#include <fp2.hpp>

Collaboration diagram for libff::Fp2_model< n, modulus >:

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Public Types
typedef Fp_model< n, modulus >	my_Fp

Public Member Functions
	Fp2_model ()

	Fp2_model (const my_Fp &c0, const my_Fp &c1)

void	clear ()

void	print () const

bool	is_zero () const

bool	operator== (const Fp2_model &other) const

bool	operator!= (const Fp2_model &other) const

Fp2_model	operator+ (const Fp2_model &other) const

Fp2_model	operator- (const Fp2_model &other) const

Fp2_model	operator* (const Fp2_model &other) const

Fp2_model	operator- () const

Fp2_model	squared () const

Fp2_model	inverse () const

Fp2_model	Frobenius_map (unsigned long power) const

Fp2_model	sqrt () const

Fp2_model	squared_karatsuba () const

Fp2_model	squared_complex () const

template<mp_size_t m>
Fp2_model	operator^ (const bigint< m > &other) const

Static Public Member Functions
static Fp2_model< n, modulus >	zero ()

static Fp2_model< n, modulus >	one ()

static Fp2_model< n, modulus >	random_element ()

static size_t	size_in_bits ()

static bigint< n >	base_field_char ()

Public Attributes
my_Fp	c0

my_Fp	c1

Static Public Attributes
static bigint< 2 *n >	euler

static size_t	s

static bigint< 2 *n >	t

static bigint< 2 *n >	t_minus_1_over_2

static my_Fp	non_residue

static Fp2_model< n, modulus >	nqr

static Fp2_model< n, modulus >	nqr_to_t

static my_Fp	Frobenius_coeffs_c1 [2]

Friends
std::ostream &	operator (std::ostream &out, const Fp2_model< n, modulus > &el)

std::istream &	operator>> (std::istream &in, Fp2_model< n, modulus > &el)

Detailed Description

template<mp_size_t n, const bigint< n > & modulus>
class libff::Fp2_model< n, modulus >

Arithmetic in the field F[p^2].

Let p := modulus. This interface provides arithmetic for the extension field Fp2 = Fp[U]/(U^2-non_residue), where non_residue is in Fp.

ASSUMPTION: p = 1 (mod 6)

Definition at line 36 of file fp2.hpp.

Member Typedef Documentation

◆ my_Fp

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

Fp_model<n, modulus> libff::Fp2_model< n, modulus >::my_Fp

Definition at line 38 of file fp2.hpp.

Constructor & Destructor Documentation

◆ Fp2_model() [1/2]

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

libff::Fp2_model< n, modulus >::Fp2_model ( )

inline

Definition at line 50 of file fp2.hpp.

50{};

◆ Fp2_model() [2/2]

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

libff::Fp2_model< n, modulus >::Fp2_model	(	const my_Fp &	c0,
		const my_Fp &	c1 )

inline

Definition at line 51 of file fp2.hpp.

51: c0(c0), c1(c1) {};

libff::Fp2_model::c0

my_Fp c0

Definition fp2.hpp:49

libff::Fp2_model::c1

my_Fp c1

Definition fp2.hpp:49

Member Function Documentation

◆ base_field_char()

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

static bigint< n > libff::Fp2_model< n, modulus >::base_field_char ( )

inlinestatic

Definition at line 79 of file fp2.hpp.

79{ return modulus; }

◆ clear()

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

void libff::Fp2_model< n, modulus >::clear ( )

inline

Definition at line 53 of file fp2.hpp.

53{ c0.clear(); c1.clear(); }

libff::Fp_model::clear

void clear()

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◆ Frobenius_map()

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

Fp2_model libff::Fp2_model< n, modulus >::Frobenius_map ( unsigned long power ) const

◆ inverse()

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

Fp2_model libff::Fp2_model< n, modulus >::inverse ( ) const

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◆ is_zero()

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

bool libff::Fp2_model< n, modulus >::is_zero ( ) const

inline

Definition at line 60 of file fp2.hpp.

60{ return c0.is_zero() && c1.is_zero(); }

libff::Fp_model::is_zero

bool is_zero() const

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◆ one()

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

static Fp2_model< n, modulus > libff::Fp2_model< n, modulus >::one ( )

static

◆ operator!=()

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

bool libff::Fp2_model< n, modulus >::operator!= ( const Fp2_model< n, modulus > & other ) const

◆ operator*()

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

Fp2_model libff::Fp2_model< n, modulus >::operator* ( const Fp2_model< n, modulus > & other ) const

◆ operator+()

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

Fp2_model libff::Fp2_model< n, modulus >::operator+ ( const Fp2_model< n, modulus > & other ) const

◆ operator-() [1/2]

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

Fp2_model libff::Fp2_model< n, modulus >::operator- ( ) const

◆ operator-() [2/2]

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

Fp2_model libff::Fp2_model< n, modulus >::operator- ( const Fp2_model< n, modulus > & other ) const

◆ operator==()

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

bool libff::Fp2_model< n, modulus >::operator== ( const Fp2_model< n, modulus > & other ) const

◆ operator^()

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

template<mp_size_t m>

Fp2_model libff::Fp2_model< n, modulus >::operator^ ( const bigint< m > & other ) const

◆ print()

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

void libff::Fp2_model< n, modulus >::print ( ) const

inline

Definition at line 54 of file fp2.hpp.

