libff::bn128_G2 Class Reference

#include <bn128_g2.hpp>

Collaboration diagram for libff::bn128_G2:

Public Types
typedef bn128_Fq	base_field
typedef bn128_Fr	scalar_field

Public Member Functions
void	fill_coord (bn::Fp2 coord[3]) const
	bn128_G2 ()
	bn128_G2 (bn::Fp2 coord[3])
void	print () const
void	print_coordinates () const
void	to_affine_coordinates ()
void	to_special ()
bool	is_special () const
bool	is_zero () const
bool	operator== (const bn128_G2 &other) const
bool	operator!= (const bn128_G2 &other) const
bn128_G2	operator+ (const bn128_G2 &other) const
bn128_G2	operator- () const
bn128_G2	operator- (const bn128_G2 &other) const
bn128_G2	add (const bn128_G2 &other) const
bn128_G2	mixed_add (const bn128_G2 &other) const
bn128_G2	dbl () const
bool	is_well_formed () const

Static Public Member Functions
static bn128_G2	zero ()
static bn128_G2	one ()
static bn128_G2	random_element ()
static size_t	size_in_bits ()
static bigint< base_field::num_limbs >	base_field_char ()
static bigint< scalar_field::num_limbs >	order ()
static void	batch_to_special_all_non_zeros (std::vector< bn128_G2 > &vec)

Public Attributes
bn::Fp2	X
bn::Fp2	Y
bn::Fp2	Z

Static Public Attributes
static std::vector< size_t >	wnaf_window_table
static std::vector< size_t >	fixed_base_exp_window_table
static bn128_G2	G2_zero = {}
static bn128_G2	G2_one = {}
static bool	initialized = false

Friends
std::ostream &	operator<< (std::ostream &out, const bn128_G2 &g)
std::istream &	operator>> (std::istream &in, bn128_G2 &g)

Detailed Description

Definition at line 24 of file bn128_g2.hpp.

Member Typedef Documentation

base_field

bn128_Fq libff::bn128_G2::base_field

Definition at line 38 of file bn128_g2.hpp.

scalar_field

bn128_Fr libff::bn128_G2::scalar_field

Definition at line 39 of file bn128_g2.hpp.

Constructor & Destructor Documentation

bn128_G2() [1/2]

libff::bn128_G2::bn128_G2

(

)

Definition at line 74 of file bn128_g2.cpp.

{
    if (bn128_G2::initialized)
    {
        this->X = G2_zero.X;
        this->Y = G2_zero.Y;
        this->Z = G2_zero.Z;
    }
}

bn128_G2() [2/2]

libff::bn128_G2::bn128_G2 ( bn::Fp2 coord[3] )

inline

Definition at line 45 of file bn128_g2.hpp.

: X(coord[0]), Y(coord[1]), Z(coord[2]) {};

Member Function Documentation

add()

bn128_G2 libff::bn128_G2::add

(

const bn128_G2 &

other

)

const

Definition at line 224 of file bn128_g2.cpp.

{
#ifdef PROFILE_OP_COUNTS
    this->add_cnt++;
#endif
 
    bn::Fp2 this_coord[3], other_coord[3], result_coord[3];
    this->fill_coord(this_coord);
    other.fill_coord(other_coord);
    bn::ecop::ECAdd(result_coord, this_coord, other_coord);
 
    bn128_G2 result(result_coord);
    return result;
}

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base_field_char()

static bigint< base_field::num_limbs > libff::bn128_G2::base_field_char ( )

inlinestatic

Definition at line 74 of file bn128_g2.hpp.

{ return base_field::field_char(); }

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batch_to_special_all_non_zeros()

void libff::bn128_G2::batch_to_special_all_non_zeros ( std::vector< bn128_G2 > & vec )

static

Definition at line 489 of file bn128_g2.cpp.

