#include <affine_element.hpp>

Classes
struct	MsgpackRawAffineElement

Public Types
using	Fq = Fq_

using	Fr = Fr_

using	Params = Params_

using	in_buf = const uint8_t *

using	vec_in_buf = const uint8_t *

using	out_buf = uint8_t *

using	vec_out_buf = uint8_t **

Public Member Functions
	affine_element () noexcept=default

	~affine_element () noexcept=default

constexpr	affine_element (const Fq &x, const Fq &y) noexcept

constexpr	affine_element (const affine_element &other) noexcept=default

constexpr	affine_element (affine_element &&other) noexcept=default

constexpr affine_element &	operator= (const affine_element &other) noexcept=default

constexpr affine_element &	operator= (affine_element &&other) noexcept=default

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

constexpr affine_element	operator* (const Fr &exponent) const noexcept

constexpr affine_element	set_infinity () const noexcept

constexpr void	self_set_infinity () noexcept

constexpr bool	is_point_at_infinity () const noexcept

constexpr bool	on_curve () const noexcept

constexpr bool	operator== (const affine_element &other) const noexcept

constexpr affine_element	operator- () const noexcept

constexpr bool	operator> (const affine_element &other) const noexcept

constexpr bool	operator< (const affine_element &other) const noexcept

std::vector< uint8_t >	to_buffer () const
	Serialize the point to a byte vector.

void	msgpack_pack (auto &packer) const

void	msgpack_unpack (auto o)

void	msgpack_schema (auto &packer) const

template<typename BaseField , typename CompileTimeEnabled >
constexpr affine_element< Fq, Fr, T >	from_compressed (const uint256_t &compressed) noexcept

template<typename BaseField , typename CompileTimeEnabled >
constexpr std::array< affine_element< Fq, Fr, T >, 2 >	from_compressed_unsafe (const uint256_t &compressed) noexcept

Static Public Member Functions
static constexpr affine_element	one () noexcept

template<typename BaseField = Fq, typename CompileTimeEnabled = std::enable_if_t<(BaseField::modulus >> 255) == uint256_t(0), void>>
static constexpr affine_element	from_compressed (const uint256_t &compressed) noexcept
	Reconstruct a point in affine coordinates from compressed form.

template<typename BaseField = Fq, typename CompileTimeEnabled = std::enable_if_t<(BaseField::modulus >> 255) == uint256_t(1), void>>
static constexpr std::array< affine_element, 2 >	from_compressed_unsafe (const uint256_t &compressed) noexcept
	Reconstruct a point in affine coordinates from compressed form.

static constexpr affine_element	infinity ()

static constexpr std::optional< affine_element >	derive_from_x_coordinate (const Fq &x, bool sign_bit) noexcept

static affine_element	random_element (numeric::RNG *engine=nullptr) noexcept
	Samples a random point on the curve.

static constexpr affine_element	hash_to_curve (const std::vector< uint8_t > &seed, uint8_t attempt_count=0) noexcept
	Hash a seed buffer into a point.

static void	serialize_to_buffer (const affine_element &value, uint8_t *buffer, bool write_x_first=false)
	Serialize the point to the given buffer.

static affine_element	serialize_from_buffer (const uint8_t *buffer, bool write_x_first=false)
	Restore point from a buffer.

static affine_element	batch_mul (std::span< const affine_element > points, std::span< const Fr > scalars, size_t max_num_bits=0, bool with_edgecases=true, const Fr &masking_scalar=Fr(1)) noexcept
	Multi-scalar multiplication: compute sum_i(scalars[i] * points[i])

Public Attributes
Fq	x

Fq	y

Static Public Attributes
static constexpr size_t	PUBLIC_INPUTS_SIZE = 2 * Fq::PUBLIC_INPUTS_SIZE

template<typename T >
static constexpr bool	is_field2_v

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

Detailed Description

template<typename Fq_, typename Fr_, typename Params_>
class bb::group_elements::affine_element< Fq_, Fr_, Params_ >

Definition at line 27 of file affine_element.hpp.

Member Typedef Documentation

◆ Fq

template<typename Fq_ , typename Fr_ , typename Params_ >

using bb::group_elements::affine_element< Fq_, Fr_, Params_ >::Fq = Fq_

Definition at line 29 of file affine_element.hpp.

◆ Fr

template<typename Fq_ , typename Fr_ , typename Params_ >

using bb::group_elements::affine_element< Fq_, Fr_, Params_ >::Fr = Fr_

Definition at line 30 of file affine_element.hpp.

