const affine_element< Fq, Fr, Params > & other )

constexprnoexcept

◆ operator+=() [2/2]

template<class Fq , class Fr , class T >

constexpr element< Fq, Fr, T > bb::group_elements::element< Fq, Fr, T >::operator+= ( const element< Fq, Fr, Params > & other )

constexprnoexcept

Definition at line 362 of file element_impl.hpp.

◆ operator-() [1/3]

template<class Fq , class Fr , class T >

constexpr element< Fq, Fr, T > bb::group_elements::element< Fq, Fr, T >::operator- ( ) const

constexprnoexcept

Definition at line 471 of file element_impl.hpp.

◆ operator-() [2/3]

template<class Fq , class Fr , class Params >

constexpr element bb::group_elements::element< Fq, Fr, Params >::operator- ( const affine_element< Fq, Fr, Params > & other ) const

constexprnoexcept

◆ operator-() [3/3]

template<class Fq , class Fr , class T >

constexpr element< Fq, Fr, T > bb::group_elements::element< Fq, Fr, T >::operator- ( const element< Fq, Fr, Params > & other ) const

constexprnoexcept

Definition at line 465 of file element_impl.hpp.

◆ operator-=() [1/2]

template<class Fq , class Fr , class Params >

constexpr element bb::group_elements::element< Fq, Fr, Params >::operator-= ( const affine_element< Fq, Fr, Params > & other )

constexprnoexcept

◆ operator-=() [2/2]

template<class Fq , class Fr , class T >

constexpr element< Fq, Fr, T > bb::group_elements::element< Fq, Fr, T >::operator-= ( const element< Fq, Fr, Params > & other )

constexprnoexcept

Definition at line 458 of file element_impl.hpp.

◆ operator=() [1/2]

template<class Fq , class Fr , class T >

constexpr element< Fq, Fr, T > & bb::group_elements::element< Fq, Fr, T >::operator= ( const element< Fq, Fr, Params > & other )

constexprnoexcept

Definition at line 46 of file element_impl.hpp.

◆ operator=() [2/2]

template<class Fq , class Fr , class T >

constexpr element< Fq, Fr, T > & bb::group_elements::element< Fq, Fr, T >::operator= ( element< Fq, Fr, Params > && other )

constexprnoexcept

Definition at line 58 of file element_impl.hpp.

◆ operator==()

template<class Fq , class Fr , class T >

constexpr bool bb::group_elements::element< Fq, Fr, T >::operator== ( const element< Fq, Fr, Params > & other ) const

constexprnoexcept

Definition at line 559 of file element_impl.hpp.

◆ random_coordinates_on_curve() [1/2]

template<class Fq , class Fr , class Params >

template<typename >

element< Fq, Fr, T > bb::group_elements::element< Fq, Fr, Params >::random_coordinates_on_curve ( numeric::RNG * engine )

noexcept

Definition at line 1067 of file element_impl.hpp.

◆ random_coordinates_on_curve() [2/2]

template<class Fq , class Fr , class Params >

template<typename = typename std::enable_if<Params::can_hash_to_curve>>

static element bb::group_elements::element< Fq, Fr, Params >::random_coordinates_on_curve ( numeric::RNG * engine = nullptr )

staticprivatenoexcept

◆ random_element()

template<class Fq , class Fr , class T >

element< Fq, Fr, T > bb::group_elements::element< Fq, Fr, T >::random_element ( numeric::RNG * engine = nullptr )

staticnoexcept

Definition at line 586 of file element_impl.hpp.

◆ self_dbl()

template<class Fq , class Fr , class T >

constexpr void bb::group_elements::element< Fq, Fr, T >::self_dbl ( )

constexprnoexcept

Definition at line 82 of file element_impl.hpp.

◆ self_mixed_add_or_sub()

template<class Fq , class Fr , class Params >

constexpr void bb::group_elements::element< Fq, Fr, T >::self_mixed_add_or_sub	(	const affine_element< Fq, Fr, Params > &	other,
		uint64_t	predicate
	)

constexprnoexcept

Definition at line 159 of file element_impl.hpp.

