libff::Fp3_model< n, modulus > Class Template Reference

#include <fp3.hpp>

Collaboration diagram for libff::Fp3_model< n, modulus >:

Public Types
typedef Fp_model< n, modulus >	my_Fp

Public Member Functions
	Fp3_model ()
	Fp3_model (const my_Fp &c0, const my_Fp &c1, const my_Fp &c2)
void	clear ()
void	print () const
bool	is_zero () const
bool	operator== (const Fp3_model &other) const
bool	operator!= (const Fp3_model &other) const
Fp3_model	operator+ (const Fp3_model &other) const
Fp3_model	operator- (const Fp3_model &other) const
Fp3_model	operator* (const Fp3_model &other) const
Fp3_model	operator- () const
Fp3_model	squared () const
Fp3_model	inverse () const
Fp3_model	Frobenius_map (unsigned long power) const
Fp3_model	sqrt () const
	HAS TO BE A SQUARE (else does not terminate) More...
template<mp_size_t m>
Fp3_model	operator^ (const bigint< m > &other) const

Static Public Member Functions
static Fp3_model< n, modulus >	zero ()
static Fp3_model< n, modulus >	one ()
static Fp3_model< n, modulus >	random_element ()
static size_t	size_in_bits ()
static bigint< n >	base_field_char ()
static constexpr size_t	extension_degree ()

Public Attributes
my_Fp	coeffs [3]

Static Public Attributes
static const size_t	tower_extension_degree = 3
static bigint< 3 *n >	euler
	(modulus^3-1)/2 More...
static size_t	s
	modulus^3 = 2^s * t + 1 More...
static bigint< 3 *n >	t
	with t odd More...
static bigint< 3 *n >	t_minus_1_over_2
	(t-1)/2 More...
static my_Fp	non_residue
static Fp3_model< n, modulus >	nqr
	a quadratic nonresidue in Fp3 More...
static Fp3_model< n, modulus >	nqr_to_t
	nqr^t More...
static my_Fp	Frobenius_coeffs_c1 [3]
	non_residue^((modulus^i-1)/3) for i=0,1,2 More...
static my_Fp	Frobenius_coeffs_c2 [3]
	non_residue^((2*modulus^i-2)/3) for i=0,1,2 More...

Friends
std::ostream &	operator (std::ostream &out, const Fp3_model< n, modulus > &el)
std::istream &	operator>> (std::istream &in, Fp3_model< n, modulus > &el)

Detailed Description

template<mp_size_t n, const bigint< n > & modulus>
class libff::Fp3_model< n, modulus >

Arithmetic in the field F[p^3].

Let p := modulus. This interface provides arithmetic for the extension field Fp3 = Fp[U]/(U^3-non_residue), where non_residue is in Fp.

ASSUMPTION: p = 1 (mod 6)

Definition at line 18 of file fp3.hpp.

Member Typedef Documentation

my_Fp

template<mp_size_t n, const bigint< n > & modulus>

typedef Fp_model<n, modulus> libff::Fp3_model< n, modulus >::my_Fp

Definition at line 35 of file fp3.hpp.

Constructor & Destructor Documentation

Fp3_model() [1/2]

template<mp_size_t n, const bigint< n > & modulus>

libff::Fp3_model< n, modulus >::Fp3_model ( )

inline

Definition at line 60 of file fp3.hpp.

{};

Fp3_model() [2/2]

template<mp_size_t n, const bigint< n > & modulus>

libff::Fp3_model< n, modulus >::Fp3_model ( const my_Fp &  c0, const my_Fp &  c1, const my_Fp &  c2  )

inline

Definition at line 63 of file fp3.hpp.

    {
        this->coeffs[0] = c0;
        this->coeffs[1] = c1;
        this->coeffs[2] = c2;
        return;
    };

Member Function Documentation

base_field_char()

template<mp_size_t n, const bigint< n > & modulus>

static bigint<n> libff::Fp3_model< n, modulus >::base_field_char ( )

inlinestatic

Definition at line 110 of file fp3.hpp.

{ return modulus; }

clear()

template<mp_size_t n, const bigint< n > & modulus>

void libff::Fp3_model< n, modulus >::clear ( )

inline

Definition at line 71 of file fp3.hpp.

    {
        coeffs[0].clear();
        coeffs[1].clear();
        coeffs[2].clear();
    }

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extension_degree()

template<mp_size_t n, const bigint< n > & modulus>

static constexpr size_t libff::Fp3_model< n, modulus >::extension_degree ( )

inlinestaticconstexpr

Definition at line 111 of file fp3.hpp.

{ return 3; }

Frobenius_map()

template<mp_size_t n, const bigint< n > & modulus>

Fp3_model libff::Fp3_model< n, modulus >::Frobenius_map

(

unsigned long

power

)

const

inverse()

template<mp_size_t n, const bigint< n > & modulus>

Fp3_model libff::Fp3_model< n, modulus >::inverse

(

)

const

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is_zero()

template<mp_size_t n, const bigint< n > & modulus>

bool libff::Fp3_model< n, modulus >::is_zero ( ) const

inline

Definition at line 89 of file fp3.hpp.

