Class: ECDSA::Ext::ProjectivePoint

Inherits:
AbstractPoint show all
Defined in:
lib/ecdsa/ext/projective_point.rb

Overview

Representing a point on elliptic curves using projective coordinates. point-at-infinity.org/ecc/Prime_Curve_Standard_Projective_Coordinates.html

Instance Attribute Summary

Attributes inherited from AbstractPoint

#group, #infinity, #x, #y, #z

Instance Method Summary collapse

Methods inherited from AbstractPoint

#coords, #field, from_affine, #infinity?, infinity_point, #infinity_point, #initialize, #multiply_by_scalar, #negate

Constructor Details

This class inherits a constructor from ECDSA::Ext::AbstractPoint

Instance Method Details

#==(other) ⇒ Object 



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# File 'lib/ecdsa/ext/projective_point.rb', line 68

def ==(other)
  return false unless other.is_a?(ProjectivePoint)
  return true if infinity? && other.infinity?

  lhs_x = field.mod(x * other.z)
  rhs_x = field.mod(other.x * z)
  lhs_y = field.mod(y * other.z)
  rhs_y = field.mod(other.y * z)

  lhs_x == rhs_x && lhs_y == rhs_y
end

#add_to_point(other) ⇒ ECDSA::Ext::ProjectivePoint Also known as: +

Add this point to another point on the same curve.

Parameters:

Returns:



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# File 'lib/ecdsa/ext/projective_point.rb', line 11

def add_to_point(other)
  unless other.is_a?(ProjectivePoint)
    raise ArgumentError, "other point must be instance of ProjectivePoint"
  end
  unless other.group == group
    raise ArgumentError, "other group must be same group of this point"
  end

  return other if infinity?
  return self if other.infinity?

  u1 = field.mod(other.y * z)
  u2 = field.mod(y * other.z)
  v1 = field.mod(other.x * z)
  v2 = field.mod(x * other.z)
  return u1 == u2 ? double : infinity_point if v1 == v2
  u = field.mod(u1 - u2)
  v = field.mod(v1 - v2)
  vv = field.power(v, 2)
  vvv = field.power(v, 3)
  w = field.mod(z * other.z)
  a = field.mod(field.power(u, 2) * w - vvv - 2 * vv * v2)
  x3 = field.mod(v * a)
  y3 = field.mod(u * (vv * v2 - a) - vvv * u2)
  z3 = field.mod(vvv * w)
  ProjectivePoint.new(group, x3, y3, z3)
end

#double ⇒ ECDSA::Ext::ProjectivePoint

Return the point added to itself.

Returns:



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# File 'lib/ecdsa/ext/projective_point.rb', line 42

def double
  return self if infinity?
  return infinity_point if y.zero?

  w = field.mod(group.param_a * field.power(z, 2) + 3 * field.power(x, 2))
  s = field.mod(y * z)
  b = field.mod(x * y * s)
  h = field.mod(field.power(w, 2) - 8 * b)
  x3 = field.mod(2 * h * s)
  y3 =
    field.mod(w * (4 * b - h) - 8 * field.power(y, 2) * field.power(s, 2))
  z3 = field.mod(8 * field.power(s, 3))
  ProjectivePoint.new(group, x3, y3, z3)
end

#to_affine ⇒ ECDSA::Point

Convert this coordinates to affine coordinates.

Returns:



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# File 'lib/ecdsa/ext/projective_point.rb', line 59

def to_affine
  if infinity?
    group.infinity
  else
    z_inv = field.inverse(z)
    ECDSA::Point.new(group, field.mod(x * z_inv), field.mod(y * z_inv))
  end
end