◆ in_buf

template<typename Fq_ , typename Fr_ , typename Params_ >

using bb::group_elements::affine_element< Fq_, Fr_, Params_ >::in_buf = const uint8_t*

Definition at line 33 of file affine_element.hpp.

◆ out_buf

template<typename Fq_ , typename Fr_ , typename Params_ >

using bb::group_elements::affine_element< Fq_, Fr_, Params_ >::out_buf = uint8_t*

Definition at line 35 of file affine_element.hpp.

◆ Params

template<typename Fq_ , typename Fr_ , typename Params_ >

using bb::group_elements::affine_element< Fq_, Fr_, Params_ >::Params = Params_

Definition at line 31 of file affine_element.hpp.

◆ vec_in_buf

template<typename Fq_ , typename Fr_ , typename Params_ >

using bb::group_elements::affine_element< Fq_, Fr_, Params_ >::vec_in_buf = const uint8_t*

Definition at line 34 of file affine_element.hpp.

◆ vec_out_buf

template<typename Fq_ , typename Fr_ , typename Params_ >

using bb::group_elements::affine_element< Fq_, Fr_, Params_ >::vec_out_buf = uint8_t**

Definition at line 36 of file affine_element.hpp.

Constructor & Destructor Documentation

◆ affine_element() [1/4]

template<typename Fq_ , typename Fr_ , typename Params_ >

bb::group_elements::affine_element< Fq_, Fr_, Params_ >::affine_element ( )

defaultnoexcept

◆ ~affine_element()

template<typename Fq_ , typename Fr_ , typename Params_ >

bb::group_elements::affine_element< Fq_, Fr_, Params_ >::~affine_element ( )

defaultnoexcept

◆ affine_element() [2/4]

template<class Fq , class Fr , class T >

constexpr bb::group_elements::affine_element< Fq, Fr, T >::affine_element	(	const Fq &	x,
		const Fq &	y
	)

constexprnoexcept

Definition at line 14 of file affine_element_impl.hpp.

◆ affine_element() [3/4]

template<typename Fq_ , typename Fr_ , typename Params_ >

constexpr bb::group_elements::affine_element< Fq_, Fr_, Params_ >::affine_element ( const affine_element< Fq_, Fr_, Params_ > & other )

constexprdefaultnoexcept

◆ affine_element() [4/4]

template<typename Fq_ , typename Fr_ , typename Params_ >

constexpr bb::group_elements::affine_element< Fq_, Fr_, Params_ >::affine_element ( affine_element< Fq_, Fr_, Params_ > && other )

constexprdefaultnoexcept

Member Function Documentation

◆ batch_mul()

template<class Fq , class Fr , class Params >

template affine_element< fr, fq, grumpkin::G1Params > bb::group_elements::affine_element< Fq_, Fr_, Params_ >::batch_mul	(	std::span< const affine_element< Fq_, Fr_, Params_ > >	points,
		std::span< const Fr >	scalars,
		size_t	max_num_bits = `0`,
		bool	with_edgecases = `true`,
		const Fr &	masking_scalar = `Fr(1)`
	)

staticnoexcept

Multi-scalar multiplication: compute sum_i(scalars[i] * points[i])

Interface matches stdlib::biggroup::element::batch_mul for unified native/stdlib usage. Delegates to Pippenger MSM algorithm.

Parameters

points	Span of affine points
scalars	Span of scalar field elements (same length as points)
max_num_bits	Ignored for native (circuit optimization hint in stdlib)
with_edgecases	If true, uses Jacobian Pippenger (safe); if false, uses affine (faster)
masking_scalar	Ignored for native (needed for safe offset generators in stdlib)

Definition at line 26 of file element_batch_mul.cpp.

◆ derive_from_x_coordinate()

template<class Fq , class Fr , class T >

constexpr std::optional< affine_element< Fq, Fr, T > > bb::group_elements::affine_element< Fq, Fr, T >::derive_from_x_coordinate	(	const Fq &	x,
		bool	sign_bit
	)

staticconstexprnoexcept

Definition at line 168 of file affine_element_impl.hpp.

◆ from_compressed() [1/2]

template<typename Fq_ , typename Fr_ , typename Params_ >

template<typename BaseField = Fq, typename CompileTimeEnabled = std::enable_if_t<(BaseField::modulus >> 255) == uint256_t(0), void>>

static constexpr affine_element bb::group_elements::affine_element< Fq_, Fr_, Params_ >::from_compressed ( const uint256_t & compressed )

staticconstexprnoexcept

Reconstruct a point in affine coordinates from compressed form.