54{ printf("c0/c1:\n"); c0.print(); c1.print(); }

libff::Fp_model::print

void print() const

Log::printf

LOGGING_API void printf(Category category, const char *format,...)

Definition Logging.cpp:30

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◆ random_element()

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

static Fp2_model< n, modulus > libff::Fp2_model< n, modulus >::random_element ( )

static

◆ size_in_bits()

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

static size_t libff::Fp2_model< n, modulus >::size_in_bits ( )

inlinestatic

Definition at line 78 of file fp2.hpp.

78{ return 2*my_Fp::size_in_bits(); }

libff::Fp_model::size_in_bits

static size_t size_in_bits()

Definition fp.hpp:114

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◆ sqrt()

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

Fp2_model libff::Fp2_model< n, modulus >::sqrt ( ) const

◆ squared()

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

Fp2_model libff::Fp2_model< n, modulus >::squared ( ) const

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◆ squared_complex()

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

Fp2_model libff::Fp2_model< n, modulus >::squared_complex ( ) const

◆ squared_karatsuba()

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

Fp2_model libff::Fp2_model< n, modulus >::squared_karatsuba ( ) const

◆ zero()

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

static Fp2_model< n, modulus > libff::Fp2_model< n, modulus >::zero ( )

static

Friends And Related Symbol Documentation

◆ operator

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

std::ostream & operator	(	std::ostream &	out,
		const Fp2_model< n, modulus > &	el )

friend

◆ operator>>

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

std::istream & operator>>	(	std::istream &	in,
		Fp2_model< n, modulus > &	el )

friend

Member Data Documentation

◆ c0

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

my_Fp libff::Fp2_model< n, modulus >::c0

Definition at line 49 of file fp2.hpp.

◆ c1

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

my_Fp libff::Fp2_model< n, modulus >::c1

Definition at line 49 of file fp2.hpp.

◆ euler

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

bigint< 2 *n > libff::Fp2_model< n, modulus >::euler

static

Definition at line 40 of file fp2.hpp.

◆ Frobenius_coeffs_c1

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

Fp_model< n, modulus > libff::Fp2_model< n, modulus >::Frobenius_coeffs_c1

static

Definition at line 47 of file fp2.hpp.

◆ non_residue

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

Fp_model< n, modulus > libff::Fp2_model< n, modulus >::non_residue

static

Definition at line 44 of file fp2.hpp.

◆ nqr

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

Fp2_model< n, modulus > libff::Fp2_model< n, modulus >::nqr

static

Definition at line 45 of file fp2.hpp.

◆ nqr_to_t

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

Fp2_model< n, modulus > libff::Fp2_model< n, modulus >::nqr_to_t

static

Definition at line 46 of file fp2.hpp.

◆ s

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

size_t libff::Fp2_model< n, modulus >::s

static

Definition at line 41 of file fp2.hpp.

◆ t

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

bigint< 2 *n > libff::Fp2_model< n, modulus >::t

static

Definition at line 42 of file fp2.hpp.

◆ t_minus_1_over_2

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

bigint< 2 *n > libff::Fp2_model< n, modulus >::t_minus_1_over_2

static

Definition at line 43 of file fp2.hpp.

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

libraries/fc/libraries/ff/libff/algebra/fields/fp2.hpp

Public Types

Public Member Functions

Static Public Member Functions

Public Attributes

Static Public Attributes

Friends

Detailed Description

Member Typedef Documentation

◆ my_Fp

Constructor & Destructor Documentation

◆ Fp2_model() [1/2]

◆ Fp2_model() [2/2]

Member Function Documentation

◆ base_field_char()

◆ clear()

◆ Frobenius_map()

◆ inverse()

◆ is_zero()

◆ one()

◆ operator!=()

◆ operator*()

◆ operator+()

◆ operator-() [1/2]

◆ operator-() [2/2]

◆ operator==()

◆ operator^()

◆ print()

◆ random_element()

◆ size_in_bits()

◆ sqrt()

◆ squared()

◆ squared_complex()

◆ squared_karatsuba()

◆ zero()

Friends And Related Symbol Documentation

◆ operator

◆ operator>>

Member Data Documentation

◆ c0

◆ c1

◆ euler

◆ Frobenius_coeffs_c1

◆ non_residue

◆ nqr

◆ nqr_to_t

◆ s

◆ t

◆ t_minus_1_over_2