◆ self_set_infinity()

template<class Fq , class Fr , class T >

constexpr void bb::group_elements::element< Fq, Fr, T >::self_set_infinity ( )

constexprnoexcept

Definition at line 511 of file element_impl.hpp.

◆ set_infinity()

template<class Fq , class Fr , class T >

constexpr element< Fq, Fr, T > bb::group_elements::element< Fq, Fr, T >::set_infinity ( ) const

constexprnoexcept

Definition at line 504 of file element_impl.hpp.

◆ zero()

template<class Fq , class Fr , class Params >

static constexpr element bb::group_elements::element< Fq, Fr, Params >::zero ( )

inlinestaticconstexprnoexcept

Definition at line 46 of file element.hpp.

Friends And Related Symbol Documentation

◆ operator+

template<class Fq , class Fr , class Params >

constexpr element operator+	(	const affine_element< Fq, Fr, Params > &	left,
		const element< Fq, Fr, Params > &	right
	)

friend

Definition at line 75 of file element.hpp.

◆ operator-

template<class Fq , class Fr , class Params >

constexpr element operator-	(	const affine_element< Fq, Fr, Params > &	left,
		const element< Fq, Fr, Params > &	right
	)

friend

Definition at line 79 of file element.hpp.

◆ operator<<

template<class Fq , class Fr , class Params >

std::ostream & operator<<	(	std::ostream &	os,
		const element< Fq, Fr, Params > &	a
	)

friend

Definition at line 144 of file element.hpp.

◆ TestElementPrivate

template<class Fq , class Fr , class Params >

friend class TestElementPrivate

friend

Definition at line 112 of file element.hpp.

Member Data Documentation

◆ curve_b

template<class Fq , class Fr , class Params >

constexpr Fq bb::group_elements::element< Fq, Fr, Params >::curve_b = Params::b

staticconstexpr

Definition at line 35 of file element.hpp.

◆ x

template<class Fq , class Fr , class Params >

Fq bb::group_elements::element< Fq, Fr, Params >::x

Definition at line 106 of file element.hpp.

◆ y

template<class Fq , class Fr , class Params >

Fq bb::group_elements::element< Fq, Fr, Params >::y

Definition at line 107 of file element.hpp.

◆ z

template<class Fq , class Fr , class Params >

Fq bb::group_elements::element< Fq, Fr, Params >::z

Definition at line 108 of file element.hpp.

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

src/barretenberg/ecc/groups/element.hpp
src/barretenberg/ecc/groups/element_impl.hpp

Public Member Functions

Static Public Member Functions

Public Attributes

Static Public Attributes

Private Member Functions

Static Private Member Functions

Friends

Detailed Description

Constructor & Destructor Documentation

◆ element() [1/5]

◆ element() [2/5]

◆ element() [3/5]

◆ element() [4/5]

◆ element() [5/5]

◆ ~element()

Member Function Documentation

◆ batch_affine_add()

◆ batch_mul_with_endomorphism()

◆ batch_normalize()

◆ conditional_negate_affine()

◆ dbl()

◆ infinity()

◆ is_point_at_infinity()

◆ mul_with_endomorphism()

◆ mul_without_endomorphism()

◆ normalize()

◆ on_curve()

◆ one()

◆ operator affine_element< Fq, Fr, Params >()

◆ operator*()

◆ operator*=()

◆ operator+() [1/2]

◆ operator+() [2/2]

◆ operator+=() [1/2]

◆ operator+=() [2/2]

◆ operator-() [1/3]

◆ operator-() [2/3]

◆ operator-() [3/3]

◆ operator-=() [1/2]

◆ operator-=() [2/2]

◆ operator=() [1/2]

◆ operator=() [2/2]

◆ operator==()

◆ random_coordinates_on_curve() [1/2]

◆ random_coordinates_on_curve() [2/2]

◆ random_element()

◆ self_dbl()

◆ self_mixed_add_or_sub()

◆ self_set_infinity()

◆ set_infinity()

◆ zero()

Friends And Related Symbol Documentation

◆ operator+

◆ operator-

◆ operator<<

◆ TestElementPrivate

Member Data Documentation

◆ curve_b

◆ x

◆ y

◆ z