#LARGE_MODULUS_AFFINE_POINT_COMPRESSION Point compression is only implemented for curves of a prime field F_p with p using < 256 bits. One possiblity for extending to a 256-bit prime field: https://patents.google.com/patent/US6252960B1/en.

Parameters

compressed compressed point

Returns: constexpr affine_element

◆ from_compressed() [2/2]

template<typename Fq_ , typename Fr_ , typename Params_ >

template<typename BaseField , typename CompileTimeEnabled >

constexpr affine_element< Fq, Fr, T > bb::group_elements::affine_element< Fq_, Fr_, Params_ >::from_compressed ( const uint256_t & compressed )

constexprnoexcept

Definition at line 21 of file affine_element_impl.hpp.

◆ from_compressed_unsafe() [1/2]

template<typename Fq_ , typename Fr_ , typename Params_ >

template<typename BaseField = Fq, typename CompileTimeEnabled = std::enable_if_t<(BaseField::modulus >> 255) == uint256_t(1), void>>

static constexpr std::array< affine_element, 2 > bb::group_elements::affine_element< Fq_, Fr_, Params_ >::from_compressed_unsafe ( const uint256_t & compressed )

staticconstexprnoexcept

Reconstruct a point in affine coordinates from compressed form.

#LARGE_MODULUS_AFFINE_POINT_COMPRESSION Point compression is implemented for curves of a prime field F_p with p being 256 bits. TODO(Suyash): Check with kesha if this is correct.

Parameters

compressed compressed point

Returns: constexpr affine_element

◆ from_compressed_unsafe() [2/2]

template<typename Fq_ , typename Fr_ , typename Params_ >

template<typename BaseField , typename CompileTimeEnabled >

constexpr std::array< affine_element< Fq, Fr, T >, 2 > bb::group_elements::affine_element< Fq_, Fr_, Params_ >::from_compressed_unsafe ( const uint256_t & compressed )

constexprnoexcept

Definition at line 45 of file affine_element_impl.hpp.

◆ hash_to_curve()

template<class Fq , class Fr , class T >
requires SupportsHashToCurve<Params>

constexpr affine_element< Fq, Fr, T > bb::group_elements::affine_element< Fq, Fr, T >::hash_to_curve	(	const std::vector< uint8_t > &	seed,
		uint8_t	attempt_count = `0`
	)

staticconstexprnoexcept

Hash a seed buffer into a point.

ALGORITHM DESCRIPTION:

Initialize unsigned integer attempt_count = 0
Copy seed into a buffer whose size is 2 bytes greater than seed (initialized to 0)
Interpret attempt_count as a byte and write into buffer at [buffer.size() - 2]
Compute Blake3s hash of buffer
Set the end byte of the buffer to 1
Compute Blake3s hash of buffer
Interpret the two hash outputs as the high / low 256 bits of a 512-bit integer (big-endian)
Derive x-coordinate of point by reducing the 512-bit integer modulo the curve's field modulus (Fq)
Compute y^2 from the curve formula y^2 = x^3 + ax + b (a, b are curve params. for BN254, a = 0, b = 3)
IF y^2 IS NOT A QUADRATIC RESIDUE 10a. increment attempt_count by 1 and go to step 2
IF y^2 IS A QUADRATIC RESIDUE 11a. derive y coordinate via y = sqrt(y) 11b. Interpret most significant bit of 512-bit integer as a 'parity' bit 11c. If parity bit is set AND y's most significant bit is not set, invert y 11d. If parity bit is not set AND y's most significant bit is set, invert y N.B. last 2 steps are because the sqrt() algorithm can return 2 values, we need to a way to canonically distinguish between these 2 values and select a "preferred" one 11e. return (x, y)

Note: This algorihm is constexpr: we can hash-to-curve (and derive generators) at compile-time!

Template Parameters

Fq
Fr
T

Parameters

seed	Bytes that uniquely define the point being generated
attempt_count

Returns: constexpr affine_element<Fq, Fr, T>

Definition at line 219 of file affine_element_impl.hpp.

◆ infinity()

template<class Fq , class Fr , class T >

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

staticconstexpr

Definition at line 83 of file affine_element_impl.hpp.

◆ is_point_at_infinity()

template<class Fq , class Fr , class T >

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

constexprnoexcept

Definition at line 113 of file affine_element_impl.hpp.