{
    std::vector<bn::Fp2> Z_vec;
    Z_vec.reserve(vec.size());
 
    for (auto &el: vec)
    {
        Z_vec.emplace_back(el.Z);
    }
    bn_batch_invert<bn::Fp2>(Z_vec);
 
    const bn::Fp2 one = 1;
 
    for (size_t i = 0; i < vec.size(); ++i)
    {
        bn::Fp2 Z2, Z3;
        bn::Fp2::square(Z2, Z_vec[i]);
        bn::Fp2::mul(Z3, Z2, Z_vec[i]);
 
        bn::Fp2::mul(vec[i].X, vec[i].X, Z2);
        bn::Fp2::mul(vec[i].Y, vec[i].Y, Z3);
        vec[i].Z = one;
    }
}

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dbl()

bn128_G2 libff::bn128_G2::dbl

(

)

const

Definition at line 326 of file bn128_g2.cpp.

{
#ifdef PROFILE_OP_COUNTS
    this->dbl_cnt++;
#endif
 
    bn::Fp2 this_coord[3], result_coord[3];
    this->fill_coord(this_coord);
    bn::ecop::ECDouble(result_coord, this_coord);
 
    bn128_G2 result(result_coord);
    return result;
}

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fill_coord()

void libff::bn128_G2::fill_coord ( bn::Fp2 coord[3] ) const

inline

Definition at line 42 of file bn128_g2.hpp.

{ coord[0] = this->X; coord[1] = this->Y; coord[2] = this->Z; };

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is_special()

bool libff::bn128_G2::is_special

(

)

const

Definition at line 136 of file bn128_g2.cpp.

{
    return (this->is_zero() || this->Z == 1);
}

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is_well_formed()

bool libff::bn128_G2::is_well_formed

(

)

const

Definition at line 340 of file bn128_g2.cpp.

{
    if (this->is_zero())
    {
        return true;
    }
    else
    {
        /*
          y^2 = x^3 + b
 
          We are using Jacobian coordinates, so equation we need to check is actually
 
          (y/z^3)^2 = (x/z^2)^3 + b
          y^2 / z^6 = x^3 / z^6 + b
          y^2 = x^3 + b z^6
        */
        bn::Fp2 X2, Y2, Z2;
        bn::Fp2::square(X2, this->X);
        bn::Fp2::square(Y2, this->Y);
        bn::Fp2::square(Z2, this->Z);
 
        bn::Fp2 X3, Z3, Z6;
        bn::Fp2::mul(X3, X2, this->X);
        bn::Fp2::mul(Z3, Z2, this->Z);
        bn::Fp2::square(Z6, Z3);
 
        return (Y2 == X3 + bn128_twist_coeff_b * Z6);
    }
}

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is_zero()

bool libff::bn128_G2::is_zero

(

)

const

Definition at line 141 of file bn128_g2.cpp.

{
    return Z.isZero();
}

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mixed_add()

bn128_G2 libff::bn128_G2::mixed_add

(

const bn128_G2 &

other

)

const

Definition at line 239 of file bn128_g2.cpp.

{
    if (this->is_zero())
    {
        return other;
    }
 
    if (other.is_zero())
    {
        return *this;
    }
 
    // no need to handle points of order 2,4
    // (they cannot exist in a prime-order subgroup)
 
#ifdef DEBUG
    assert(other.is_special());
#endif
 
    // check for doubling case
 
    // using Jacobian coordinates so:
    // (X1:Y1:Z1) = (X2:Y2:Z2)
    // iff
    // X1/Z1^2 == X2/Z2^2 and Y1/Z1^3 == Y2/Z2^3
    // iff
    // X1 * Z2^2 == X2 * Z1^2 and Y1 * Z2^3 == Y2 * Z1^3
 
    // we know that Z2 = 1
 
    bn::Fp2 Z1Z1;
    bn::Fp2::square(Z1Z1, this->Z);
    const bn::Fp2 &U1 = this->X;
    bn::Fp2 U2;
    bn::Fp2::mul(U2, other.X, Z1Z1);
    bn::Fp2 Z1_cubed;
    bn::Fp2::mul(Z1_cubed, this->Z, Z1Z1);
 
    const bn::Fp2 &S1 = this->Y;
    bn::Fp2 S2;
    bn::Fp2::mul(S2, other.Y, Z1_cubed); // S2 = Y2*Z1*Z1Z1
 
    if (U1 == U2 && S1 == S2)
    {
        // dbl case; nothing of above can be reused
        return this->dbl();
    }
 