    {
        return coeffs[0].is_zero() && coeffs[1].is_zero() &&
               coeffs[2].is_zero();
    }

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one()

template<mp_size_t n, const bigint< n > & modulus>

static Fp3_model<n, modulus> libff::Fp3_model< n, modulus >::one ( )

static

operator!=()

template<mp_size_t n, const bigint< n > & modulus>

bool libff::Fp3_model< n, modulus >::operator!=

(

const Fp3_model< n, modulus > &

other

)

const

operator*()

template<mp_size_t n, const bigint< n > & modulus>

Fp3_model libff::Fp3_model< n, modulus >::operator*

(

const Fp3_model< n, modulus > &

other

)

const

operator+()

template<mp_size_t n, const bigint< n > & modulus>

Fp3_model libff::Fp3_model< n, modulus >::operator+

(

const Fp3_model< n, modulus > &

other

)

const

operator-() [1/2]

template<mp_size_t n, const bigint< n > & modulus>

Fp3_model libff::Fp3_model< n, modulus >::operator-

(

)

const

operator-() [2/2]

template<mp_size_t n, const bigint< n > & modulus>

Fp3_model libff::Fp3_model< n, modulus >::operator-

(

const Fp3_model< n, modulus > &

other

)

const

operator==()

template<mp_size_t n, const bigint< n > & modulus>

bool libff::Fp3_model< n, modulus >::operator==

(

const Fp3_model< n, modulus > &

other

)

const

operator^()

template<mp_size_t n, const bigint< n > & modulus>

template<mp_size_t m>

Fp3_model libff::Fp3_model< n, modulus >::operator^

(

const bigint< m > &

other

)

const

print()

template<mp_size_t n, const bigint< n > & modulus>

void libff::Fp3_model< n, modulus >::print ( ) const

inline

Definition at line 77 of file fp3.hpp.

    {
        printf("c0/c1/c2:\n");
        coeffs[0].print();
        coeffs[1].print();
        coeffs[2].print();
    }

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random_element()

template<mp_size_t n, const bigint< n > & modulus>

static Fp3_model<n, modulus> libff::Fp3_model< n, modulus >::random_element ( )

static

size_in_bits()

template<mp_size_t n, const bigint< n > & modulus>

static size_t libff::Fp3_model< n, modulus >::size_in_bits ( )

inlinestatic

Definition at line 109 of file fp3.hpp.

{ return 3 * my_Fp::size_in_bits(); }

sqrt()

template<mp_size_t n, const bigint< n > & modulus>

Fp3_model libff::Fp3_model< n, modulus >::sqrt

(

)

const

HAS TO BE A SQUARE (else does not terminate)

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squared()

template<mp_size_t n, const bigint< n > & modulus>

Fp3_model libff::Fp3_model< n, modulus >::squared

(

)

const

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zero()

template<mp_size_t n, const bigint< n > & modulus>

static Fp3_model<n, modulus> libff::Fp3_model< n, modulus >::zero ( )

static

Friends And Related Function Documentation

operator

template<mp_size_t n, const bigint< n > & modulus>

std::ostream& operator ( std::ostream &  out, const Fp3_model< n, modulus > &  el  )

friend

operator>>

template<mp_size_t n, const bigint< n > & modulus>

std::istream& operator>> ( std::istream &  in, Fp3_model< n, modulus > &  el  )

friend

Member Data Documentation

coeffs

template<mp_size_t n, const bigint< n > & modulus>

my_Fp libff::Fp3_model< n, modulus >::coeffs[3]

Definition at line 59 of file fp3.hpp.

euler

template<mp_size_t n, const bigint< n > & modulus>

bigint< 3 *n > libff::Fp3_model< n, modulus >::euler

static

(modulus^3-1)/2

Definition at line 40 of file fp3.hpp.

Frobenius_coeffs_c1

template<mp_size_t n, const bigint< n > & modulus>

Fp_model< n, modulus > libff::Fp3_model< n, modulus >::Frobenius_coeffs_c1

static

non_residue^((modulus^i-1)/3) for i=0,1,2

Definition at line 55 of file fp3.hpp.

Frobenius_coeffs_c2

template<mp_size_t n, const bigint< n > & modulus>

Fp_model< n, modulus > libff::Fp3_model< n, modulus >::Frobenius_coeffs_c2

static

non_residue^((2*modulus^i-2)/3) for i=0,1,2

Definition at line 57 of file fp3.hpp.

non_residue

template<mp_size_t n, const bigint< n > & modulus>

Fp_model< n, modulus > libff::Fp3_model< n, modulus >::non_residue

static

X^6-non_residue irreducible over Fp; used for constructing aFp3 = Fp[X] / (X^3 - non_residue)

Definition at line 49 of file fp3.hpp.

nqr

template<mp_size_t n, const bigint< n > & modulus>

Fp3_model< n, modulus > libff::Fp3_model< n, modulus >::nqr

static

a quadratic nonresidue in Fp3

Definition at line 51 of file fp3.hpp.

nqr_to_t

template<mp_size_t n, const bigint< n > & modulus>

Fp3_model< n, modulus > libff::Fp3_model< n, modulus >::nqr_to_t

static

nqr^t

Definition at line 53 of file fp3.hpp.

s

template<mp_size_t n, const bigint< n > & modulus>

size_t libff::Fp3_model< n, modulus >::s

static

modulus^3 = 2^s * t + 1

Definition at line 42 of file fp3.hpp.

t

template<mp_size_t n, const bigint< n > & modulus>

bigint< 3 *n > libff::Fp3_model< n, modulus >::t

static

with t odd

Definition at line 44 of file fp3.hpp.

t_minus_1_over_2

template<mp_size_t n, const bigint< n > & modulus>

bigint< 3 *n > libff::Fp3_model< n, modulus >::t_minus_1_over_2

static

(t-1)/2

Definition at line 46 of file fp3.hpp.

tower_extension_degree

template<mp_size_t n, const bigint< n > & modulus>

const size_t libff::Fp3_model< n, modulus >::tower_extension_degree = 3

static

Definition at line 37 of file fp3.hpp.

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

• /home/runner/work/libff/libff/libff/algebra/fields/fp3.hpp