◆ msgpack_pack()

template<typename Fq_ , typename Fr_ , typename Params_ >

void bb::group_elements::affine_element< Fq_, Fr_, Params_ >::msgpack_pack ( auto & packer ) const

inline

Definition at line 224 of file affine_element.hpp.

◆ msgpack_schema()

template<typename Fq_ , typename Fr_ , typename Params_ >

void bb::group_elements::affine_element< Fq_, Fr_, Params_ >::msgpack_schema ( auto & packer ) const

inline

Definition at line 286 of file affine_element.hpp.

◆ msgpack_unpack()

template<typename Fq_ , typename Fr_ , typename Params_ >

void bb::group_elements::affine_element< Fq_, Fr_, Params_ >::msgpack_unpack ( auto o )

inline

Definition at line 254 of file affine_element.hpp.

◆ on_curve()

template<class Fq , class Fr , class T >

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

constexprnoexcept

Definition at line 125 of file affine_element_impl.hpp.

◆ one()

template<typename Fq_ , typename Fr_ , typename Params_ >

static constexpr affine_element bb::group_elements::affine_element< Fq_, Fr_, Params_ >::one ( )

inlinestaticconstexprnoexcept

Definition at line 52 of file affine_element.hpp.

◆ operator*()

template<class Fq , class Fr , class T >

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

constexprnoexcept

Definition at line 78 of file affine_element_impl.hpp.

◆ operator+()

template<typename Fq_ , typename Fr_ , typename Params_ >

constexpr affine_element< Fq, Fr, T > bb::group_elements::affine_element< Fq, Fr, T >::operator+ ( const affine_element< Fq_, Fr_, Params_ > & other ) const

constexprnoexcept

Definition at line 71 of file affine_element_impl.hpp.

◆ operator-()

template<typename Fq_ , typename Fr_ , typename Params_ >

constexpr affine_element bb::group_elements::affine_element< Fq_, Fr_, Params_ >::operator- ( ) const

inlineconstexprnoexcept

Definition at line 109 of file affine_element.hpp.

◆ operator<()

template<typename Fq_ , typename Fr_ , typename Params_ >

constexpr bool bb::group_elements::affine_element< Fq_, Fr_, Params_ >::operator< ( const affine_element< Fq_, Fr_, Params_ > & other ) const

inlineconstexprnoexcept

Definition at line 112 of file affine_element.hpp.

◆ operator=() [1/2]

template<typename Fq_ , typename Fr_ , typename Params_ >

constexpr affine_element & bb::group_elements::affine_element< Fq_, Fr_, Params_ >::operator= ( affine_element< Fq_, Fr_, Params_ > && other )

constexprdefaultnoexcept

◆ operator=() [2/2]

template<typename Fq_ , typename Fr_ , typename Params_ >

constexpr affine_element & bb::group_elements::affine_element< Fq_, Fr_, Params_ >::operator= ( const affine_element< Fq_, Fr_, Params_ > & other )

constexprdefaultnoexcept

◆ operator==()

template<class Fq , class Fr , class T >

constexpr bool bb::group_elements::affine_element< Fq, Fr, T >::operator== ( const affine_element< Fq_, Fr_, Params_ > & other ) const

constexprnoexcept

Definition at line 139 of file affine_element_impl.hpp.

◆ operator>()

template<class Fq , class Fr , class T >

constexpr bool bb::group_elements::affine_element< Fq, Fr, T >::operator> ( const affine_element< Fq_, Fr_, Params_ > & other ) const

constexprnoexcept

Definition at line 149 of file affine_element_impl.hpp.

◆ random_element()

template<typename Fq , typename Fr , typename T >

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

staticnoexcept

Samples a random point on the curve.

Returns: A randomly chosen point on the curve

Definition at line 260 of file affine_element_impl.hpp.

◆ self_set_infinity()

template<class Fq , class Fr , class T >

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

constexprnoexcept

Definition at line 98 of file affine_element_impl.hpp.

◆ serialize_from_buffer()

template<typename Fq_ , typename Fr_ , typename Params_ >

static affine_element bb::group_elements::affine_element< Fq_, Fr_, Params_ >::serialize_from_buffer	(	const uint8_t *	buffer,
		bool	write_x_first = `false`
	)

inlinestatic

Restore point from a buffer.

Parameters

buffer Buffer from which we deserialize the point

Returns: Deserialized point

We support serializing the point at infinity for curves defined over a bb::field (i.e., a native field of prime order) and for points of bb::g2.

Warning: This will need to be updated if we serialize points over composite-order fields other than fq2!

Definition at line 150 of file affine_element.hpp.