#ifdef PROFILE_OP_COUNTS
    this->add_cnt++;
#endif
 
    bn128_G2 result;
    bn::Fp2 H, HH, I, J, r, V, tmp;
    // H = U2-X1
    bn::Fp2::sub(H, U2, this->X);
    // HH = H^2
    bn::Fp2::square(HH, H);
    // I = 4*HH
    bn::Fp2::add(tmp, HH, HH);
    bn::Fp2::add(I, tmp, tmp);
    // J = H*I
    bn::Fp2::mul(J, H, I);
    // r = 2*(S2-Y1)
    bn::Fp2::sub(tmp, S2, this->Y);
    bn::Fp2::add(r, tmp, tmp);
    // V = X1*I
    bn::Fp2::mul(V, this->X, I);
    // X3 = r^2-J-2*V
    bn::Fp2::square(result.X, r);
    bn::Fp2::sub(result.X, result.X, J);
    bn::Fp2::sub(result.X, result.X, V);
    bn::Fp2::sub(result.X, result.X, V);
    // Y3 = r*(V-X3)-2*Y1*J
    bn::Fp2::sub(tmp, V, result.X);
    bn::Fp2::mul(result.Y, r, tmp);
    bn::Fp2::mul(tmp, this->Y, J);
    bn::Fp2::sub(result.Y, result.Y, tmp);
    bn::Fp2::sub(result.Y, result.Y, tmp);
    // Z3 = (Z1+H)^2-Z1Z1-HH
    bn::Fp2::add(tmp, this->Z, H);
    bn::Fp2::square(result.Z, tmp);
    bn::Fp2::sub(result.Z, result.Z, Z1Z1);
    bn::Fp2::sub(result.Z, result.Z, HH);
    return result;
}

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one()

bn128_G2 libff::bn128_G2::one ( )

static

Definition at line 376 of file bn128_g2.cpp.

{
    return G2_one;
}

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operator!=()

bool libff::bn128_G2::operator!=

(

const bn128_G2 &

other

)

const

Definition at line 180 of file bn128_g2.cpp.

{
    return !(operator==(other));
}

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operator+()

bn128_G2 libff::bn128_G2::operator+

(

const bn128_G2 &

other

)

const

Definition at line 185 of file bn128_g2.cpp.

{
    // handle special cases having to do with O
    if (this->is_zero())
    {
        return other;
    }
 
    if (other.is_zero())
    {
        return *this;
    }
 
    // no need to handle points of order 2,4
    // (they cannot exist in a prime-order subgroup)
 
    // handle double case, and then all the rest
    if (this->operator==(other))
    {
        return this->dbl();
    }
    else
    {
        return this->add(other);
    }
}

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operator-() [1/2]

bn128_G2 libff::bn128_G2::operator-

(

)

const

Definition at line 212 of file bn128_g2.cpp.

{
    bn128_G2 result(*this);
    bn::Fp2::neg(result.Y, result.Y);
    return result;
}

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operator-() [2/2]

bn128_G2 libff::bn128_G2::operator-

(

const bn128_G2 &

other

)

const

Definition at line 219 of file bn128_g2.cpp.

{
    return (*this) + (-other);
}

operator==()

bool libff::bn128_G2::operator==

(

const bn128_G2 &

other

)

const

Definition at line 146 of file bn128_g2.cpp.

