Classes
struct	wide_array

Public Types
using	View = field

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
constexpr	field (const numeric::uint256_t &input) noexcept

constexpr	field (const unsigned long input) noexcept

constexpr	field (const unsigned int input) noexcept

constexpr	field (const unsigned long long input) noexcept

constexpr	field (const int input) noexcept

constexpr	field (const uint64_t a, const uint64_t b, const uint64_t c, const uint64_t d) noexcept

constexpr	field (const uint512_t &input) noexcept
	Convert a 512-bit big integer into a field element.

constexpr	field (std::string input) noexcept

constexpr	operator uint32_t () const

constexpr	operator uint64_t () const

constexpr	operator uint128_t () const

constexpr	operator uint256_t () const noexcept

constexpr uint256_t	uint256_t_no_montgomery_conversion () const noexcept

constexpr	field (const field &other) noexcept=default

constexpr	field (field &&other) noexcept=default

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

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

BBERG_INLINE constexpr field	operator* (const field &other) const noexcept

BBERG_INLINE constexpr field	operator+ (const field &other) const noexcept

BBERG_INLINE constexpr field	operator- (const field &other) const noexcept

BBERG_INLINE constexpr field	operator- () const noexcept

constexpr field	operator/ (const field &other) const noexcept

BBERG_INLINE constexpr field	operator++ () noexcept

BBERG_INLINE constexpr field	operator++ (int) noexcept

BBERG_INLINE constexpr field &	*operator=** (const field &other) noexcept

BBERG_INLINE constexpr field &	operator+= (const field &other) noexcept

BBERG_INLINE constexpr field &	operator-= (const field &other) noexcept

constexpr field &	operator/= (const field &other) noexcept

BBERG_INLINE constexpr bool	operator> (const field &other) const noexcept
	Greater-than operator.

BBERG_INLINE constexpr bool	operator< (const field &other) const noexcept
	Less-than operator.

BBERG_INLINE constexpr bool	operator== (const field &other) const noexcept

BBERG_INLINE constexpr bool	operator!= (const field &other) const noexcept

BBERG_INLINE constexpr field	to_montgomery_form () const noexcept

BBERG_INLINE constexpr field	from_montgomery_form () const noexcept

BBERG_INLINE constexpr field	sqr () const noexcept

BBERG_INLINE constexpr void	self_sqr () noexcept

BBERG_INLINE constexpr field	pow (const uint256_t &exponent) const noexcept

BBERG_INLINE constexpr field	pow (uint64_t exponent) const noexcept

constexpr field	invert () const noexcept

constexpr std::pair< bool, field >	sqrt () const noexcept
	Compute square root of the field element.

BBERG_INLINE constexpr void	self_neg () noexcept

BBERG_INLINE constexpr void	self_to_montgomery_form () noexcept

BBERG_INLINE constexpr void	self_from_montgomery_form () noexcept

BBERG_INLINE constexpr void	self_conditional_negate (uint64_t predicate) noexcept

BBERG_INLINE constexpr field	reduce_once () const noexcept

BBERG_INLINE constexpr void	self_reduce_once () noexcept

BBERG_INLINE constexpr void	self_set_msb () noexcept

BBERG_INLINE constexpr bool	is_msb_set () const noexcept

BBERG_INLINE constexpr uint64_t	is_msb_set_word () const noexcept

BBERG_INLINE constexpr bool	is_zero () const noexcept

BBERG_INLINE std::vector< uint8_t >	to_buffer () const

BBERG_INLINE constexpr wide_array	mul_512 (const field &other) const noexcept

BBERG_INLINE constexpr wide_array	sqr_512 () const noexcept

BBERG_INLINE constexpr field	conditionally_subtract_from_double_modulus (const uint64_t predicate) const noexcept

void	msgpack_pack (auto &packer) const

void	msgpack_unpack (auto o)

void	msgpack_schema (auto &packer) const

Static Public Member Functions
static constexpr field	cube_root_of_unity ()

static constexpr field	zero ()

static constexpr field	neg_one ()

static constexpr field	one ()

static constexpr field	external_coset_generator ()

static constexpr field	tag_coset_generator ()

static constexpr field	coset_generator (const size_t idx)

static void	batch_invert (std::span< field > coeffs) noexcept

static void	batch_invert (field *coeffs, size_t n) noexcept

static constexpr field	get_root_of_unity (size_t subgroup_size) noexcept

static void	serialize_to_buffer (const field &value, uint8_t *buffer)

static field	serialize_from_buffer (const uint8_t *buffer)

static void	split_into_endomorphism_scalars (const field &k, field &k1, field &k2)

static void	split_into_endomorphism_scalars_384 (const field &input, field &k1_out, field &k2_out)

static BBERG_INLINE void	__copy (const field &a, field &r) noexcept

static BBERG_INLINE void	__swap (field &src, field &dest) noexcept

static field	random_element (numeric::random::Engine *engine=nullptr) noexcept

static constexpr field	multiplicative_generator () noexcept

Public Attributes
uint64_t	data [4]

Static Public Attributes
static constexpr uint256_t	modulus

static constexpr uint256_t	modulus_minus_two

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

Constructor & Destructor Documentation

◆ field()

template<class Params_ >

constexpr barretenberg::field< Params_ >::field ( const uint512_t & input )

inlineexplicitconstexprnoexcept

Convert a 512-bit big integer into a field element.