◆ serialize_to_buffer()

template<typename Fq_ , typename Fr_ , typename Params_ >

static void bb::group_elements::affine_element< Fq_, Fr_, Params_ >::serialize_to_buffer	(	const affine_element< Fq_, Fr_, Params_ > &	value,
		uint8_t *	buffer,
		bool	write_x_first = `false`
	)

inlinestatic

Serialize the point to the given buffer.

We support serializing the point at infinity for curves defined over a bb::field (i.e., a native field of prime order) and for points of bb::g2.

Warning: This will need to be updated if we serialize points over composite-order fields other than fq2!

Definition at line 123 of file affine_element.hpp.

◆ set_infinity()

template<class Fq , class Fr , class T >

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

constexprnoexcept

Definition at line 91 of file affine_element_impl.hpp.

◆ to_buffer()

template<typename Fq_ , typename Fr_ , typename Params_ >

std::vector< uint8_t > bb::group_elements::affine_element< Fq_, Fr_, Params_ >::to_buffer ( ) const

inline

Serialize the point to a byte vector.

Returns: Vector with serialized representation of the point

Definition at line 174 of file affine_element.hpp.

Friends And Related Symbol Documentation

◆ operator<<

template<typename Fq_ , typename Fr_ , typename Params_ >

std::ostream & operator<<	(	std::ostream &	os,
		const affine_element< Fq_, Fr_, Params_ > &	a
	)

friend

Definition at line 181 of file affine_element.hpp.

Member Data Documentation

◆ is_field2_v

template<typename Fq_ , typename Fr_ , typename Params_ >

template<typename T >

constexpr bool bb::group_elements::affine_element< Fq_, Fr_, Params_ >::is_field2_v

staticconstexpr

Initial value:

= requires(T t) {
        t.c0;
        t.c1;
    }

Definition at line 208 of file affine_element.hpp.

◆ PUBLIC_INPUTS_SIZE

template<typename Fq_ , typename Fr_ , typename Params_ >

constexpr size_t bb::group_elements::affine_element< Fq_, Fr_, Params_ >::PUBLIC_INPUTS_SIZE = 2 * Fq::PUBLIC_INPUTS_SIZE

staticconstexpr

Number of bb::fr elements required to represent an affine_element in the public inputs (2 frs per coordinate)

Definition at line 41 of file affine_element.hpp.

◆ x

template<typename Fq_ , typename Fr_ , typename Params_ >

Fq bb::group_elements::affine_element< Fq_, Fr_, Params_ >::x

Definition at line 203 of file affine_element.hpp.

◆ y

template<typename Fq_ , typename Fr_ , typename Params_ >

Fq bb::group_elements::affine_element< Fq_, Fr_, Params_ >::y

Definition at line 204 of file affine_element.hpp.

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

src/barretenberg/ecc/groups/affine_element.hpp
src/barretenberg/ecc/groups/affine_element_impl.hpp
src/barretenberg/ecc/groups/element_batch_mul.cpp

Classes

Public Types

Public Member Functions

Static Public Member Functions

Public Attributes

Static Public Attributes

Friends

Detailed Description

Member Typedef Documentation

◆ Fq

◆ Fr

◆ in_buf

◆ out_buf

◆ Params

◆ vec_in_buf

◆ vec_out_buf

Constructor & Destructor Documentation

◆ affine_element() [1/4]

◆ ~affine_element()

◆ affine_element() [2/4]

◆ affine_element() [3/4]

◆ affine_element() [4/4]

Member Function Documentation

◆ batch_mul()

◆ derive_from_x_coordinate()

◆ from_compressed() [1/2]

◆ from_compressed() [2/2]

◆ from_compressed_unsafe() [1/2]

◆ from_compressed_unsafe() [2/2]

◆ hash_to_curve()

◆ infinity()

◆ is_point_at_infinity()

◆ msgpack_pack()

◆ msgpack_schema()

◆ msgpack_unpack()

◆ on_curve()

◆ one()

◆ operator*()

◆ operator+()

◆ operator-()

◆ operator<()

◆ operator=() [1/2]

◆ operator=() [2/2]

◆ operator==()

◆ operator>()

◆ random_element()

◆ self_set_infinity()

◆ serialize_from_buffer()

◆ serialize_to_buffer()

◆ set_infinity()

◆ to_buffer()

Friends And Related Symbol Documentation

◆ operator<<

Member Data Documentation

◆ is_field2_v

◆ PUBLIC_INPUTS_SIZE

◆ x

◆ y