libff::edwards_G1 Class Reference

#include <edwards_g1.hpp>

Collaboration diagram for libff::edwards_G1:

Public Types
typedef edwards_Fq	base_field
typedef edwards_Fr	scalar_field

Public Member Functions
	edwards_G1 ()
	edwards_G1 (const edwards_Fq &X, const edwards_Fq &Y)
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 edwards_G1 &other) const
bool	operator!= (const edwards_G1 &other) const
edwards_G1	operator+ (const edwards_G1 &other) const
edwards_G1	operator- () const
edwards_G1	operator- (const edwards_G1 &other) const
edwards_G1	add (const edwards_G1 &other) const
edwards_G1	mixed_add (const edwards_G1 &other) const
edwards_G1	dbl () const
bool	is_well_formed () const

Static Public Member Functions
static edwards_G1	zero ()
static edwards_G1	one ()
static edwards_G1	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< edwards_G1 > &vec)

Public Attributes
edwards_Fq	X
edwards_Fq	Y
edwards_Fq	Z

Static Public Attributes
static std::vector< size_t >	wnaf_window_table
static std::vector< size_t >	fixed_base_exp_window_table
static edwards_G1	G1_zero = {}
static edwards_G1	G1_one = {}
static bool	initialized = false

Friends
std::ostream &	operator<< (std::ostream &out, const edwards_G1 &g)
std::istream &	operator>> (std::istream &in, edwards_G1 &g)

Detailed Description

Definition at line 21 of file edwards_g1.hpp.

Member Typedef Documentation

base_field

edwards_Fq libff::edwards_G1::base_field

Definition at line 39 of file edwards_g1.hpp.

scalar_field

edwards_Fr libff::edwards_G1::scalar_field

Definition at line 40 of file edwards_g1.hpp.

Constructor & Destructor Documentation

edwards_G1() [1/2]

libff::edwards_G1::edwards_G1

(

)

Definition at line 23 of file edwards_g1.cpp.

{
    if (initialized)
    {
        this->X = G1_zero.X;
        this->Y = G1_zero.Y;
        this->Z = G1_zero.Z;
    }
}

Here is the caller graph for this function:

edwards_G1() [2/2]

libff::edwards_G1::edwards_G1 ( const edwards_Fq & X, const edwards_Fq & Y )

inline

Definition at line 42 of file edwards_g1.hpp.

: X(Y), Y(X), Z(X*Y) {};

Member Function Documentation

add()

edwards_G1 libff::edwards_G1::add

(

const edwards_G1 &

other

)

const

Definition at line 178 of file edwards_g1.cpp.

{
#ifdef PROFILE_OP_COUNTS
    this->add_cnt++;
#endif
    // NOTE: does not handle O and pts of order 2,4
    // http://www.hyperelliptic.org/EFD/g1p/auto-edwards-inverted.html#addition-add-2007-bl
 
    edwards_Fq A = (this->Z) * (other.Z);                   // A = Z1*Z2
    edwards_Fq B = edwards_coeff_d * A.squared();           // B = d*A^2
    edwards_Fq C = (this->X) * (other.X);                   // C = X1*X2
    edwards_Fq D = (this->Y) * (other.Y);                   // D = Y1*Y2
    edwards_Fq E = C * D;                                   // E = C*D
    edwards_Fq H = C - D;                                   // H = C-D
    edwards_Fq I = (this->X+this->Y)*(other.X+other.Y)-C-D; // I = (X1+Y1)*(X2+Y2)-C-D
    edwards_Fq X3 = (E+B)*H;                                // X3 = c*(E+B)*H
    edwards_Fq Y3 = (E-B)*I;                                // Y3 = c*(E-B)*I
    edwards_Fq Z3 = A*H*I;                                  // Z3 = A*H*I
 
    return edwards_G1(X3, Y3, Z3);
}

Here is the call graph for this function:

Here is the caller graph for this function:

base_field_char()

static bigint< base_field::num_limbs > libff::edwards_G1::base_field_char ( )

inlinestatic

Definition at line 71 of file edwards_g1.hpp.

{ return base_field::field_char(); }

Here is the call graph for this function:

batch_to_special_all_non_zeros()

void libff::edwards_G1::batch_to_special_all_non_zeros ( std::vector< edwards_G1 > & vec )

static

Definition at line 395 of file edwards_g1.cpp.