Used for deriving field elements from random values. 512-bits prevents biased output as 2^512>>modulus

Member Function Documentation

◆ operator*()

template<class T >

constexpr field< T > barretenberg::field< T >::operator* ( const field< Params_ > & other ) const

constexprnoexcept

Mutiplication

◆ operator+()

template<class T >

constexpr field< T > barretenberg::field< T >::operator+ ( const field< Params_ > & other ) const

constexprnoexcept

Addition

◆ operator-()

template<class T >

constexpr field< T > barretenberg::field< T >::operator- ( const field< Params_ > & other ) const

constexprnoexcept

Subtraction

◆ operator<()

template<class T >

constexpr bool barretenberg::field< T >::operator< ( const field< Params_ > & other ) const

constexprnoexcept

Less-than operator.

comparison operators exist so that field is comparible with stl methods that require them. (e.g. std::sort) Finite fields do not have an explicit ordering, these should NEVER be used in algebraic algorithms.

Template Parameters

T

Parameters

other

Returns: true; false

◆ operator>()

template<class T >

constexpr bool barretenberg::field< T >::operator> ( const field< Params_ > & other ) const

constexprnoexcept

Greater-than operator.

comparison operators exist so that field is comparible with stl methods that require them. (e.g. std::sort) Finite fields do not have an explicit ordering, these should NEVER be used in algebraic algorithms.

Template Parameters

T

Parameters

other

Returns: true; false

◆ split_into_endomorphism_scalars()

template<class Params_ >

static void barretenberg::field< Params_ >::split_into_endomorphism_scalars	(	const field< Params_ > &	k,
		field< Params_ > &	k1,
		field< Params_ > &	k2
	)

inlinestatic

For short Weierstrass curves y^2 = x^3 + b mod r, if there exists a cube root of unity mod r, we can take advantage of an enodmorphism to decompose a 254 bit scalar into 2 128 bit scalars. \beta = cube root of 1, mod q (q = order of fq) \lambda = cube root of 1, mod r (r = order of fr)

For a point P1 = (X, Y), where Y^2 = X^3 + b, we know that the point P2 = (X * \beta, Y) is also a point on the curve We can represent P2 as a scalar multiplication of P1, where P2 = \lambda * P1

For a generic multiplication of P1 by a 254 bit scalar k, we can decompose k into 2 127 bit scalars (k1, k2), such that k = k1 - (k2 * \lambda)

We can now represent (k * P1) as (k1 * P1) - (k2 * P2), where P2 = (X * \beta, Y). As k1, k2 have half the bit length of k, we have reduced the number of loop iterations of our scalar multiplication algorithm in half

To find k1, k2, We use the extended euclidean algorithm to find 4 short scalars [a1, a2], [b1, b2] such that modulus = (a1 * b2) - (b1 * a2) We then compute scalars c1 = round(b2 * k / r), c2 = round(b1 * k / r), where k1 = (c1 * a1) + (c2 * a2), k2 = -((c1 * b1) + (c2 * b2)) We pre-compute scalars g1 = (2^256 * b1) / n, g2 = (2^256 * b2) / n, to avoid having to perform long division on 512-bit scalars

◆ sqr()

template<class T >

constexpr field< T > barretenberg::field< T >::sqr

constexprnoexcept

Squaring

◆ sqrt()

template<class T >

constexpr std::pair< bool, field< T > > barretenberg::field< T >::sqrt

constexprnoexcept

Compute square root of the field element.

Returns: <true, root> if the element is a quadratic remainder, <false, 0> if it's not

Member Data Documentation

◆ modulus

template<class Params_ >

constexpr uint256_t barretenberg::field< Params_ >::modulus

staticconstexpr

Initial value:

=

uint256_t{ Params::modulus_0, Params::modulus_1, Params::modulus_2, Params::modulus_3 }

◆ modulus_minus_two

template<class Params_ >

constexpr uint256_t barretenberg::field< Params_ >::modulus_minus_two

staticconstexpr

Initial value:

=

uint256_t(Params::modulus_0 - 2ULL, Params::modulus_1, Params::modulus_2, Params::modulus_3)

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

src/barretenberg/ecc/fields/field_declarations.hpp
src/barretenberg/ecc/fields/field_impl.hpp
src/barretenberg/ecc/fields/field_impl_generic.hpp

Classes

Public Types

Public Member Functions

Static Public Member Functions

Public Attributes

Static Public Attributes

Friends

Constructor & Destructor Documentation

◆ field()

Member Function Documentation

◆ operator*()

◆ operator+()

◆ operator-()

◆ operator<()

◆ operator>()

◆ split_into_endomorphism_scalars()

◆ sqr()

◆ sqrt()

Member Data Documentation

◆ modulus

◆ modulus_minus_two