#include <field12.hpp>

Classes
struct	ell_coeffs

Public Member Functions
constexpr	field12 (const base_field &a=base_field::zero(), const base_field &b=base_field::zero())

constexpr	field12 (const field12 &other)

constexpr	field12 (field12 &&other) noexcept

constexpr field12 &	operator= (const field12 &other) noexcept

constexpr field12 &	operator= (field12 &&other) noexcept

constexpr	~field12 () noexcept=default

constexpr field12	operator+ (const field12 &other) const

constexpr field12	operator- (const field12 &other) const

constexpr field12	operator- () const

constexpr field12	operator* (const field12 &other) const

constexpr field12	operator/ (const field12 &other) const

constexpr field12	operator+= (const field12 &other)

constexpr field12	operator-= (const field12 &other)

constexpr field12	operator*= (const field12 &other)

constexpr field12	operator/= (const field12 &other)

constexpr void	self_neg ()

constexpr void	self_sqr ()

constexpr void	self_sparse_mul (const ell_coeffs &ell)
	Multiply the element by a sparse element of the form ell.o + ell.w * w + ell.vw * wv.

constexpr field12	sqr () const

constexpr field12	invert () const

constexpr field12	frobenius_map_three () const

constexpr field12	frobenius_map_two () const

constexpr field12	frobenius_map_one () const

constexpr field12	cyclotomic_squared () const

constexpr field12	unitary_inverse () const

constexpr field12	to_montgomery_form ()

constexpr field12	from_montgomery_form () const

constexpr bool	is_zero () const

constexpr bool	operator== (const field12 &other) const

Static Public Member Functions
static constexpr field12	zero ()

static constexpr field12	one ()

static constexpr base_field	mul_by_non_residue (const base_field &a)

static constexpr field12	random_element (numeric::RNG *engine=nullptr)

Public Attributes
base_field	c0

base_field	c1

Detailed Description

template<typename quadratic_field, typename base_field, typename Fq12Params>
class bb::field12< quadratic_field, base_field, Fq12Params >

Definition at line 11 of file field12.hpp.

Constructor & Destructor Documentation

◆ field12() [1/3]

template<typename quadratic_field , typename base_field , typename Fq12Params >

constexpr bb::field12< quadratic_field, base_field, Fq12Params >::field12	(	const base_field &	a = `base_field::zero()`,
		const base_field &	b = `base_field::zero()`
	)

inlineconstexpr

Definition at line 13 of file field12.hpp.

◆ field12() [2/3]

template<typename quadratic_field , typename base_field , typename Fq12Params >

constexpr bb::field12< quadratic_field, base_field, Fq12Params >::field12 ( const field12< quadratic_field, base_field, Fq12Params > & other )

inlineconstexpr

Definition at line 18 of file field12.hpp.

◆ field12() [3/3]

template<typename quadratic_field , typename base_field , typename Fq12Params >

constexpr bb::field12< quadratic_field, base_field, Fq12Params >::field12 ( field12< quadratic_field, base_field, Fq12Params > && other )

inlineconstexprnoexcept

Definition at line 23 of file field12.hpp.

◆ ~field12()

template<typename quadratic_field , typename base_field , typename Fq12Params >

constexpr bb::field12< quadratic_field, base_field, Fq12Params >::~field12 ( )

constexprdefaultnoexcept

Member Function Documentation

◆ cyclotomic_squared()

template<typename quadratic_field , typename base_field , typename Fq12Params >

constexpr field12 bb::field12< quadratic_field, base_field, Fq12Params >::cyclotomic_squared ( ) const

inlineconstexpr

Definition at line 223 of file field12.hpp.

◆ frobenius_map_one()

template<typename quadratic_field , typename base_field , typename Fq12Params >

constexpr field12 bb::field12< quadratic_field, base_field, Fq12Params >::frobenius_map_one ( ) const

inlineconstexpr

Definition at line 215 of file field12.hpp.

◆ frobenius_map_three()

template<typename quadratic_field , typename base_field , typename Fq12Params >

constexpr field12 bb::field12< quadratic_field, base_field, Fq12Params >::frobenius_map_three ( ) const

inlineconstexpr

Definition at line 199 of file field12.hpp.

◆ frobenius_map_two()

template<typename quadratic_field , typename base_field , typename Fq12Params >

constexpr field12 bb::field12< quadratic_field, base_field, Fq12Params >::frobenius_map_two ( ) const

inlineconstexpr

Definition at line 207 of file field12.hpp.

◆ from_montgomery_form()

template<typename quadratic_field , typename base_field , typename Fq12Params >

constexpr field12 bb::field12< quadratic_field, base_field, Fq12Params >::from_montgomery_form ( ) const

inlineconstexpr

Definition at line 250 of file field12.hpp.

◆ invert()

template<typename quadratic_field , typename base_field , typename Fq12Params >

constexpr field12 bb::field12< quadratic_field, base_field, Fq12Params >::invert ( ) const

inlineconstexpr

Definition at line 188 of file field12.hpp.