{
    std::vector<edwards_Fq> Z_vec;
    Z_vec.reserve(vec.size());
 
    for (auto &el: vec)
    {
        Z_vec.emplace_back(el.Z);
    }
    batch_invert<edwards_Fq>(Z_vec);
 
    const edwards_Fq one = edwards_Fq::one();
 
    for (size_t i = 0; i < vec.size(); ++i)
    {
        vec[i].X = vec[i].X * Z_vec[i];
        vec[i].Y = vec[i].Y * Z_vec[i];
        vec[i].Z = one;
    }
}

Here is the call graph for this function:

dbl()

edwards_G1 libff::edwards_G1::dbl

(

)

const

Definition at line 237 of file edwards_g1.cpp.

{
#ifdef PROFILE_OP_COUNTS
    this->dbl_cnt++;
#endif
    if (this->is_zero())
    {
        return (*this);
    }
    else
    {
        // NOTE: does not handle O and pts of order 2,4
        // http://www.hyperelliptic.org/EFD/g1p/auto-edwards-inverted.html#doubling-dbl-2007-bl
 
        edwards_Fq A = (this->X).squared();                      // A = X1^2
        edwards_Fq B = (this->Y).squared();                      // B = Y1^2
        edwards_Fq C = A+B;                                      // C = A+B
        edwards_Fq D = A-B;                                      // D = A-B
        edwards_Fq E = (this->X+this->Y).squared()-C;            // E = (X1+Y1)^2-C
        edwards_Fq X3 = C*D;                                     // X3 = C*D
        edwards_Fq dZZ = edwards_coeff_d * this->Z.squared();
        edwards_Fq Y3 = E*(C-dZZ-dZZ);                           // Y3 = E*(C-2*d*Z1^2)
        edwards_Fq Z3 = D*E;                                     // Z3 = D*E
 
        return edwards_G1(X3, Y3, Z3);
    }
}

Here is the call graph for this function:

is_special()

bool libff::edwards_G1::is_special

(

)

const

Definition at line 107 of file edwards_g1.cpp.

{
    return (this->is_zero() || this->Z == edwards_Fq::one());
}

Here is the call graph for this function:

is_well_formed()

bool libff::edwards_G1::is_well_formed

(

)

const

Definition at line 265 of file edwards_g1.cpp.

{
    /* Note that point at infinity is the only special case we must check as
       inverted representation does no cover points (0, +-c) and (+-c, 0). */
    if (this->is_zero())
    {
        return true;
    }
    else
    {
        /*
          a x^2 + y^2 = 1 + d x^2 y^2
 
          We are using inverted, so equation we need to check is actually
 
          a (z/x)^2 + (z/y)^2 = 1 + d z^4 / (x^2 * y^2)
          z^2 (a y^2 + x^2 - dz^2) = x^2 y^2
        */
        edwards_Fq X2 = this->X.squared();
        edwards_Fq Y2 = this->Y.squared();
        edwards_Fq Z2 = this->Z.squared();
 
        // for G1 a = 1
        return (Z2 * (Y2 + X2 - edwards_coeff_d * Z2) == X2 * Y2);
    }
}

Here is the call graph for this function:

is_zero()

bool libff::edwards_G1::is_zero

(

)

const

Definition at line 112 of file edwards_g1.cpp.

{
    return (this->Y.is_zero() && this->Z.is_zero());
}

Here is the call graph for this function:

Here is the caller graph for this function:

mixed_add()

edwards_G1 libff::edwards_G1::mixed_add

(

const edwards_G1 &

other

)

const

Definition at line 200 of file edwards_g1.cpp.

{
#ifdef PROFILE_OP_COUNTS
    this->add_cnt++;
#endif
    // handle special cases having to do with O
    if (this->is_zero())
    {
        return other;
    }
 
    if (other.is_zero())
    {
        return *this;
    }
 
#ifdef DEBUG
    assert(other.is_special());
#endif
 
    // NOTE: does not handle O and pts of order 2,4
    // http://www.hyperelliptic.org/EFD/g1p/auto-edwards-inverted.html#addition-madd-2007-lb
 
    edwards_Fq A = this->Z;                                 // A = Z1
    edwards_Fq B = edwards_coeff_d * A.squared();           // B = d*A^2
    edwards_Fq C = (this->X) * (other.X);                   // C = X1*X2
    edwards_Fq D = (this->Y) * (other.Y);                   // D = Y1*Y2
    edwards_Fq E = C * D;                                   // E = C*D
    edwards_Fq H = C - D;                                   // H = C-D
    edwards_Fq I = (this->X+this->Y)*(other.X+other.Y)-C-D; // I = (X1+Y1)*(X2+Y2)-C-D
    edwards_Fq X3 = (E+B)*H;                                // X3 = c*(E+B)*H
    edwards_Fq Y3 = (E-B)*I;                                // Y3 = c*(E-B)*I
    edwards_Fq Z3 = A*H*I;                                  // Z3 = A*H*I
 
    return edwards_G1(X3, Y3, Z3);
}

Here is the call graph for this function:

one()

edwards_G1 libff::edwards_G1::one ( )

static

Definition at line 297 of file edwards_g1.cpp.