{
    if (this->is_zero())
    {
        return other.is_zero();
    }
 
    if (other.is_zero())
    {
        return false;
    }
 
    /* now neither is O */
 
    bn::Fp2 Z1sq, Z2sq, lhs, rhs;
    bn::Fp2::square(Z1sq, this->Z);
    bn::Fp2::square(Z2sq, other.Z);
    bn::Fp2::mul(lhs, Z2sq, this->X);
    bn::Fp2::mul(rhs, Z1sq, other.X);
 
    if (lhs != rhs)
    {
        return false;
    }
 
    bn::Fp2 Z1cubed, Z2cubed;
    bn::Fp2::mul(Z1cubed, Z1sq, this->Z);
    bn::Fp2::mul(Z2cubed, Z2sq, other.Z);
    bn::Fp2::mul(lhs, Z2cubed, this->Y);
    bn::Fp2::mul(rhs, Z1cubed, other.Y);
 
    return (lhs == rhs);
}

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order()

static bigint< scalar_field::num_limbs > libff::bn128_G2::order ( )

inlinestatic

Definition at line 75 of file bn128_g2.hpp.

{ return scalar_field::field_char(); }

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print()

void libff::bn128_G2::print

(

)

const

Definition at line 84 of file bn128_g2.cpp.

{
    if (this->is_zero())
    {
        printf("O\n");
    }
    else
    {
        bn128_G2 copy(*this);
        copy.to_affine_coordinates();
        std::cout << "(" << copy.X.toString(10) << " : " << copy.Y.toString(10) << " : " << copy.Z.toString(10) << ")\n";
    }
}

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print_coordinates()

void libff::bn128_G2::print_coordinates

(

)

const

Definition at line 98 of file bn128_g2.cpp.

{
    if (this->is_zero())
    {
        printf("O\n");
    }
    else
    {
        std::cout << "(" << X.toString(10) << " : " << Y.toString(10) << " : " << Z.toString(10) << ")\n";
    }
}

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random_element()

bn128_G2 libff::bn128_G2::random_element ( )

static

Definition at line 381 of file bn128_g2.cpp.

{
    return bn128_Fr::random_element().as_bigint() * G2_one;
}

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size_in_bits()

static size_t libff::bn128_G2::size_in_bits ( )

inlinestatic

Definition at line 73 of file bn128_g2.hpp.

{ return 2*base_field::size_in_bits() + 1; }

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to_affine_coordinates()

void libff::bn128_G2::to_affine_coordinates

(

)

Definition at line 110 of file bn128_g2.cpp.

{
    if (this->is_zero())
    {
        X = 0;
        Y = 1;
        Z = 0;
    }
    else
    {
        bn::Fp2 r;
        r = Z;
        r.inverse();
        bn::Fp2::square(Z, r);
        X *= Z;
        r *= Z;
        Y *= r;
        Z = 1;
    }
}

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to_special()

void libff::bn128_G2::to_special

(

)

Definition at line 131 of file bn128_g2.cpp.

{
    this->to_affine_coordinates();
}

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zero()

bn128_G2 libff::bn128_G2::zero ( )

static

Definition at line 371 of file bn128_g2.cpp.

{
    return G2_zero;
}

Friends And Related Symbol Documentation

operator<<

std::ostream & operator<< ( std::ostream & out, const bn128_G2 & g )

friend

Definition at line 386 of file bn128_g2.cpp.

{
    bn128_G2 gcopy(g);
    gcopy.to_affine_coordinates();
 
    out << (gcopy.is_zero() ? '1' : '0') << OUTPUT_SEPARATOR;
 
#ifdef NO_PT_COMPRESSION
    /* no point compression case */
#ifndef BINARY_OUTPUT
    out << gcopy.X.a_ << OUTPUT_SEPARATOR << gcopy.X.b_ << OUTPUT_SEPARATOR;
    out << gcopy.Y.a_ << OUTPUT_SEPARATOR << gcopy.Y.b_;
#else
    out.write((char*) &gcopy.X.a_, sizeof(gcopy.X.a_));
    out.write((char*) &gcopy.X.b_, sizeof(gcopy.X.b_));
    out.write((char*) &gcopy.Y.a_, sizeof(gcopy.Y.a_));
    out.write((char*) &gcopy.Y.b_, sizeof(gcopy.Y.b_));
#endif
 
#else
    /* point compression case */
#ifndef BINARY_OUTPUT
    out << gcopy.X.a_ << OUTPUT_SEPARATOR << gcopy.X.b_;
#else
    out.write((char*) &gcopy.X.a_, sizeof(gcopy.X.a_));
    out.write((char*) &gcopy.X.b_, sizeof(gcopy.X.b_));
#endif
    out << OUTPUT_SEPARATOR << (((unsigned char*)&gcopy.Y.a_)[0] & 1 ? '1' : '0');
#endif
 
    return out;
}

operator>>

std::istream & operator>> ( std::istream & in, bn128_G2 & g )

friend

Definition at line 419 of file bn128_g2.cpp.