◆ is_zero()

template<typename quadratic_field , typename base_field , typename Fq12Params >

constexpr bool bb::field12< quadratic_field, base_field, Fq12Params >::is_zero ( ) const

inlineconstexpr

Definition at line 258 of file field12.hpp.

◆ mul_by_non_residue()

template<typename quadratic_field , typename base_field , typename Fq12Params >

static constexpr base_field bb::field12< quadratic_field, base_field, Fq12Params >::mul_by_non_residue ( const base_field & a )

inlinestaticconstexpr

Definition at line 59 of file field12.hpp.

◆ one()

template<typename quadratic_field , typename base_field , typename Fq12Params >

static constexpr field12 bb::field12< quadratic_field, base_field, Fq12Params >::one ( )

inlinestaticconstexpr

Definition at line 57 of file field12.hpp.

◆ operator*()

template<typename quadratic_field , typename base_field , typename Fq12Params >

constexpr field12 bb::field12< quadratic_field, base_field, Fq12Params >::operator* ( const field12< quadratic_field, base_field, Fq12Params > & other ) const

inlineconstexpr

Definition at line 86 of file field12.hpp.

◆ operator*=()

template<typename quadratic_field , typename base_field , typename Fq12Params >

constexpr field12 bb::field12< quadratic_field, base_field, Fq12Params >::operator*= ( const field12< quadratic_field, base_field, Fq12Params > & other )

inlineconstexpr

Definition at line 115 of file field12.hpp.

◆ operator+()

template<typename quadratic_field , typename base_field , typename Fq12Params >

constexpr field12 bb::field12< quadratic_field, base_field, Fq12Params >::operator+ ( const field12< quadratic_field, base_field, Fq12Params > & other ) const

inlineconstexpr

Definition at line 68 of file field12.hpp.

◆ operator+=()

template<typename quadratic_field , typename base_field , typename Fq12Params >

constexpr field12 bb::field12< quadratic_field, base_field, Fq12Params >::operator+= ( const field12< quadratic_field, base_field, Fq12Params > & other )

inlineconstexpr

Definition at line 101 of file field12.hpp.

◆ operator-() [1/2]

template<typename quadratic_field , typename base_field , typename Fq12Params >

constexpr field12 bb::field12< quadratic_field, base_field, Fq12Params >::operator- ( ) const

inlineconstexpr

Definition at line 84 of file field12.hpp.

◆ operator-() [2/2]

template<typename quadratic_field , typename base_field , typename Fq12Params >

constexpr field12 bb::field12< quadratic_field, base_field, Fq12Params >::operator- ( const field12< quadratic_field, base_field, Fq12Params > & other ) const

inlineconstexpr

Definition at line 76 of file field12.hpp.

◆ operator-=()

template<typename quadratic_field , typename base_field , typename Fq12Params >

constexpr field12 bb::field12< quadratic_field, base_field, Fq12Params >::operator-= ( const field12< quadratic_field, base_field, Fq12Params > & other )

inlineconstexpr

Definition at line 108 of file field12.hpp.

◆ operator/()

template<typename quadratic_field , typename base_field , typename Fq12Params >

constexpr field12 bb::field12< quadratic_field, base_field, Fq12Params >::operator/ ( const field12< quadratic_field, base_field, Fq12Params > & other ) const

inlineconstexpr

Definition at line 99 of file field12.hpp.

◆ operator/=()

template<typename quadratic_field , typename base_field , typename Fq12Params >

constexpr field12 bb::field12< quadratic_field, base_field, Fq12Params >::operator/= ( const field12< quadratic_field, base_field, Fq12Params > & other )

inlineconstexpr

Definition at line 121 of file field12.hpp.

◆ operator=() [1/2]

template<typename quadratic_field , typename base_field , typename Fq12Params >

constexpr field12 & bb::field12< quadratic_field, base_field, Fq12Params >::operator= ( const field12< quadratic_field, base_field, Fq12Params > & other )

inlineconstexprnoexcept

Definition at line 28 of file field12.hpp.

◆ operator=() [2/2]

template<typename quadratic_field , typename base_field , typename Fq12Params >

constexpr field12 & bb::field12< quadratic_field, base_field, Fq12Params >::operator= ( field12< quadratic_field, base_field, Fq12Params > && other )

inlineconstexprnoexcept

Definition at line 38 of file field12.hpp.

◆ operator==()

template<typename quadratic_field , typename base_field , typename Fq12Params >

constexpr bool bb::field12< quadratic_field, base_field, Fq12Params >::operator== ( const field12< quadratic_field, base_field, Fq12Params > & other ) const

inlineconstexpr

Definition at line 260 of file field12.hpp.

◆ random_element()

template<typename quadratic_field , typename base_field , typename Fq12Params >

static constexpr field12 bb::field12< quadratic_field, base_field, Fq12Params >::random_element ( numeric::RNG * engine = nullptr )

inlinestaticconstexpr

Definition at line 233 of file field12.hpp.