{
    return G1_one;
}

Here is the caller graph for this function:

operator!=()

bool libff::edwards_G1::operator!=

(

const edwards_G1 &

other

)

const

Definition at line 146 of file edwards_g1.cpp.

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

Here is the call graph for this function:

operator+()

edwards_G1 libff::edwards_G1::operator+

(

const edwards_G1 &

other

)

const

Definition at line 151 of file edwards_g1.cpp.

{
    // handle special cases having to do with O
    if (this->is_zero())
    {
        return other;
    }
 
    if (other.is_zero())
    {
        return (*this);
    }
 
    return this->add(other);
}

Here is the call graph for this function:

operator-() [1/2]

edwards_G1 libff::edwards_G1::operator-

(

)

const

Definition at line 167 of file edwards_g1.cpp.

{
    return edwards_G1(-(this->X), this->Y, this->Z);
}

Here is the call graph for this function:

operator-() [2/2]

edwards_G1 libff::edwards_G1::operator-

(

const edwards_G1 &

other

)

const

Definition at line 173 of file edwards_g1.cpp.

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

operator==()

bool libff::edwards_G1::operator==

(

const edwards_G1 &

other

)

const

Definition at line 117 of file edwards_g1.cpp.

{
    if (this->is_zero())
    {
        return other.is_zero();
    }
 
    if (other.is_zero())
    {
        return false;
    }
 
    /* now neither is O */
 
    // X1/Z1 = X2/Z2 <=> X1*Z2 = X2*Z1
    if ((this->X * other.Z) != (other.X * this->Z))
    {
        return false;
    }
 
    // Y1/Z1 = Y2/Z2 <=> Y1*Z2 = Y2*Z1
    if ((this->Y * other.Z) != (other.Y * this->Z))
    {
        return false;
    }
 
    return true;
}

Here is the call graph for this function:

Here is the caller graph for this function:

order()

static bigint< scalar_field::num_limbs > libff::edwards_G1::order ( )

inlinestatic

Definition at line 72 of file edwards_g1.hpp.

{ return scalar_field::field_char(); }

Here is the call graph for this function:

print()

void libff::edwards_G1::print

(

)

const

Definition at line 33 of file edwards_g1.cpp.

{
    if (this->is_zero())
    {
        printf("O\n");
    }
    else
    {
        edwards_G1 copy(*this);
        copy.to_affine_coordinates();
        gmp_printf("(%Nd , %Nd)\n",
                   copy.X.as_bigint().data, edwards_Fq::num_limbs,
                   copy.Y.as_bigint().data, edwards_Fq::num_limbs);
    }
}

Here is the call graph for this function:

print_coordinates()

void libff::edwards_G1::print_coordinates

(

)

const

Definition at line 49 of file edwards_g1.cpp.

{
    if (this->is_zero())
    {
        printf("O\n");
    }
    else
    {
        gmp_printf("(%Nd : %Nd : %Nd)\n",
                   this->X.as_bigint().data, edwards_Fq::num_limbs,
                   this->Y.as_bigint().data, edwards_Fq::num_limbs,
                   this->Z.as_bigint().data, edwards_Fq::num_limbs);
    }
}

Here is the call graph for this function:

random_element()

edwards_G1 libff::edwards_G1::random_element ( )

static

Definition at line 302 of file edwards_g1.cpp.

{
    return edwards_Fr::random_element().as_bigint() * G1_one;
}

Here is the call graph for this function:

size_in_bits()

static size_t libff::edwards_G1::size_in_bits ( )

inlinestatic

Definition at line 70 of file edwards_g1.hpp.

{ return edwards_Fq::size_in_bits() + 1; }

Here is the call graph for this function:

to_affine_coordinates()

void libff::edwards_G1::to_affine_coordinates

(

)

Definition at line 64 of file edwards_g1.cpp.