{
    char is_zero;
    in.read((char*)&is_zero, 1); // this reads is_zero;
    is_zero -= '0';
    consume_OUTPUT_SEPARATOR(in);
 
#ifdef NO_PT_COMPRESSION
    /* no point compression case */
#ifndef BINARY_OUTPUT
    in >> g.X.a_;
    consume_OUTPUT_SEPARATOR(in);
    in >> g.X.b_;
    consume_OUTPUT_SEPARATOR(in);
    in >> g.Y.a_;
    consume_OUTPUT_SEPARATOR(in);
    in >> g.Y.b_;
#else
    in.read((char*) &g.X.a_, sizeof(g.X.a_));
    in.read((char*) &g.X.b_, sizeof(g.X.b_));
    in.read((char*) &g.Y.a_, sizeof(g.Y.a_));
    in.read((char*) &g.Y.b_, sizeof(g.Y.b_));
#endif
 
#else
    /* point compression case */
    bn::Fp2 tX;
#ifndef BINARY_OUTPUT
    in >> tX.a_;
    consume_OUTPUT_SEPARATOR(in);
    in >> tX.b_;
#else
    in.read((char*)&tX.a_, sizeof(tX.a_));
    in.read((char*)&tX.b_, sizeof(tX.b_));
#endif
    consume_OUTPUT_SEPARATOR(in);
    unsigned char Y_lsb;
    in.read((char*)&Y_lsb, 1);
    Y_lsb -= '0';
 
    // y = +/- sqrt(x^3 + b)
    if (!is_zero)
    {
        g.X = tX;
        bn::Fp2 tX2, tY2;
        bn::Fp2::square(tX2, tX);
        bn::Fp2::mul(tY2, tX2, tX);
        bn::Fp2::add(tY2, tY2, bn128_twist_coeff_b);
 
        g.Y = bn128_G2::sqrt(tY2);
        if ((((unsigned char*)&g.Y.a_)[0] & 1) != Y_lsb)
        {
            bn::Fp2::neg(g.Y, g.Y);
        }
    }
#endif
 
    /* finalize */
    if (!is_zero)
    {
        g.Z = bn::Fp2(bn::Fp(1), bn::Fp(0));
    }
    else
    {
        g = bn128_G2::zero();
    }
 
    return in;
}

Member Data Documentation

fixed_base_exp_window_table

std::vector< size_t > libff::bn128_G2::fixed_base_exp_window_table

static

Definition at line 33 of file bn128_g2.hpp.

G2_one

bn128_G2 libff::bn128_G2::G2_one = {}

static

Definition at line 35 of file bn128_g2.hpp.

G2_zero

bn128_G2 libff::bn128_G2::G2_zero = {}

static

Definition at line 34 of file bn128_g2.hpp.

initialized

bool libff::bn128_G2::initialized = false

static

Definition at line 36 of file bn128_g2.hpp.

wnaf_window_table

std::vector< size_t > libff::bn128_G2::wnaf_window_table

static

Definition at line 32 of file bn128_g2.hpp.

X

bn::Fp2 libff::bn128_G2::X

Definition at line 41 of file bn128_g2.hpp.

Y

bn::Fp2 libff::bn128_G2::Y

Definition at line 41 of file bn128_g2.hpp.

Z

bn::Fp2 libff::bn128_G2::Z

Definition at line 41 of file bn128_g2.hpp.

---

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

• libraries/fc/libraries/ff/libff/algebra/curves/bn128/bn128_g2.hpp
• libraries/fc/libraries/ff/libff/algebra/curves/bn128/bn128_g2.cpp