◆ self_neg()

template<typename quadratic_field , typename base_field , typename Fq12Params >

constexpr void bb::field12< quadratic_field, base_field, Fq12Params >::self_neg ( )

inlineconstexpr

Definition at line 127 of file field12.hpp.

◆ self_sparse_mul()

template<typename quadratic_field , typename base_field , typename Fq12Params >

constexpr void bb::field12< quadratic_field, base_field, Fq12Params >::self_sparse_mul ( const ell_coeffs & ell )

inlineconstexpr

Multiply the element by a sparse element of the form ell.o + ell.w * w + ell.vw * wv.

Algorithm 5 from https://cacr.uwaterloo.ca/techreports/2012/cacr2012-17.pdf

Tower structure: Fq12 = Fq6[w]/(w² - v), so an Fq12 element is (c0 + c1·w) with c0, c1 in Fq6. The sparse element is s = (s0 + s1·w) where s0 = {ell.o, 0, 0} and s1 = {ell.w, ell.vw, 0} in Fq6.

Generic multiplication gives: result.c0 = c0·s0 + c1·s1·v (since w² = v) result.c1 = c0·s1 + c1·s0 (cross terms)

We use Karatsuba to compute the cross terms with one fewer Fq6 multiplication: A = c0·s0 (computed directly: s0 = {ell.o,0,0}, so A = {ell.o·c0.c0, ell.o·c0.c1, ell.o·c0.c2}) B = c1·s1 (via field6::sparse_mul, since s1 = {ell.w, ell.vw, 0} = ell.w + ell.vw·v) E = (c0+c1)·(s0+s1) (via field6::sparse_mul, since s0+s1 = {ell.o+ell.w, ell.vw, 0}) F = E - A - B = c0·s1 + c1·s0 (Karatsuba cross term = result.c1) G = v·B (constructed inline as {ξ·B.c2, B.c0, B.c1}, since v·(b0+b1·v+b2·v²) = ξ·b2 + b0·v + b1·v²; uses Fq6::mul_by_non_residue on B.c2 to get ξ·B.c2) H = A + G = c0·s0 + c1·s1·v (= result.c0)

Parameters

ell

Definition at line 158 of file field12.hpp.

◆ self_sqr()

template<typename quadratic_field , typename base_field , typename Fq12Params >

constexpr void bb::field12< quadratic_field, base_field, Fq12Params >::self_sqr ( )

inlineconstexpr

Definition at line 133 of file field12.hpp.

◆ sqr()

template<typename quadratic_field , typename base_field , typename Fq12Params >

constexpr field12 bb::field12< quadratic_field, base_field, Fq12Params >::sqr ( ) const

inlineconstexpr

Definition at line 174 of file field12.hpp.

◆ to_montgomery_form()

template<typename quadratic_field , typename base_field , typename Fq12Params >

constexpr field12 bb::field12< quadratic_field, base_field, Fq12Params >::to_montgomery_form ( )

inlineconstexpr

Definition at line 242 of file field12.hpp.

◆ unitary_inverse()

template<typename quadratic_field , typename base_field , typename Fq12Params >

constexpr field12 bb::field12< quadratic_field, base_field, Fq12Params >::unitary_inverse ( ) const

inlineconstexpr

Definition at line 225 of file field12.hpp.

◆ zero()

template<typename quadratic_field , typename base_field , typename Fq12Params >

static constexpr field12 bb::field12< quadratic_field, base_field, Fq12Params >::zero ( )

inlinestaticconstexpr

Definition at line 56 of file field12.hpp.

Member Data Documentation

◆ c0

template<typename quadratic_field , typename base_field , typename Fq12Params >

base_field bb::field12< quadratic_field, base_field, Fq12Params >::c0

Definition at line 47 of file field12.hpp.

◆ c1

template<typename quadratic_field , typename base_field , typename Fq12Params >

base_field bb::field12< quadratic_field, base_field, Fq12Params >::c1

Definition at line 48 of file field12.hpp.

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

src/barretenberg/ecc/fields/field12.hpp

Classes

Public Member Functions

Static Public Member Functions

Public Attributes

Detailed Description

Constructor & Destructor Documentation

◆ field12() [1/3]

◆ field12() [2/3]

◆ field12() [3/3]

◆ ~field12()

Member Function Documentation

◆ cyclotomic_squared()

◆ frobenius_map_one()

◆ frobenius_map_three()

◆ frobenius_map_two()

◆ from_montgomery_form()

◆ invert()

◆ is_zero()

◆ mul_by_non_residue()

◆ one()

◆ operator*()

◆ operator*=()

◆ operator+()

◆ operator+=()

◆ operator-() [1/2]

◆ operator-() [2/2]

◆ operator-=()

◆ operator/()

◆ operator/=()

◆ operator=() [1/2]

◆ operator=() [2/2]

◆ operator==()

◆ random_element()

◆ self_neg()

◆ self_sparse_mul()

◆ self_sqr()

◆ sqr()

◆ to_montgomery_form()

◆ unitary_inverse()

◆ zero()

Member Data Documentation

◆ c0

◆ c1