{
    if (this->is_zero())
    {
        this->X = edwards_Fq::zero();
        this->Y = edwards_Fq::one();
        this->Z = edwards_Fq::one();
    }
    else
    {
        // go from inverted coordinates to projective coordinates
        edwards_Fq tX = this->Y * this->Z;
        edwards_Fq tY = this->X * this->Z;
        edwards_Fq tZ = this->X * this->Y;
        // go from projective coordinates to affine coordinates
        edwards_Fq tZ_inv = tZ.inverse();
        this->X = tX * tZ_inv;
        this->Y = tY * tZ_inv;
        this->Z = edwards_Fq::one();
    }
}

Here is the call graph for this function:

Here is the caller graph for this function:

to_special()

void libff::edwards_G1::to_special

(

)

Definition at line 86 of file edwards_g1.cpp.

{
    if (this->Z.is_zero())
    {
        return;
    }
 
#ifdef DEBUG
    const edwards_G1 copy(*this);
#endif
 
    edwards_Fq Z_inv = this->Z.inverse();
    this->X = this->X * Z_inv;
    this->Y = this->Y * Z_inv;
    this->Z = edwards_Fq::one();
 
#ifdef DEBUG
    assert((*this) == copy);
#endif
}

Here is the call graph for this function:

zero()

edwards_G1 libff::edwards_G1::zero ( )

static

Definition at line 292 of file edwards_g1.cpp.

{
    return G1_zero;
}

Friends And Related Symbol Documentation

operator<<

std::ostream & operator<< ( std::ostream & out, const edwards_G1 & g )

friend

Definition at line 307 of file edwards_g1.cpp.

{
    edwards_G1 copy(g);
    copy.to_affine_coordinates();
#ifdef NO_PT_COMPRESSION
    out << copy.X << OUTPUT_SEPARATOR << copy.Y;
#else
    /* storing LSB of Y */
    out << copy.X << OUTPUT_SEPARATOR << (copy.Y.as_bigint().data[0] & 1);
#endif
 
    return out;
}

operator>>

std::istream & operator>> ( std::istream & in, edwards_G1 & g )

friend

Definition at line 321 of file edwards_g1.cpp.

{
    edwards_Fq tX, tY;
 
#ifdef NO_PT_COMPRESSION
    in >> tX;
    consume_OUTPUT_SEPARATOR(in);
    in >> tY;
#else
    /*
      a x^2 + y^2 = 1 + d x^2 y^2
      y = sqrt((1-ax^2)/(1-dx^2))
    */
    unsigned char Y_lsb;
    in >> tX;
 
    consume_OUTPUT_SEPARATOR(in);
    in.read((char*)&Y_lsb, 1);
    Y_lsb -= '0';
 
    edwards_Fq tX2 = tX.squared();
    edwards_Fq tY2 = (edwards_Fq::one() - tX2) * // a = 1 for G1 (not a twist)
        (edwards_Fq::one() - edwards_coeff_d * tX2).inverse();
    tY = tY2.sqrt();
 
    if ((tY.as_bigint().data[0] & 1) != Y_lsb)
    {
        tY = -tY;
    }
#endif
 
    // using inverted coordinates
    g.X = tY;
    g.Y = tX;
    g.Z = tX * tY;
 
#ifdef USE_MIXED_ADDITION
    g.to_special();
#endif
 
    return in;
}

Member Data Documentation

fixed_base_exp_window_table

std::vector< size_t > libff::edwards_G1::fixed_base_exp_window_table

static

Definition at line 28 of file edwards_g1.hpp.

G1_one

edwards_G1 libff::edwards_G1::G1_one = {}

static

Definition at line 30 of file edwards_g1.hpp.

G1_zero

edwards_G1 libff::edwards_G1::G1_zero = {}

static

Definition at line 29 of file edwards_g1.hpp.

initialized

bool libff::edwards_G1::initialized = false

static

Definition at line 31 of file edwards_g1.hpp.

wnaf_window_table

std::vector< size_t > libff::edwards_G1::wnaf_window_table

static

Definition at line 27 of file edwards_g1.hpp.

X

edwards_Fq libff::edwards_G1::X

Definition at line 33 of file edwards_g1.hpp.

Y

edwards_Fq libff::edwards_G1::Y

Definition at line 33 of file edwards_g1.hpp.

Z

edwards_Fq libff::edwards_G1::Z

Definition at line 33 of file edwards_g1.hpp.

---

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

• libraries/fc/libraries/ff/libff/algebra/curves/edwards/edwards_g1.hpp
• libraries/fc/libraries/ff/libff/algebra/curves/edwards/edwards_g1.cpp