Class: ECDSA::Ext::JacobianPoint

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

Overview

Point of Jacobian coordinates point-at-infinity.org/ecc/Prime_Curve_Jacobian_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) ⇒ Boolean

Check whether same jacobian point or not.

Parameters:

Returns:

  • (Boolean) 


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# File 'lib/ecdsa/ext/jacobian_point.rb', line 71

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

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

  lhs_x == rhs_x && lhs_y == rhs_y
end

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

Add this point to another point on the same curve.

Parameters:

Returns:



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

def add_to_point(other)
  unless other.is_a?(JacobianPoint)
    raise ArgumentError, "other point must be instance of JacobianPoint"
  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(x * field.power(other.z, 2))
  u2 = field.mod(other.x * field.power(z, 2))
  s1 = field.mod(y * field.power(other.z, 3))
  s2 = field.mod(other.y * field.power(z, 3))

  return s1 == s2 ? double : infinity_point if u1 == u2

  h = field.mod(u2 - u1)
  h2 = field.power(h, 2)
  h3 = field.power(h, 3)
  r = field.mod(s2 - s1)
  x3 = field.mod(field.power(r, 2) - h3 - 2 * u1 * h2)
  y3 = field.mod(r * (u1 * h2 - x3) - s1 * h3)
  z3 = field.mod(h * z * other.z)
  JacobianPoint.new(group, x3, y3, z3)
end

#double ⇒ ECDSA::Ext::JacobianPoint

Return the point added to itself.

Returns:



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

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

  s = field.mod(4 * x * field.power(y, 2))
  m = field.mod(3 * field.power(x, 2) + group.param_a * field.power(z, 4))
  x3 = field.mod(field.power(m, 2) - 2 * s)
  y3 = field.mod(m * (s - x3) - 8 * field.power(y, 4))
  z3 = field.mod(2 * y * z)
  JacobianPoint.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/jacobian_point.rb', line 56

def to_affine
  if infinity?
    group.infinity
  else
    z_inv = field.inverse(z)
    tmp_z = field.square(z_inv)
    new_x = field.mod(x * tmp_z) # x = x * (1/z)^2
    new_y = field.mod(y * tmp_z * z_inv) # y = y * (1/z)^3
    ECDSA::Point.new(group, new_x, new_y)
  end
end